Abstract

We give the general expressions of intensity-difference squeezing (IDS) generated from two types of optical parametric amplifiers [i.e. phase-sensitive amplifier (PSA) and phase-insensitive amplifier (PIA)] based on the four-wave mixing process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We find that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number especially in the ultra-low average input photon number regime. This result is substantially different from the result in the ultra-high average input photon number regime where the IDS does not vary with the average input photon number. Moreover, under the same intensity gain, we find that the optimal IDS of the PSA is better than the IDS of the PIA in the ultra-low average input photon number regime. Our theoretical work predicts the presence of strong quantum correlation in the ultra-low average input photon number regime, which may have potential applications for probing photon-sensitive biological samples.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Quantum squeezing is an important quantum resource due to its advantage in quantum noise reduction [1] and thus has been proved to be useful to improve the performance of measurement systems. For example, it has been used to enhance measurement precision of microcantilever displacement [2] and rotation angle [3,4]. It has also been exploited to increase the sensitivities of the Laser Interferometer Gravitational-Wave Observatory (LIGO) [57], optical magnetometer [8], cavity optomechanical magnetometer [9] and various interferometers [1014].

A number of different techniques for the generation of quantum squeezing have been widely studied [1520]. Among them, a phase-insensitive amplifier (PIA) based on a four-wave mixing (FWM) process in a $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$ vapor cell with a double-$\Lambda$ energy level configuration has been shown to be a promising technique to generate quantum squeezed light due to its strong nonlinearity, multispatial mode nature and natural spatial separation of the output beams [2035]. In this system, a strong pump beam and a weak coherent beam (i.e. probe beam) are crossed at the center of the $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$ vapor cell. Then, a pair of intensity-difference squeezed beams (i.e. the amplified probe beam and a simultaneously generated conjugate beam) is produced, which has been used in several recent advances, such as quantum imaging [23,3639], the tunable delay of Einstein-Podolsky-Rosen entanglement [40], the implementation of an SU(1,1) nonlinear interferometer [4145] and the generation of the orbital-angular-momentum multiplexed continuous-variable entanglement [46,47]. Recently, our group has theoretically proposed [48] and experimentally realized [49] a phase-sensitive amplifier (PSA) in which two weak coherent beams (i.e. the probe and conjugate beams) are simultaneously and symmetrically crossed with a strong pump beam at the center of the $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$ vapor cell. The intensity-difference squeezing (IDS) generated from this system is better than the IDS generated from the PIA under the same experimental situation.

However, the IDS generated from the PIA and the PSA mentioned above is limited to the bright-beam approximation regime [2028,48,49], which means both the PIA and the PSA are working in the ultra-high average input photon number regime. In other words, the IDS analysis of the PIA and the PSA based on the FWM process in the ultra-low average input photon number regime is still missing. In this paper, different from the previous works considering the case without seeding [50,51], we theoretically give the general expressions of IDS generated from the PSA and the PIA based on the FWM process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We pay more attention to the characterization of IDS in the ultra-low average input photon number regime and report several significant results. We find that both the IDS of the PSA and the IDS of the PIA get enhanced with the increase of the intensity gain. The maximal IDS of the PSA can be obtained when its phase is equal to zero. These results are similar to the bright-beam input case. More importantly, we find that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number. This result is substantially different from the case of ultra-high average input photon number with the bright-beam approximation. In addition, under the same intensity gain, we find that the optimal IDS of the PSA is always better than the IDS of the PIA in the ultra-low average input photon number regime. Our theoretical results here predict the presence of strong quantum correlation in the ultra-low average input photon number regime, which may have potential applications for probing photon-sensitive biological samples [5255].

2. Quantum squeezing of the PIA and the PSA

We start with the derivation of the IDS of the PSA. The basic configuration of the PSA is shown in Fig. 1(a). Two weak coherent beams [i.e. the probe ($\hat {a}$) and conjugate ($\hat {b}$) beams] are simultaneously and symmetrically crossed with a strong pump beam ($\hat {c}$) at the center of the $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$ vapor cell. As shown in Fig. 1(b), the probe and the conjugate beams are red- and blueshifted by 3.04 GHz from the pump beam, respectively. Two pump photons are annihilated in this process, inducing the emission of one probe photon and one conjugate photon. Labeling the interaction strength of the PSA by the parameter $\kappa$, the interaction Hamiltonian can be expressed as [56,57]

$$\hat{H}=i\hbar \kappa e^{i\theta }\hat{b}^{\dagger }\hat{a}^{\dagger }+h.c.,$$
where $\theta =2{\phi }_{c}$, ${\phi }_{c}$ is the phase of the pump field. The value of $\kappa$ is not only dependent on the pump power, but also dependent on one-photon detuning ($\Delta$) and two-photon detuning ($\delta$). From Eq. (1), the output probe and conjugate fields of the PSA can be written as
$$\begin{aligned} \hat{a}(\tau)=\sqrt{G} \hat{a}(0)+e^{i\theta }\sqrt{G-1}\hat{b}^{\dagger }(0), \end{aligned}$$
$$\begin{aligned} \hat{b}^{\dagger} (\tau)= e^{-i\theta } \sqrt{G-1} \hat{a}(0)+ \sqrt{G} \hat{b}^{\dagger }(0), \end{aligned}$$
where G = ${\cosh }^2 (\kappa \tau )$ is the intensity gain of the PSA and $\tau$ is the interaction length.

 figure: Fig. 1.

Fig. 1. The PSA scheme for generating IDS. (a) Schematic view of the PSA. $\hat {a}$, $\hat {b}$ and $\hat {c}$ stand for the probe, conjugate and pump fields respectively. The solid line denotes the coherent state input. (b) Energy-level diagram of the double-$\Lambda$ scheme in the D1 line of $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$. $\Delta$ and $\delta$ stand for the one-photon detuning and two-photon detuning, respectively.

Download Full Size | PPT Slide | PDF

Defining the photon number operator of the input probe and conjugate fields as $\hat {N}_{a,in}=\hat {a}^{\dagger }(0)\hat {a}(0)$ and $\hat {N}_{b,in}=\hat {b}^{\dagger }(0)\hat {b}(0)$ respectively, the average photon number of the two output fields of the PSA are given by [48]

$$\begin{aligned} \left\langle\hat{N}_{a,out}\right\rangle & \equiv \left\langle\hat{a}^{\dagger}(\tau)\hat{a}(\tau)\right\rangle\\ & =G \left\langle\hat{N}_{a,in}\right\rangle+ (G-1) \left\langle\hat{N}_{b,in}\right\rangle+G-1+2 \cos(\phi)\sqrt{\left\langle\hat{N}_{a,in}\right\rangle\left\langle\hat{N}_{b,in}\right\rangle G(G-1)}, \end{aligned}$$
$$\begin{aligned} \left\langle\hat{N}_{b,out}\right\rangle & \equiv \left\langle\hat{b}^{\dagger}(\tau)\hat{b}(\tau)\right\rangle\\ & =G \left\langle\hat{N}_{b,in}\right\rangle+ (G-1) \left\langle\hat{N}_{a,in}\right\rangle+G-1+2 \cos(\phi)\sqrt{\left\langle\hat{N}_{a,in}\right\rangle\left\langle\hat{N}_{b,in}\right\rangle G(G-1)}, \end{aligned}$$
where $\phi =2{\phi }_{c}-{\phi }_{a}-{\phi }_{b}$, ${\phi }_{a}$ and ${\phi }_{b}$ are the phases of the probe and conjugate fields respectively. For convenience, we define the $\phi$ as the phase of the PSA. The intensity-difference noise between the two output fields of the PSA can be shown as
$${Var({N}_{a,out}-{N}_{b,out})}_{SQZ}=\left\langle\hat{N}_{a,in}\right\rangle+\left\langle\hat{N}_{b,in}\right\rangle,$$
The corresponding shot-noise limit (SNL) is just the sum of the average photon number of the two output fields, which can be expressed as
$$\begin{aligned} & {Var({N}_{a,out}-{N}_{b,out})}_{SNL}\equiv \left\langle\hat{N}_{a,out}\right\rangle+\left\langle\hat{N}_{b,out}\right\rangle\\ & =(2G-1) (\left\langle\hat{N}_{a,in}\right\rangle+\left\langle\hat{N}_{b,in}\right\rangle)+4 \cos(\phi)\sqrt{\left\langle\hat{N}_{a,in}\right\rangle\left\langle\hat{N}_{b,in}\right\rangle G(G-1)}+2(G-1), \end{aligned}$$
The first two terms in the second line correspond to contributions from the stimulated parametric process, while the last term results from the spontaneous process. Hence the output beams have been amplified without increasing the intensity-difference noise, which agrees well with the result in [26].

Therefore, the degree of IDS for the PSA can be described as

$$\textrm{IDS}=\displaystyle\frac{Var{(\hat{N}_{a,out}-\hat{N}_{b,out})}_{SQZ}}{Var{(\hat{N}_{a,out}-\hat{N}_{b,out})}_{SNL}} =\displaystyle\frac{1}{(2G-1)+4\cos(\phi)\sqrt{G(G-1)}\frac{\sqrt{\gamma}}{1+\gamma}+\frac{2(G-1)}{\left\langle\hat{N}_{a,in}\right\rangle(1+\gamma)}},$$
where $\gamma$ is the input conjugate-probe power ratio, $\gamma =\left \langle \hat {N}_{b,in}\right \rangle /\left \langle \hat {N}_{a,in}\right \rangle$.

When seeding a vacuum field to one of the input ports of the PSA, the PIA configuration can be obtained as shown in Fig. 2. Note that we seed a vacuum field to the conjugate port which means $\gamma =0$. From Eq. (8), the degree of IDS for the PIA can be expressed as

$$\textrm{IDS}=\displaystyle\frac{1}{(2G-1)+\frac{2(G-1)}{\left\langle\hat{N}_{a,in}\right\rangle}},$$

 figure: Fig. 2.

Fig. 2. The PIA scheme for generating IDS. $\hat {a}$, $\hat {b}$ and $\hat {c}$ stand for the probe, conjugate and pump fields respectively. The solid line denotes the coherent state input while the dashed line denotes the vacuum state input.

Download Full Size | PPT Slide | PDF

As we can see from Eq. (8) and Eq. (9), the terms $2(G-1)/\left \langle \hat {N}_{a,in}\right \rangle (1+\gamma)$ and $2(G-1)/\left \langle \hat {N}_{a,in}\right \rangle$ will be negligible in the ultra-high average input photon number regime with the bright-beam approximation since $\left \langle \hat {N}_{a,in}\right \rangle >>1$. Therefore, both the IDS of the PSA and the IDS of the PIA will be independent on the average input photon number. These models well explain the previous works [2028,48,49]. However, as the decrease of the average input photon number, especially in the ultra-low average input photon number regime, these two terms can not be neglected anymore. Therefore, both the IDS of the PSA and the IDS of the PIA are dependent on the intensity gain G and the average input photon number of probe field $\left \langle \hat {N}_{a,in}\right \rangle$. Meanwhile, the IDS of the PSA also depends on the phase $\phi$ and the input conjugate-probe power ratio $\gamma$. Therefore, it is valuable to study how these factors influence the performance of the PSA and the PIA. Firstly, in order to analyze the effect of gain on the IDS of these two systems, we set the phase of the PSA at 0 and plot the intensity-difference noise powers of the PSA and the PIA as a function of the gain when the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle =1$ as shown in Fig. 3. It should be noted that for convenience, we consider that two input ports of the PSA have the same average input photon number (i.e. $\gamma =1$). From Fig. 3, we can directly see that for a given $\left \langle \hat {N}_{a,in}\right \rangle$, both the IDS of the PSA and the IDS of the PIA can be enhanced with the increase of the gain G.

 figure: Fig. 3.

Fig. 3. The intensity-difference noise powers of the PIA and the PSA with the phase $\phi =0$ and the input conjugate-probe ratio $\gamma =1$ as a function of the gain G when the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle =1$. Pink dashed line: the intensity-difference noise power of the PIA; pink solid line: the intensity-difference noise power of the PSA; blue solid line: SNL.

Download Full Size | PPT Slide | PDF

Secondly, we illustrate how the IDS of the PSA and the IDS of the PIA depend on the phase $\phi$. In order to study these effects, we plot the intensity-difference noise powers of the PSA and the PIA as a function of the phase $\phi$ by setting the gain G at 10 and the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ at 1 as shown in Fig. 4. Here we also fix the ratio $\gamma$ of the PSA at 1. It can be seen intuitively that the IDS of the PSA can be manipulated by the phase and achieves its maximal degree of squeezing when $\phi =0$, while the IDS of the PIA does not depend on the phase. These results are similar to our previous studies in the ultra-high average input photon number regime [48,49].

 figure: Fig. 4.

Fig. 4. The intensity-difference noise powers of the PIA and the PSA with the input conjugate-probe power ratio $\gamma =1$ as a function of the phase $\phi$ under the same gain G=10 and the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle =1$. Pink dashed line: the intensity-difference noise power of the PIA; pink solid line: the intensity-difference noise power of the PSA; blue solid line: SNL.

Download Full Size | PPT Slide | PDF

Thirdly, in order to explore how the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ and the input conjugate-probe power ratio $\gamma$ together influence the IDS of the PSA and the IDS of the PIA, we fix the gain G at 10, the phase $\phi$ at 0, and plot the intensity-difference noise power of the PSA as a function of $\left \langle \hat {N}_{a,in}\right \rangle$ and $\gamma$ as shown in Fig. 5(a). The red solid line corresponding to the case of $\gamma =0$ is the dependence relation of the intensity-difference noise power of the PIA on $\left \langle \hat {N}_{a,in}\right \rangle$. The Fig. 5(b) is the expanded plot where $0<\gamma <0.5$ and $0.01<\left \langle \hat {N}_{a,in}\right \rangle <1$. First of all, it can be seen that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number of probe field $\left \langle \hat {N}_{a,in}\right \rangle$. Then it can also be found that for a given $\left \langle \hat {N}_{a,in}\right \rangle$, the IDS of the PSA gets better first and then gets worse with the decrease of $\gamma$. In other words, there exists an optimal $\gamma$ which can optimize the IDS of the PSA. It can be expressed as

$$\gamma=1+\displaystyle\frac{G-1}{2G{\cos}^{2}(\phi){\left\langle\hat{N}_{a,in}\right\rangle}^{2}}- \sqrt{\displaystyle\frac{G-1}{G{\cos}^{2}(\phi){\left\langle\hat{N}_{a,in}\right\rangle}^{2}}+{\left(\displaystyle\frac{G-1}{2G{\cos}^{2}(\phi){\left\langle\hat{N}_{a,in}\right\rangle}^{2}}\right)}^{2}},$$
which is a function of $\left \langle \hat {N}_{a,in}\right \rangle$ under the certain gain G and phase $\phi$. The dependence relation of the corresponding optimal intensity-difference noise power of the PSA on $\left \langle \hat {N}_{a,in}\right \rangle$ and $\gamma$ is indicated as the black dashed line in Fig. 5.

 figure: Fig. 5.

Fig. 5. (a) The intensity-difference noise power of the PSA as a function of the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ and the input conjugate-probe power ratio $\gamma$ when G=10 and $\phi =0$. The red solid line corresponding to the case of $\gamma =0$ is the dependence relation of the intensity-difference noise power of the PIA on $\left \langle \hat {N}_{a,in}\right \rangle$. The black dashed line is the dependence relation of the optimal intensity-difference noise power of the PSA on $\left \langle \hat {N}_{a,in}\right \rangle$ and $\gamma$. (b) The expanded plot where $0<\gamma <0.5$ and $0.01<\left \langle \hat {N}_{a,in}\right \rangle <1$.

Download Full Size | PPT Slide | PDF

In order to better compare the IDS of the PIA and the IDS of the PSA in the ultra-low average input photon number regime, we set the phase of the PSA at 0 and plot the intensity-difference noise power of the PIA, the optimal intensity-difference noise power of the PSA and the optimal $\gamma$ of the PSA as a function of the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ under the same gain G=10 as shown in Fig. 6(a). The Figs. 6(b), (c) and (d) are the expanded plots where $0.001<\left \langle \hat {N}_{a,in}\right \rangle <1$, $0.001<\left \langle \hat {N}_{a,in}\right \rangle <0.1$ and $0.001<\left \langle \hat {N}_{a,in}\right \rangle <0.01$, respectively. As we can see that the optimal IDS of the PSA is always better than the IDS of the PIA. Moreover, as the decrease of the average input photon number, the optimal IDS of the PSA becomes almost the same as the IDS of the PIA. This means that the IDS enhancement of the PSA decreases with the decrease of the average input photon number. In addition, we can see that the optimal $\gamma$ decreases with the decrease of the average input photon number and tends to 0 when the average input photon number is sufficiently low. Since there are unavoidable loss in any real experiment, we take two types of losses into consideration, namely, the external loss that occurs after mixing (imperfect optical transmission and detection efficiency) and the internal loss (the atomic absorption in $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$ vapor cell). In general, the external loss can be modeled by a beamsplitter with an empty port whose output state is a combination of the input and vacuum modes [58]. For simplicity, we also consider the internal loss as a beamsplitter with an empty port, contributing vacuum fluctuations to the transmitted beams. Denoting the vacuum modes introduced by loss on the probe and conjugate by the annihilation operators ${\hat {\nu }}_{i}$ ($i=1, 2, 3, 4$) respectively [59], the standard beamsplitter input-output relations give

$$\begin{aligned} \hat{a}(\tau) \rightarrow \sqrt{\eta_1} (\sqrt{\mathit{L}_1}\hat{a}(\tau)+\sqrt{1-{\mathit{L}}_1}\hat{\nu}_1)+\sqrt{1-\eta_1}\hat{\nu}_2, \end{aligned}$$
$$\begin{aligned} \hat{b}(\tau) \rightarrow \sqrt{\eta_2} (\sqrt{\mathit{L}_2}\hat{b}(\tau)+\sqrt{1-{\mathit{L}}_2}\hat{\nu}_3)+\sqrt{1-\eta_2}\hat{\nu}_4. \end{aligned}$$
Here $\eta _1$ and $\eta _2$ are the transmission ratios of the light beam intensities due to the external loss. $\textit {L}_1$ and $\textit {L}_2$ stand for the transmission ratios in the $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$ vapor cell for probe and conjugate fields, respectively. For simplicity, we consider the transmission ratios $\eta _1$ and $\eta _2$ after mixing as $\eta$ and the transmission ratios $\textit {L}_1$ and $\textit {L}_2$ in the $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$ vapor cell as L. Then, we can easily calculate the degrees of IDS of the PIA and the PSA followed by optical loss. The results are shown in Fig. 7. As shown in Fig. 7, we plot the intensity-difference noise powers of the PIA and the optimal PSA with phase $\phi =0$ as a function of the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ under the same gain $\textit {G}=10$ followed by optical loss. It can be found that the degrees of IDS of two types of optical parametric amplifiers decrease with the increase of loss. Moreover, as the increase of the average input photon number, the variation of IDS decreases. This is because the higher the IDS is, the more sensitive it is to the loss. In addition, the IDS of the optimal PSA is still better than the IDS of the PIA, which is consistent with the case of without loss.

 figure: Fig. 6.

Fig. 6. (a) Comparison of two types of optical parametric amplifiers. The green dashed line represents the intensity-difference noise power of the PIA with the gain G=10. The pink solid line represents the optimal intensity-difference noise power of the PSA with the gain G=10 and phase $\phi =0$. The red solid line is the dependence relation of the optimal $\gamma$ of the PSA on the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$. (b) The expanded plot where $0.001<\left \langle \hat {N}_{a,in}\right \rangle <1$. (c) The expanded plot where $0.001<\left \langle \hat {N}_{a,in}\right \rangle <0.1$. (d) The expanded plot where $0.001<\left \langle \hat {N}_{a,in}\right \rangle <0.01$.

Download Full Size | PPT Slide | PDF

 figure: Fig. 7.

Fig. 7. The intensity-difference noise powers of the PIA and the optimal PSA with phase $\phi =0$ as a function of the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ under the same gain $\textit {G}=10$ followed by optical loss.

Download Full Size | PPT Slide | PDF

3. Conclusion

In conclusion, we have given the general expressions of the IDS generated from the PSA and the PIA based on the FWM process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We pay more attention to the characterization of IDS in the ultra-low average input photon number regime and report several significant results. We show that both the IDS of the PSA and the IDS of the PIA can be enhanced with the increase of the intensity gain. We also show that the maximal IDS of the PSA can be obtained when its phase is equal to zero. These results are similar to the bright-beam input case of our previous studies in the ultra-high average input photon number regime [48,49]. More importantly, we show that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number. In addition, we show that the optimal IDS of the PSA is always better than the IDS of the PIA with the same intensity gain. On the one hand, these theoretical findings are valuable for better and fully understanding the quantum squeezing generated from the FWM process. On the other hand, they predict the presence of strong quantum correlation in the ultra-low average input photon number regime and hence may have potential applications for probing photon-sensitive biological samples [5255].

Funding

National Natural Science Foundation of China (11874155, 91436211, 11374104); Basic Research Project of Science and Technology Commission of Shanghai Municipality (20JC1416100); Natural Science Foundation of Shanghai (17ZR1442900); Minhang Leading Talents (201971); ECNU Academic Innovation Promotion Program for Excellent Doctoral Students (YBNLTS2020-046); Program of Scientific and Technological Innovation of Shanghai (17JC1400401); the National Basic Research Program of China (2016YFA0302103); the 111 project (B12024).

Disclosures

The authors declare no conflicts of interest.

References

1. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23(8), 1693–1708 (1981). [CrossRef]  

2. R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015). [CrossRef]  

3. K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018). [CrossRef]  

4. R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016). [CrossRef]  

5. The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011). [CrossRef]  

6. The LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013). [CrossRef]  

7. H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013). [CrossRef]  

8. F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010). [CrossRef]  

9. B. Li, J. Blek, U. B. Hoff, L. S. Madsen, S. Forstner, V. Prakash, C. Schäfermeier, T. Gehring, W. P. Bowen, and U. L. Andersen, “Quantum enhanced optomechanical magnetometry,” Optica 5(7), 850 (2018). [CrossRef]  

10. M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987). [CrossRef]  

11. P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987). [CrossRef]  

12. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005). [CrossRef]  

13. M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017). [CrossRef]  

14. R. Schnabel, “Squeezed states of light and their applications in laser interferometers,” Phys. Rep. 684, 1–51 (2017). [CrossRef]  

15. L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986). [CrossRef]  

16. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992). [CrossRef]  

17. M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Opt. Lett. 12(3), 161 (1987). [CrossRef]  

18. M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006). [CrossRef]  

19. R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, “In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber,” Opt. Express 16(12), 9046 (2008). [CrossRef]  

20. C. F. McCormick, V. Boyer, E. Arimonda, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178 (2007). [CrossRef]  

21. C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008). [CrossRef]  

22. Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010). [CrossRef]  

23. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef]  

24. R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009). [CrossRef]  

25. C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011). [CrossRef]  

26. M. Jasperse, L. D. Turner, and R. E. Scholten, “Relative intensity squeezing by four-wave mixing with loss: an analytic model and experimental diagnostic,” Opt. Express 19(4), 3765 (2011). [CrossRef]  

27. Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011). [CrossRef]  

28. Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, and W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37(15), 3141 (2012). [CrossRef]  

29. A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012). [CrossRef]  

30. U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014). [CrossRef]  

31. M. W. Holtfrerich and A. M. Marino, “Control of the size of the coherence area in entangled twin beams,” Phys. Rev. A 93(6), 063821 (2016). [CrossRef]  

32. J. D. Swaim and R. T. Glasser, “Squeezed-twin-beam generation in strongly absorbing media,” Phys. Rev. A 96(3), 033818 (2017). [CrossRef]  

33. S. Lohani and R. T. Glasser, “Turbulence correction with artificial neural networks,” Opt. Lett. 43(11), 2611 (2018). [CrossRef]  

34. M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014). [CrossRef]  

35. A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017). [CrossRef]  

36. C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015). [CrossRef]  

37. B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013). [CrossRef]  

38. B. J. Lawrie and R. C. Pooser, “Toward real-time quantum imaging with a single pixel camera,” Opt. Express 21(6), 7549 (2013). [CrossRef]  

39. A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008). [CrossRef]  

40. A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009). [CrossRef]  

41. J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011). [CrossRef]  

42. A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86(2), 023844 (2012). [CrossRef]  

43. F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014). [CrossRef]  

44. B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4(7), 752 (2017). [CrossRef]  

45. S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018). [CrossRef]  

46. X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019). [CrossRef]  

47. S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020). [CrossRef]  

48. Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phasesensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015). [CrossRef]  

49. S. Liu, Y. Lou, and J. Jing, “Interference-induced quantum squeezing enhancement in a two-beam phase-sensitive amplifier,” Phys. Rev. Lett. 123(11), 113602 (2019). [CrossRef]  

50. M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015). [CrossRef]  

51. A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017). [CrossRef]  

52. P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015). [CrossRef]  

53. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013). [CrossRef]  

54. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014). [CrossRef]  

55. A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012). [CrossRef]  

56. H. Chen and J. Zhang, “Phase-sensitive manipulations of the two-mode entangled state by a type-II nondegenerate optical parametric amplifier inside an optical cavity,” Phys. Rev. A 79(6), 063826 (2009). [CrossRef]  

57. J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233 (1993). [CrossRef]  

58. H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004).

59. C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45(2), 75–79 (1980). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23(8), 1693–1708 (1981).
    [Crossref]
  2. R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015).
    [Crossref]
  3. K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
    [Crossref]
  4. R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
    [Crossref]
  5. The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011).
    [Crossref]
  6. The LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013).
    [Crossref]
  7. H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
    [Crossref]
  8. F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
    [Crossref]
  9. B. Li, J. Blek, U. B. Hoff, L. S. Madsen, S. Forstner, V. Prakash, C. Schäfermeier, T. Gehring, W. P. Bowen, and U. L. Andersen, “Quantum enhanced optomechanical magnetometry,” Optica 5(7), 850 (2018).
    [Crossref]
  10. M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
    [Crossref]
  11. P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
    [Crossref]
  12. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
    [Crossref]
  13. M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
    [Crossref]
  14. R. Schnabel, “Squeezed states of light and their applications in laser interferometers,” Phys. Rep. 684, 1–51 (2017).
    [Crossref]
  15. L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986).
    [Crossref]
  16. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
    [Crossref]
  17. M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Opt. Lett. 12(3), 161 (1987).
    [Crossref]
  18. M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
    [Crossref]
  19. R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, “In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber,” Opt. Express 16(12), 9046 (2008).
    [Crossref]
  20. C. F. McCormick, V. Boyer, E. Arimonda, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178 (2007).
    [Crossref]
  21. C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
    [Crossref]
  22. Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
    [Crossref]
  23. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
    [Crossref]
  24. R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
    [Crossref]
  25. C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011).
    [Crossref]
  26. M. Jasperse, L. D. Turner, and R. E. Scholten, “Relative intensity squeezing by four-wave mixing with loss: an analytic model and experimental diagnostic,” Opt. Express 19(4), 3765 (2011).
    [Crossref]
  27. Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
    [Crossref]
  28. Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, and W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37(15), 3141 (2012).
    [Crossref]
  29. A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
    [Crossref]
  30. U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
    [Crossref]
  31. M. W. Holtfrerich and A. M. Marino, “Control of the size of the coherence area in entangled twin beams,” Phys. Rev. A 93(6), 063821 (2016).
    [Crossref]
  32. J. D. Swaim and R. T. Glasser, “Squeezed-twin-beam generation in strongly absorbing media,” Phys. Rev. A 96(3), 033818 (2017).
    [Crossref]
  33. S. Lohani and R. T. Glasser, “Turbulence correction with artificial neural networks,” Opt. Lett. 43(11), 2611 (2018).
    [Crossref]
  34. M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
    [Crossref]
  35. A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
    [Crossref]
  36. C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015).
    [Crossref]
  37. B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
    [Crossref]
  38. B. J. Lawrie and R. C. Pooser, “Toward real-time quantum imaging with a single pixel camera,” Opt. Express 21(6), 7549 (2013).
    [Crossref]
  39. A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
    [Crossref]
  40. A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009).
    [Crossref]
  41. J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011).
    [Crossref]
  42. A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86(2), 023844 (2012).
    [Crossref]
  43. F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
    [Crossref]
  44. B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4(7), 752 (2017).
    [Crossref]
  45. S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018).
    [Crossref]
  46. X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
    [Crossref]
  47. S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
    [Crossref]
  48. Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phasesensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
    [Crossref]
  49. S. Liu, Y. Lou, and J. Jing, “Interference-induced quantum squeezing enhancement in a two-beam phase-sensitive amplifier,” Phys. Rev. Lett. 123(11), 113602 (2019).
    [Crossref]
  50. M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
    [Crossref]
  51. A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
    [Crossref]
  52. P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
    [Crossref]
  53. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
    [Crossref]
  54. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
    [Crossref]
  55. A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
    [Crossref]
  56. H. Chen and J. Zhang, “Phase-sensitive manipulations of the two-mode entangled state by a type-II nondegenerate optical parametric amplifier inside an optical cavity,” Phys. Rev. A 79(6), 063826 (2009).
    [Crossref]
  57. J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233 (1993).
    [Crossref]
  58. H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004).
  59. C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45(2), 75–79 (1980).
    [Crossref]

2020 (1)

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

2019 (2)

S. Liu, Y. Lou, and J. Jing, “Interference-induced quantum squeezing enhancement in a two-beam phase-sensitive amplifier,” Phys. Rev. Lett. 123(11), 113602 (2019).
[Crossref]

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

2018 (4)

S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018).
[Crossref]

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

B. Li, J. Blek, U. B. Hoff, L. S. Madsen, S. Forstner, V. Prakash, C. Schäfermeier, T. Gehring, W. P. Bowen, and U. L. Andersen, “Quantum enhanced optomechanical magnetometry,” Optica 5(7), 850 (2018).
[Crossref]

S. Lohani and R. T. Glasser, “Turbulence correction with artificial neural networks,” Opt. Lett. 43(11), 2611 (2018).
[Crossref]

2017 (6)

A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
[Crossref]

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

R. Schnabel, “Squeezed states of light and their applications in laser interferometers,” Phys. Rep. 684, 1–51 (2017).
[Crossref]

B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4(7), 752 (2017).
[Crossref]

J. D. Swaim and R. T. Glasser, “Squeezed-twin-beam generation in strongly absorbing media,” Phys. Rev. A 96(3), 033818 (2017).
[Crossref]

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

2016 (2)

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
[Crossref]

M. W. Holtfrerich and A. M. Marino, “Control of the size of the coherence area in entangled twin beams,” Phys. Rev. A 93(6), 063821 (2016).
[Crossref]

2015 (5)

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015).
[Crossref]

R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015).
[Crossref]

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phasesensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
[Crossref]

2014 (4)

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

2013 (5)

B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
[Crossref]

B. J. Lawrie and R. C. Pooser, “Toward real-time quantum imaging with a single pixel camera,” Opt. Express 21(6), 7549 (2013).
[Crossref]

The LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013).
[Crossref]

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

2012 (4)

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86(2), 023844 (2012).
[Crossref]

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, and W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37(15), 3141 (2012).
[Crossref]

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

2011 (5)

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011).
[Crossref]

M. Jasperse, L. D. Turner, and R. E. Scholten, “Relative intensity squeezing by four-wave mixing with loss: an analytic model and experimental diagnostic,” Opt. Express 19(4), 3765 (2011).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
[Crossref]

The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011).
[Crossref]

2010 (2)

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
[Crossref]

2009 (3)

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009).
[Crossref]

H. Chen and J. Zhang, “Phase-sensitive manipulations of the two-mode entangled state by a type-II nondegenerate optical parametric amplifier inside an optical cavity,” Phys. Rev. A 79(6), 063826 (2009).
[Crossref]

2008 (4)

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, “In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber,” Opt. Express 16(12), 9046 (2008).
[Crossref]

2007 (1)

2006 (1)

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

2005 (1)

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

1993 (1)

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
[Crossref]

1987 (3)

M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Opt. Lett. 12(3), 161 (1987).
[Crossref]

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

1986 (1)

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986).
[Crossref]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23(8), 1693–1708 (1981).
[Crossref]

1980 (1)

C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45(2), 75–79 (1980).
[Crossref]

Abram, I.

Achal, R.

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

Andersen, U. L.

Anderson, B. E.

Arimonda, E.

Aspden, R. S.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Ast, S.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Avella, A

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Bachor, H. A.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004).

Bachor, H.-A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Beduini, F. A.

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

Bell, J. E. C.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Blek, J.

Bowen, W. P.

B. Li, J. Blek, U. B. Hoff, L. S. Madsen, S. Forstner, V. Prakash, C. Schäfermeier, T. Gehring, W. P. Bowen, and U. L. Andersen, “Quantum enhanced optomechanical magnetometry,” Optica 5(7), 850 (2018).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Boyd, R. W.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Boyer, V.

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015).
[Crossref]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

C. F. McCormick, V. Boyer, E. Arimonda, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178 (2007).
[Crossref]

Bramati, A.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Brannan, T.

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

Cai, C.

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

Caves, C. M.

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23(8), 1693–1708 (1981).
[Crossref]

C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45(2), 75–79 (1980).
[Crossref]

Cerè, A.

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

Chekhova, M.

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

Chelkowski, S.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Chen, H.

H. Chen and J. Zhang, “Phase-sensitive manipulations of the two-mode entangled state by a type-II nondegenerate optical parametric amplifier inside an optical cavity,” Phys. Rev. A 79(6), 063826 (2009).
[Crossref]

Chen, Y.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Clark, J. B.

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

Corzo, N. V.

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

Corzo Trejo, N. V.

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86(2), 023844 (2012).
[Crossref]

Coudreau, T.

Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
[Crossref]

Crespi, A.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Cviklinski, J.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Dantan, A.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Danzmann, K.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Daria, V.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Devgan, P. S.

Dooley, K. L.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

Embrey, C. S.

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015).
[Crossref]

Evans, P. G.

B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
[Crossref]

Fang, Y.

Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phasesensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
[Crossref]

Forstner, S.

Franzen, A.

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Gao, J.

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

Gehring, T.

Genovese, M

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Glasser, R. T.

S. Lohani and R. T. Glasser, “Turbulence correction with artificial neural networks,” Opt. Lett. 43(11), 2611 (2018).
[Crossref]

J. D. Swaim and R. T. Glasser, “Squeezed-twin-beam generation in strongly absorbing media,” Phys. Rev. A 96(3), 033818 (2017).
[Crossref]

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

Glorieux, Q.

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
[Crossref]

Grangier, P.

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233 (1993).
[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

Grigoryan, V. S.

Grote, H.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

Guibal, S.

Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
[Crossref]

Guidoni, L.

Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
[Crossref]

Guo, M.

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

Gupta, P.

Hage, B.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Hall, J. L.

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986).
[Crossref]

Harb, C. C.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Hermann-Avigliano, C.

Hétet, G.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Hoff, U. B.

Holtfrerich, M. W.

M. W. Holtfrerich and A. M. Marino, “Control of the size of the coherence area in entangled twin beams,” Phys. Rev. A 93(6), 063821 (2016).
[Crossref]

Hope, J. J.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Horrom, T.

Hsu, M. T. L.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Hudelist, F.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011).
[Crossref]

Janousek, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Jasperse, M.

Jing, J.

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

S. Liu, Y. Lou, and J. Jing, “Interference-induced quantum squeezing enhancement in a two-beam phase-sensitive amplifier,” Phys. Rev. Lett. 123(11), 113602 (2019).
[Crossref]

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018).
[Crossref]

Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phasesensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, and W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37(15), 3141 (2012).
[Crossref]

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011).
[Crossref]

Johnsson, M. T.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Jones, K. M.

B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4(7), 752 (2017).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

Kimble, H. J.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
[Crossref]

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref]

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986).
[Crossref]

Kleybolte, L.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Knittel, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Kong, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Korobko, M.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Koschorreck, M.

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

Kumar, A.

A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
[Crossref]

Kumar, P.

Lam, P. K.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

LaPorta, A.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

Lawrie, B.

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
[Crossref]

R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015).
[Crossref]

Lawrie, B. J.

B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
[Crossref]

B. J. Lawrie and R. C. Pooser, “Toward real-time quantum imaging with a single pixel camera,” Opt. Express 21(6), 7549 (2013).
[Crossref]

Lemons, K.

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

Lett, P. D.

B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, “Phase sensing beyond the standard quantum limit with a variation on the SU(1,1) interferometer,” Optica 4(7), 752 (2017).
[Crossref]

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86(2), 023844 (2012).
[Crossref]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

C. F. McCormick, V. Boyer, E. Arimonda, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178 (2007).
[Crossref]

Leuchs, G.

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

Levenson, J. A.

Li, B.

Li, J.

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

Li, S.

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

Li, T.

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

Likforman, J. P.

Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
[Crossref]

Likforman, J.-P.

Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
[Crossref]

Liu, C.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, and W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37(15), 3141 (2012).
[Crossref]

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011).
[Crossref]

Liu, H.

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

Liu, K.

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

Liu, S.

S. Liu, Y. Lou, and J. Jing, “Interference-induced quantum squeezing enhancement in a two-beam phase-sensitive amplifier,” Phys. Rev. Lett. 123(11), 113602 (2019).
[Crossref]

S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018).
[Crossref]

Lobino, M.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Lohani, S.

Losero, E

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Lou, Y.

S. Liu, Y. Lou, and J. Jing, “Interference-induced quantum squeezing enhancement in a two-beam phase-sensitive amplifier,” Phys. Rev. Lett. 123(11), 113602 (2019).
[Crossref]

S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018).
[Crossref]

Lv, S.

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

Lvovsky, A. I.

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

Ma, L.

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

MacRae, A.

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

Madsen, L. S.

Maeda, M. W.

Marino, A. M.

A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
[Crossref]

M. W. Holtfrerich and A. M. Marino, “Control of the size of the coherence area in entangled twin beams,” Phys. Rev. A 93(6), 063821 (2016).
[Crossref]

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86(2), 023844 (2012).
[Crossref]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

Matthews, J.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

McCormick, C. F.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

C. F. McCormick, V. Boyer, E. Arimonda, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178 (2007).
[Crossref]

Meda, A

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Miao, H.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

Mitchell, M. W.

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

Morris, P. A.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Neal, C.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Nunley, H.

A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
[Crossref]

O’BrienBrien, J.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Osellame, R.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Ou, Z. Y.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011).
[Crossref]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
[Crossref]

Padgett, M. J.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Pan, X.

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

Peng, A.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Peng, K. C.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
[Crossref]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
[Crossref]

Petrov, P. G.

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015).
[Crossref]

Pinard, M.

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Politi, A.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Pooser, R. C.

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
[Crossref]

R. C. Pooser and B. Lawrie, “Ultrasensitive measurement of microcantilever displacement below the shot-noise limit,” Optica 2(5), 393 (2015).
[Crossref]

B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
[Crossref]

B. J. Lawrie and R. C. Pooser, “Toward real-time quantum imaging with a single pixel camera,” Opt. Express 21(6), 7549 (2013).
[Crossref]

Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, and W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37(15), 3141 (2012).
[Crossref]

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009).
[Crossref]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

Pradyumna, S

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Prakash, V.

Predojevic, A.

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

Qin, Z.

Ralph, T. C.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004).

Ramponi, R.

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

Ren, Y.

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

Rivera, T.

Ruo-Berchera, I

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Samantaray, N

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Scafirimuto, F

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

Schäfermeier, C.

Schmittberger, B. L.

Schnabel, R.

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

R. Schnabel, “Squeezed states of light and their applications in laser interferometers,” Phys. Rep. 684, 1–51 (2017).
[Crossref]

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Scholten, R. E.

Shapiro, J. H.

Slusher, R. E.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

Slutsky, J.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

Sun, H.

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

Swaim, J. D.

J. D. Swaim and R. T. Glasser, “Squeezed-twin-beam generation in strongly absorbing media,” Phys. Rev. A 96(3), 033818 (2017).
[Crossref]

Tang, R.

Taylor, M. A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Turnbull, M. T.

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015).
[Crossref]

Turner, L. D.

Vahlbruch, H.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

Vasilyev, M.

Vogl, U.

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

Wang, D.

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

Wang, W.

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

Wolfgramm, F.

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

Wu, H.

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986).
[Crossref]

Wu, L. A.

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref]

Wu, L.-A.

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986).
[Crossref]

Xiao, M.

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref]

Xin, J.

S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018).
[Crossref]

Yu, S.

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

Yurke, B.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

Zhang, J.

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

H. Chen and J. Zhang, “Phase-sensitive manipulations of the two-mode entangled state by a type-II nondegenerate optical parametric amplifier inside an optical cavity,” Phys. Rev. A 79(6), 063826 (2009).
[Crossref]

Zhang, K.

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

Zhang, W.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, and W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37(15), 3141 (2012).
[Crossref]

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36(15), 2979 (2011).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011).
[Crossref]

Zhou, H.

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

Zhou, J.

Zhou, L.

Zhou, Y

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

Zhou, Z.

Zhu, S.

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

Zukowski, M.

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

ACS Photonics (1)

R. C. Pooser and B. Lawrie, “Plasmonic trace sensing below the photon shot noise limit,” ACS Photonics 3(1), 8–13 (2016).
[Crossref]

Appl. Phys. Lett. (3)

K. Liu, C. Cai, J. Li, L. Ma, H. Sun, and J. Gao, “Squeezing-enhanced rotating-angle measurement beyond the quantum limit,” Appl. Phys. Lett. 113(26), 261103 (2018).
[Crossref]

J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, “Realization of a nonlinear interferometer with parametric amplifiers,” Appl. Phys. Lett. 99(1), 011110 (2011).
[Crossref]

A. Crespi, M. Lobino, J. Matthews, A. Politi, C. Neal, R. Ramponi, R. Osellame, and J. O’BrienBrien, “Measuringprotein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

J. Opt. (1)

A Meda, E Losero, N Samantaray, F Scafirimuto, S Pradyumna, A Avella, I Ruo-Berchera, and M Genovese, “Photon-number correlation for quantum enhanced imaging and sensing,” J. Opt. 19(9), 094002 (2017).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Commun. (2)

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Nat. Photonics (2)

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

The LIGO Scientific Collaboration, “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photonics 7(8), 613–619 (2013).
[Crossref]

Nat. Phys. (1)

The LIGO Scientific Collaboration, “A gravitational wave observatory operating beyond the quantum shot-noise limit,” Nat. Phys. 7(12), 962–965 (2011).
[Crossref]

Nature (London) (1)

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature (London) 457(7231), 859–862 (2009).
[Crossref]

New J. Phys. (2)

Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phasesensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
[Crossref]

U. Vogl, R. T. Glasser, J. B. Clark, Q. Glorieux, T. Li, N. V. Corzo, and P. D. Lett, “Advanced quantum noise correlations,” New J. Phys. 16(1), 013011 (2014).
[Crossref]

Opt. Commun. (1)

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Optica (3)

Phys. Rep. (1)

R. Schnabel, “Squeezed states of light and their applications in laser interferometers,” Phys. Rep. 684, 1–51 (2017).
[Crossref]

Phys. Rev. A (9)

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

M. Guo, H. Zhou, D. Wang, J. Gao, J. Zhang, and S. Zhu, “Experimental investigation of high-frequency-difference twin beams in hot cesium atoms,” Phys. Rev. A 89(3), 033813 (2014).
[Crossref]

A. Kumar, H. Nunley, and A. M. Marino, “Observation of spatial quantum correlations in the macroscopic regime,” Phys. Rev. A 95(5), 053849 (2017).
[Crossref]

M. W. Holtfrerich and A. M. Marino, “Control of the size of the coherence area in entangled twin beams,” Phys. Rev. A 93(6), 063821 (2016).
[Crossref]

J. D. Swaim and R. T. Glasser, “Squeezed-twin-beam generation in strongly absorbing media,” Phys. Rev. A 96(3), 033818 (2017).
[Crossref]

M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, and M. Pinard, “Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell,” Phys. Rev. A 73(2), 023806 (2006).
[Crossref]

Q. Glorieux, L. Guidoni, S. Guibal, J.-P. Likforman, and T. Coudreau, “Quantum correlations by four-wave mixing in an atomic vapor in a nonamplifying regime: Quantum beam splitter for photons,” Phys. Rev. A 84(5), 053826 (2011).
[Crossref]

A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, “Effect of losses on the performance of an SU(1,1) interferometer,” Phys. Rev. A 86(2), 023844 (2012).
[Crossref]

H. Chen and J. Zhang, “Phase-sensitive manipulations of the two-mode entangled state by a type-II nondegenerate optical parametric amplifier inside an optical cavity,” Phys. Rev. A 79(6), 063826 (2009).
[Crossref]

Phys. Rev. Appl. (1)

S. Liu, Y. Lou, J. Xin, and J. Jing, “Quantum enhancement of phase sensitivity for the bright-seeded SU(1,1) interferometer with direct intensity setection,” Phys. Rev. Appl. 10(6), 064046 (2018).
[Crossref]

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23(8), 1693–1708 (1981).
[Crossref]

Phys. Rev. Lett. (16)

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59(3), 278–281 (1987).
[Crossref]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light–enhanced polarization interferometer,” Phys. Rev. Lett. 59(19), 2153–2156 (1987).
[Crossref]

H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Demonstration of a squeezed-light-enhanced power- and signal-recycled michelson interferometer,” Phys. Rev. Lett. 95(21), 211102 (2005).
[Crossref]

M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, “Beating the standard sensitivity-bandwidth limit of cavity-enhanced interferometers with internal squeezed-light generation,” Phys. Rev. Lett. 118(14), 143601 (2017).
[Crossref]

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57(20), 2520–2523 (1986).
[Crossref]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68(25), 3663–3666 (1992).
[Crossref]

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110(18), 181101 (2013).
[Crossref]

F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, “Squeezed-light optical magnetometry,” Phys. Rev. Lett. 105(5), 053601 (2010).
[Crossref]

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a high-purity narrowband photon from a transient atomic collective excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009).
[Crossref]

B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
[Crossref]

X. Pan, S. Yu, Y Zhou, K. Zhang, K. Zhang, S. Lv, S. Li, W. Wang, and J. Jing, “Orbital-angular-momentum multiplexed continuous-variable entanglement from four-wave mixing in hot atomic vapor,” Phys. Rev. Lett. 123(7), 070506 (2019).
[Crossref]

S. Li, X. Pan, Y. Ren, H. Liu, S. Yu, and J. Jing, “Deterministic generation of orbital-angular-momentum multiplexed tripartite entanglement,” Phys. Rev. Lett. 124(8), 083605 (2020).
[Crossref]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101(9), 093602 (2008).
[Crossref]

S. Liu, Y. Lou, and J. Jing, “Interference-induced quantum squeezing enhancement in a two-beam phase-sensitive amplifier,” Phys. Rev. Lett. 123(11), 113602 (2019).
[Crossref]

C. M. Caves, “Quantum-mechanical radiation-pressure fluctuations in an interferometer,” Phys. Rev. Lett. 45(2), 75–79 (1980).
[Crossref]

Phys. Rev. X (2)

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Subdiffraction-limited quantum imaging within a living cell,” Phys. Rev. X 4(1), 011017 (2014).
[Crossref]

C. S. Embrey, M. T. Turnbull, P. G. Petrov, and V. Boyer, “Observation of localized multi-spatial-mode quadrature squeezing,” Phys. Rev. X 5(3), 031004 (2015).
[Crossref]

Proc. SPIE (1)

Q. Glorieux, L. Guidoni, S. Guibal, J. P. Likforman, and T. Coudreau, “Strong quantum correlations in four wave mixing in 85Rb vapor,” Proc. SPIE 7727, 772703 (2010).
[Crossref]

Science (1)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

Other (1)

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. The PSA scheme for generating IDS. (a) Schematic view of the PSA. $\hat {a}$, $\hat {b}$ and $\hat {c}$ stand for the probe, conjugate and pump fields respectively. The solid line denotes the coherent state input. (b) Energy-level diagram of the double-$\Lambda$ scheme in the D1 line of $\sideset {^{85}}{}{\mathop {\mathrm {Rb}}}$. $\Delta$ and $\delta$ stand for the one-photon detuning and two-photon detuning, respectively.
Fig. 2.
Fig. 2. The PIA scheme for generating IDS. $\hat {a}$, $\hat {b}$ and $\hat {c}$ stand for the probe, conjugate and pump fields respectively. The solid line denotes the coherent state input while the dashed line denotes the vacuum state input.
Fig. 3.
Fig. 3. The intensity-difference noise powers of the PIA and the PSA with the phase $\phi =0$ and the input conjugate-probe ratio $\gamma =1$ as a function of the gain G when the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle =1$. Pink dashed line: the intensity-difference noise power of the PIA; pink solid line: the intensity-difference noise power of the PSA; blue solid line: SNL.
Fig. 4.
Fig. 4. The intensity-difference noise powers of the PIA and the PSA with the input conjugate-probe power ratio $\gamma =1$ as a function of the phase $\phi$ under the same gain G=10 and the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle =1$. Pink dashed line: the intensity-difference noise power of the PIA; pink solid line: the intensity-difference noise power of the PSA; blue solid line: SNL.
Fig. 5.
Fig. 5. (a) The intensity-difference noise power of the PSA as a function of the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ and the input conjugate-probe power ratio $\gamma$ when G=10 and $\phi =0$. The red solid line corresponding to the case of $\gamma =0$ is the dependence relation of the intensity-difference noise power of the PIA on $\left \langle \hat {N}_{a,in}\right \rangle$. The black dashed line is the dependence relation of the optimal intensity-difference noise power of the PSA on $\left \langle \hat {N}_{a,in}\right \rangle$ and $\gamma$. (b) The expanded plot where $0<\gamma <0.5$ and $0.01<\left \langle \hat {N}_{a,in}\right \rangle <1$.
Fig. 6.
Fig. 6. (a) Comparison of two types of optical parametric amplifiers. The green dashed line represents the intensity-difference noise power of the PIA with the gain G=10. The pink solid line represents the optimal intensity-difference noise power of the PSA with the gain G=10 and phase $\phi =0$. The red solid line is the dependence relation of the optimal $\gamma$ of the PSA on the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$. (b) The expanded plot where $0.001<\left \langle \hat {N}_{a,in}\right \rangle <1$. (c) The expanded plot where $0.001<\left \langle \hat {N}_{a,in}\right \rangle <0.1$. (d) The expanded plot where $0.001<\left \langle \hat {N}_{a,in}\right \rangle <0.01$.
Fig. 7.
Fig. 7. The intensity-difference noise powers of the PIA and the optimal PSA with phase $\phi =0$ as a function of the average input photon number of the probe field $\left \langle \hat {N}_{a,in}\right \rangle$ under the same gain $\textit {G}=10$ followed by optical loss.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

H ^ = i κ e i θ b ^ a ^ + h . c . ,
a ^ ( τ ) = G a ^ ( 0 ) + e i θ G 1 b ^ ( 0 ) ,
b ^ ( τ ) = e i θ G 1 a ^ ( 0 ) + G b ^ ( 0 ) ,
N ^ a , o u t a ^ ( τ ) a ^ ( τ ) = G N ^ a , i n + ( G 1 ) N ^ b , i n + G 1 + 2 cos ( ϕ ) N ^ a , i n N ^ b , i n G ( G 1 ) ,
N ^ b , o u t b ^ ( τ ) b ^ ( τ ) = G N ^ b , i n + ( G 1 ) N ^ a , i n + G 1 + 2 cos ( ϕ ) N ^ a , i n N ^ b , i n G ( G 1 ) ,
V a r ( N a , o u t N b , o u t ) S Q Z = N ^ a , i n + N ^ b , i n ,
V a r ( N a , o u t N b , o u t ) S N L N ^ a , o u t + N ^ b , o u t = ( 2 G 1 ) ( N ^ a , i n + N ^ b , i n ) + 4 cos ( ϕ ) N ^ a , i n N ^ b , i n G ( G 1 ) + 2 ( G 1 ) ,
IDS = V a r ( N ^ a , o u t N ^ b , o u t ) S Q Z V a r ( N ^ a , o u t N ^ b , o u t ) S N L = 1 ( 2 G 1 ) + 4 cos ( ϕ ) G ( G 1 ) γ 1 + γ + 2 ( G 1 ) N ^ a , i n ( 1 + γ ) ,
IDS = 1 ( 2 G 1 ) + 2 ( G 1 ) N ^ a , i n ,
γ = 1 + G 1 2 G cos 2 ( ϕ ) N ^ a , i n 2 G 1 G cos 2 ( ϕ ) N ^ a , i n 2 + ( G 1 2 G cos 2 ( ϕ ) N ^ a , i n 2 ) 2 ,
a ^ ( τ ) η 1 ( L 1 a ^ ( τ ) + 1 L 1 ν ^ 1 ) + 1 η 1 ν ^ 2 ,
b ^ ( τ ) η 2 ( L 2 b ^ ( τ ) + 1 L 2 ν ^ 3 ) + 1 η 2 ν ^ 4 .

Metrics