Abstract

Phase-sensitive nonlinear gain processes have been implemented as noise-reduced optical amplifiers, which have the potential to achieve signal-to-noise ratios beyond the classical limit. We experimentally demonstrate a novel phase-sensitive four-wave mixing amplification process in a single atomic vapor cell with only two input frequencies and two input vacuum modes. The amount of phase sensitivity depends on the power ratio between the inserted probes as well as on the input frequency of the probes. We find that, for certain phase values, the intensity noise of an output mode is lower than that of its phase-insensitive counterpart.

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

1. Introduction

Phase-sensitive four-wave mixing (FWM) processes in atomic vapor have numerous applications relating to quantum noise reduction. They have been used to generate single-mode squeezing [1], enhanced two-mode squeezing [24], and have been revealed to act as theoretically-noiseless optical phase-sensitive amplifiers (PSAs) [3,5] that may improve upon continuous-variable quantum key distribution protocols [6] and can amplify two-dimensional images with less noise than allowed classically [7]. All of these experimental schemes involve a pump, probe, and conjugate field as inputs, each at a different frequency, and therefore require either the use of at least three lasers or two frequency modulators. (Note that different terms for conjugate, probe and pump are used in some texts, e.g. [1]). Here we demonstrate a dual-pump FWM process requiring only two frequency inputs (i.e. only one laser and frequency modulator) that results in four phase-sensitive output modes. This is a seeded extension of the geometry discussed in our previous work [8], in which we demonstrated a novel unseeded four-output-mode FWM setup. That setup is stable and balanced due to an interplay between two different phase-matched FWM mechanisms, namely the single-pump and dual-pump processes, but does not exhibit phase sensitivity. The configuration described in this manuscript induces a phase-sensitivity on the intensity of all four output modes. The result is a phase-sensitive amplifier that allows for intensity noise reduced below the phase-insensitive level.

2. Methods

A Ti:Sapph laser is tuned to the pump frequency (795 nm) and a small portion is double-passed through an acoustic-optical modulator (AOM), resulting in a weak (~20 $\mu$W) probe frequency beam detuned approximately 3.05 GHz from the pump (see level schemes in our previous work [8]). The pump and the probe are split into $\textrm {P}_{\textrm {A}}$ and $\textrm {P}_{\textrm {B}}$ and $\textrm {p}_{\textrm {A}}$ and $\textrm {p}_{\textrm {B}}$ respectively on polarizing beamsplitters (PBS), with half-waveplates before and after to make, and then compensate for, the required polarization change. When the geometry is symmetric and balanced, the powers in each pump and probe beam are approximately 100 mW and 10 $\mu$W respectively. These beams, $\textrm {P}_{\textrm {A}}$, $\textrm {P}_{\textrm {B}}$, $\textrm {p}_{\textrm {A}}$ and $\textrm {p}_{\textrm {B}}$, are all then inserted into a rubidium vapor cell, using PBSs and waveplates to more easily align them at small angles relative to one another (approximately 2.5$^\circ$ between $\textrm {P}_{\textrm {A}}$ ($\textrm {p}_{\textrm {A}}$) and $\textrm {P}_{\textrm {B}}$ ($\textrm {p}_{\textrm {B}}$), and 1$^\circ$ between the plane of the pumps and the plane of the probes) as shown in Fig. 1.

 figure: Fig. 1.

Fig. 1. Experimental setup. Left: Simplified diagram of the atomic vapor cell (purple) and the relevant FWM beams (yellow: pumps, red: probe, blue: conjugate). Each beam travels from left to right within the cell. The blue cubes are polarizing beam splitters (PBS). Note that the beamsplitters are not necessary for the creation of a nonlinear interferometer, and are present simply to ease the alignment process for the four tightly-angled input beams. Right: Labeling scheme for probes (p$_{A/B}$; inserted and amplified), pumps (P$_{A/B}$; inserted and partially annihilated) and conjugates (c$_{A/B}$; generated) as seen from the input face of the second PBS, looking towards the cell. The dashed lines represent modes paired together by either the single-pump (purple) or the dual-pump (brown) FWM process.

Download Full Size | PPT Slide | PDF

The cell is kept at approximately 125$^\circ$C, hot enough for the nonlinear interaction to simultaneously amplify the probe beams and generate two new frequency-shifted beams, $\textrm {c}_{\textrm {A}}$ and $\textrm {c}_{\textrm {B}}$, but not so hot that Doppler-broadened absorption takes over as the dominant effect. This nonlinear interaction consists of two separate phase-matched FWM processes [8], involving one and both pumps respectively.

The data from Figs. 25 were recorded by placing a piezo-actuated mirror with a 50-100 Hz sine wave in the path of input probe B and aligning the relevant output beam to a detector (Thorlabs PDA10A). “Fluctuations” in Figs. 3 and 4 were calculated using the variance function in Matlab on the output conjugate voltage traces recorded on an oscilloscope. Thus, they are measured in units of V$^2$. The data from Fig. 6 were recorded on a spectrum analyzer at 2.5 MHz (zero span), with a piezo frequency of 50 Hz, using one port of a balanced detector (Thorlabs PDB450A).

 figure: Fig. 2.

Fig. 2. Signal of each output beam measured on a photodetector over 240 ms, with a 50 Hz signal applied to a piezoelectric mirror on probe B (before the cell). The power of probes A and B is approximately 10 $\mu \textrm {W}$ each. The probe detuning is 3.060 GHz. Note that the four scans were taken independently of one another and are not phase-synchronized. Non-zero signals on unseeded modes are due to spontaneous FWM as well as imperfect detector calibration and residual pump light. Red: cell seeded with probe A. Yellow: cell seeded with probe B. Blue: cell seeded with both probes.

Download Full Size | PPT Slide | PDF

 figure: Fig. 3.

Fig. 3. Signal fluctuations on conjugate B on detector as the power ratio between probes A and B is varied, when probe A only (red), probe B only (blue) or both probes A and B (orange) are inserted. In all cases, the probe detuning is 3.05 GHz and a 0-8V 100 Hz sine signal is applied to a piezoelectric mirror in the path of input probe B. Shaded error bars are calculated from 12 trials at each sampled power ratio. (Note that the “power ratio” does not take into account if the beams were blocked or unblocked, i.e. for the “Probe X only” cases.)

Download Full Size | PPT Slide | PDF

 figure: Fig. 4.

Fig. 4. Fluctuations in the signal of conjugate B as probe detuning (from the pump frequency) is varied, while a 0-8V 100 Hz sine signal is applied to a piezoelectric mirror in the path of input probe B. As before, the legend denotes which seed beams are inserted into the cell for each case. Shaded error bars are calculated from 12 trials at each sampled power ratio.

Download Full Size | PPT Slide | PDF

 figure: Fig. 5.

Fig. 5. Mean signal (left) and fluctuations (right) in probe A as a function of pump power ratio (P$_A$/P$_B$). As before, the legend denotes which seed beams are inserted into the cell for each case. (Note that the false negative signal is due to detector calibration, i.e. darkness on the detector corresponds to a signal between 0 and -0.1 V, as seen in the “Probe B only” case on the left.) Shaded error bars for the fluctuations are calculated as in Fig. 3 (there are error bars for all three cases; however, the error bars are smaller than the data markers for the “Probe X only” cases).

Download Full Size | PPT Slide | PDF

 figure: Fig. 6.

Fig. 6. Noise power of probe A on a spectrum analyzer, with a 50 Hz signal applied to a piezo mirror in the path of probe B (before the cell). Yellow: detector noise, with no incident light. Red: both probes inserted into cell. Blue: probe A only. For both of the latter two cases, the minimum power on the detector was equal. RBW = 100 kHz; VBW = 1 kHz.

Download Full Size | PPT Slide | PDF

3. Results

We measure the intensities of the individual output beams p$_A$, p$_B$, c$_A$ and c$_B$ on a detector, with various combinations of the two seed beams p$_A$ and p$_B$ inserted. We find that all of the output beams exhibit strong phase sensitivity when both seeds are present. Figure 2 shows the signal of each output beam when a 100 Hz signal is applied to a piezoelectric mirror before the cell in order to vary the phase difference between input probes p$_A$ and p$_B$. The power ratio between the probes is approximately 1 for all four cases. Any asymmetry in gain values and phase dependence between corresponding plots, e.g. between the “Both inserted” cases in the Probe A and Probe B plots, arises from minute alignment and size differences in the system. It is clear that the intensity of each output beam has a significant dependence on the relative phase of the input modes. The “Probe B only” cases do display non-negligible fluctuations under these conditions, as probe B is incident on the piezo mirror and FWM interaction strength can depend strongly on the alignment of input beams. That said, the fluctuations on the “Probe B only” signal are always significantly less than the fluctuations on the “Probes A and B” signal at this detuning (see Figs. 3 and 4). (Furthermore, qualitatively, the “Probe B only” signal is flat and unchanging when no voltage is applied to the piezo, in contrast with the “Probes A and B” signal which fluctuates considerably.) Note that the extra, smaller peaks in the Probe A signal are simply due to a mismatch between the piezo oscillation phase and the phase difference between the probes; i.e. zero displacement on the piezo does not correspond to a phase difference of zero. This mismatch is highly sensitive to environmental disruptions, e.g. movement in the hallway outside our laboratory. Figure 3 reveals the dependence of these fluctuations on the power ratio between the probes, where a sharp peak about $\textrm {p}_A/\textrm {p}_B=1$ is evident only when both probes are inserted into the cell. Negligible fluctuations are detected for the one-seed cases. Likewise, Fig. 4 shows the relationship between phase-sensitivity and the probe frequency. The phase-sensitivity peak is close but not equal to 3.036 GHz, the hyperfine splitting between the $5^2S_{1/2}$ $F=2$ and $F=3$ ground states. The cell temperature was hotter, around 130 degrees C, during the data collection in Fig. 4, hence the disparity between 3.060-GHz detuning data in Figs. 2 and 4.

Next, in Fig. 5 we consider the effect of the pump power ratio on one of the output modes, $\textrm {p}_A$. The data in Fig. 5 were taken with a probe detuning of 3.04 GHz. As the power ratio $\textrm {P}_A/\textrm {P}_B$ increases, the configuration approaches the case of standard twin-beam FWM about $\textrm {P}_A$, with an extra nearby probe $\textrm {p}_B$. As the simple twin-beam process yields more light overall (i.e. has a higher gain than the four-output process) [8], there is a straightforward positive trend for the mean output signal, and the “Probes A and B” case follows the “Probe A only” case. The fluctuations likewise exhibit a slight positive trend, and notably do not drop off even at high or low values of $\textrm {P}_A/\textrm {P}_B$. It is evident that the addition of a second probe-frequency beam at the correct angle to twin-beam FWM produces appreciable phase-sensitivity, regardless of the strength of the second pump (if any). We reiterate here that the two input conjugate modes are vacuum.

Finally, in Fig. 6 we investigate the amplification noise of this technique. To ensure that any noise reduction in the measurement is due to phase-sensitivity and not simply a lower signal, we choose experimental variables (probe frequency, cell temperature, and pump/probe powers) that lead to the same minimum optical power on $\textrm {p}_A$ whether or not the system is phase-sensitive or insensitive (i.e. whether or not $\textrm {p}_B$ is also injected). We find that, for certain phase values, the output modes in this four-spot configuration possesses about 0.5 dB lower noise when phase-sensitive than when phase-insensitive.

4. Discussion

The configuration described here behaves as a phase-sensitive amplifier (PSA). The noise and gain of PSAs depend on the input phase of the beams involved, unlike their phase-insensitive counterparts (PIAs) [9]. In theory, certain types of ideal PSAs can allow for noiseless amplification. This means that for certain phase values of the input signal, the signal-to-noise ratio (SNR) of the output matches the SNR of the input, or equivalently, the Noise Factor (NF) reaches 0 dB [10]. Noiseless amplification has obvious advantages in many research areas; for example, it can compensate for loss and detector imperfections in long-haul optical transmission systems, and it allows for the augmentation of faint optical signals [7,11], e.g. in microscopy or astronomy. The results shown in Fig. 6, namely that the output modes in this four-spot configuration possess lower noise when phase-sensitive (for certain phase values) than when phase-insensitive, indicate that this PSA has potential as a “less-noisy” amplifier and may be useful in some of the aforementioned research areas – especially in applications that require the simultaneous amplification of multiple correlated spatial modes. In such cases it will be vital to differentiate between the PSA and PIA gain behavior of this configuration, for example by comparing double the standard (1 pump, 1 probe) FWM gain with the situation shown here.

Additionally, assuming the pumps are phase-locked to one another, any input phase shift of the probes may be characterized by one of the output beams – say $\textrm {p}_A$ – leaving beams $\textrm {p}_B$, $\textrm {c}_A$ and $\textrm {c}_B$ free for other use, with the advantage that the phase difference between each pair is already known. This means that a phase-difference measurement may be made on a pair or even a trio of correlated modes without introducing loss or destroying any squeezing between them. While this is true of other FWM-based interferometers, this method naturally begets four phase-correlated output modes, instead of two. In addition, this nonlinear interferometer could further prove to be advantageous to metrological applications if it could be shown to act as a truncated SU(1,1) interferometer [1221], which would allow for sensing beyond the standard quantum limit (SQL). Further analysis is required to determine the nature of interferometry present in this multimode FWM configuration.

In summary, one might reasonably expect the setup described here to be phase insensitive, because standard twin-beam FWM in atomic vapor does not depend on the phase difference between the pump and the probe, even though that process also involves two inserted frequencies. Instead, phase-sensitivity generally only occurs in twin-beam FWM when all three frequencies, including conjugate, are inserted [1,2,7]. Additionally, most, if not all, previous PSA demonstrations require that no input modes are left as vacuum. The configuration in this manuscript involves the same two input, three output frequencies as standard twin-beam FWM. However, we find here that the addition of two input spatial modes (at appropriate locations to satisfy multiple phase-matching constraints) results in a significantly phase-sensitive output that arises after the use of only one vapor cell. In this work we focus on introducing the phase-sensitivity of this new system and characterizing the phase-sensitive fluctuations on its output modes with respect to experimental variables. A natural extension would be to further analyze and quantify the improvement in signal-to-noise ratio this setup allows compared to the SQL, especially when looking at combinations of output modes.

Funding

Louisiana Board of Regents; National Science Foundation (DGE-1154145).

Acknowledgments

We are grateful for helpful and interesting discussions with Wenlei Zhang. EMK acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1154145, and SW acknowledges support from the Louisiana State Board of Regents.

Disclosures

The authors declare no conflicts of interest.

References

1. N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express 19(22), 21358 (2011). [CrossRef]  

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

3. T. Li, B. E. Anderson, T. Horrom, B. L. Schmittberger, K. M. Jones, and P. D. Lett, “Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier,” Opt. Express 25(18), 21301 (2017). ArXiv: 1708.08334. [CrossRef]  

4. C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020). [CrossRef]  

5. 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]  

6. S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314. [CrossRef]  

7. N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless Optical Amplifier Operating on Hundreds of Spatial Modes,” Phys. Rev. Lett. 109(4), 043602 (2012). [CrossRef]  

8. E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018). [CrossRef]  

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]  

10. W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003). [CrossRef]  

11. M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52(6), 4930–4940 (1995). [CrossRef]  

12. B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33(6), 4033–4054 (1986). [CrossRef]  

13. P. Gupta, B. L. Schmittberger, B. E. Anderson, K. M. Jones, and P. D. Lett, “Optimized phase sensing in a truncated SU(1,1) interferometer,” Opt. Express 26(1), 391 (2018). [CrossRef]  

14. N. Prajapati and I. Novikova, “Polarization-Based Truncated SU(1,1) Interferometer based on Four-wave Mixing in Rb vapor,” arXiv:1906.07213 [physics, physics:quant-ph] ArXiv: 1906.07213 (2019).

15. Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85(2), 023815 (2012). [CrossRef]  

16. W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12(8), 083014 (2010). [CrossRef]  

17. 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]  

18. 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]  

19. 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]  

20. 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 truncated SU(1,1) interferometer,” Optica 4(7), 752 (2017). [CrossRef]  

21. M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer,” Phys. Rev. Lett. 119(22), 223604 (2017). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express 19(22), 21358 (2011).
    [Crossref]
  2. Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phase-sensitive amplifier via four-wave mixing in rubidium vapor,” New J. Phys. 17(2), 023027 (2015).
    [Crossref]
  3. T. Li, B. E. Anderson, T. Horrom, B. L. Schmittberger, K. M. Jones, and P. D. Lett, “Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier,” Opt. Express 25(18), 21301 (2017). ArXiv: 1708.08334.
    [Crossref]
  4. C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
    [Crossref]
  5. 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]
  6. S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
    [Crossref]
  7. N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless Optical Amplifier Operating on Hundreds of Spatial Modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
    [Crossref]
  8. E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
    [Crossref]
  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]
  10. W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
    [Crossref]
  11. M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52(6), 4930–4940 (1995).
    [Crossref]
  12. B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33(6), 4033–4054 (1986).
    [Crossref]
  13. P. Gupta, B. L. Schmittberger, B. E. Anderson, K. M. Jones, and P. D. Lett, “Optimized phase sensing in a truncated SU(1,1) interferometer,” Opt. Express 26(1), 391 (2018).
    [Crossref]
  14. N. Prajapati and I. Novikova, “Polarization-Based Truncated SU(1,1) Interferometer based on Four-wave Mixing in Rb vapor,” arXiv:1906.07213 [physics, physics:quant-ph] ArXiv: 1906.07213 (2019).
  15. Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85(2), 023815 (2012).
    [Crossref]
  16. W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12(8), 083014 (2010).
    [Crossref]
  17. 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]
  18. 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]
  19. 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]
  20. 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 truncated SU(1,1) interferometer,” Optica 4(7), 752 (2017).
    [Crossref]
  21. M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer,” Phys. Rev. Lett. 119(22), 223604 (2017).
    [Crossref]

2020 (1)

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[Crossref]

2019 (1)

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]

2018 (2)

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

P. Gupta, B. L. Schmittberger, B. E. Anderson, K. M. Jones, and P. D. Lett, “Optimized phase sensing in a truncated SU(1,1) interferometer,” Opt. Express 26(1), 391 (2018).
[Crossref]

2017 (3)

2015 (1)

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

2014 (1)

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]

2012 (3)

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless Optical Amplifier Operating on Hundreds of Spatial Modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85(2), 023815 (2012).
[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]

2011 (2)

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]

N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express 19(22), 21358 (2011).
[Crossref]

2010 (1)

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12(8), 083014 (2010).
[Crossref]

2009 (1)

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
[Crossref]

2008 (1)

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]

2003 (1)

W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
[Crossref]

1995 (1)

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52(6), 4930–4940 (1995).
[Crossref]

1986 (1)

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33(6), 4033–4054 (1986).
[Crossref]

Agarwal, G. S.

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12(8), 083014 (2010).
[Crossref]

Anderson, B. E.

Boyer, V.

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]

Chekhova, M.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer,” Phys. Rev. Lett. 119(22), 223604 (2017).
[Crossref]

Corzo, N.

Corzo, N. V.

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless Optical Amplifier Operating on Hundreds of Spatial Modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[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]

Debuisschert, T.

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
[Crossref]

Diamanti, E.

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
[Crossref]

Dowling, J. P.

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12(8), 083014 (2010).
[Crossref]

Fang, Y.

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

Fossier, S.

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
[Crossref]

Glasser, R. T.

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

Grangier, P.

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
[Crossref]

Gu, B.

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[Crossref]

Gupta, P.

Hermann-Avigliano, C.

Horrom, T.

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]

Imajuku, W.

W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
[Crossref]

Jing, J.

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]

Y. Fang and J. Jing, “Quantum squeezing and entanglement from a two-mode phase-sensitive 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]

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]

Jones, K. M.

Khalili, F.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer,” Phys. Rev. Lett. 119(22), 223604 (2017).
[Crossref]

Klauder, J. R.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33(6), 4033–4054 (1986).
[Crossref]

Knutson, E. M.

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

Kolobov, M. I.

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52(6), 4930–4940 (1995).
[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]

Lett, P. D.

Leuchs, G.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer,” Phys. Rev. Lett. 119(22), 223604 (2017).
[Crossref]

Li, C.

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[Crossref]

Li, K.

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[Crossref]

Li, T.

Li, W.

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[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]

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, 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]

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]

Lugiato, L. A.

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52(6), 4930–4940 (1995).
[Crossref]

Manceau, M.

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer,” Phys. Rev. Lett. 119(22), 223604 (2017).
[Crossref]

Marino, A. M.

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]

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless Optical Amplifier Operating on Hundreds of Spatial Modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[Crossref]

N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express 19(22), 21358 (2011).
[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]

McCall, S. L.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33(6), 4033–4054 (1986).
[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]

Novikova, I.

N. Prajapati and I. Novikova, “Polarization-Based Truncated SU(1,1) Interferometer based on Four-wave Mixing in Rb vapor,” arXiv:1906.07213 [physics, physics:quant-ph] ArXiv: 1906.07213 (2019).

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]

Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85(2), 023815 (2012).
[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]

Plick, W. N.

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12(8), 083014 (2010).
[Crossref]

Prajapati, N.

N. Prajapati and I. Novikova, “Polarization-Based Truncated SU(1,1) Interferometer based on Four-wave Mixing in Rb vapor,” arXiv:1906.07213 [physics, physics:quant-ph] ArXiv: 1906.07213 (2019).

Schmittberger, B. L.

Swaim, J. D.

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

Takada, A.

W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
[Crossref]

Tualle-Brouri, R.

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
[Crossref]

Wyllie, S.

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

Yurke, B.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33(6), 4033–4054 (1986).
[Crossref]

zhang, D.

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[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]

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]

Zhang, Y.

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[Crossref]

Zhang, Z.

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[Crossref]

Zhou, Z.

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]

Appl. Phys. Lett. (1)

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]

IEEE J. Quantum Electron. (1)

W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
[Crossref]

J. Phys. B: At., Mol. Opt. Phys. (1)

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009). ArXiv: 0812.4314.
[Crossref]

Laser Phys. Lett. (1)

C. Li, W. Li, D. zhang, Z. Zhang, B. Gu, K. Li, and Y. Zhang, “Enhanced squeezing of four-wave mixing by phase-sensitive dressed effect in a hot atomic system,” Laser Phys. Lett. 17(1), 015401 (2020).
[Crossref]

Nat. Commun. (1)

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]

New J. Phys. (2)

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

W. N. Plick, J. P. Dowling, and G. S. Agarwal, “Coherent-light-boosted, sub-shot noise, quantum interferometry,” New J. Phys. 12(8), 083014 (2010).
[Crossref]

Opt. Express (3)

Optica (1)

Phys. Rev. A (6)

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[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]

M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52(6), 4930–4940 (1995).
[Crossref]

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33(6), 4033–4054 (1986).
[Crossref]

Z. Y. Ou, “Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer,” Phys. Rev. A 85(2), 023815 (2012).
[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]

Phys. Rev. Lett. (3)

N. V. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Noiseless Optical Amplifier Operating on Hundreds of Spatial Modes,” Phys. Rev. Lett. 109(4), 043602 (2012).
[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]

M. Manceau, G. Leuchs, F. Khalili, and M. Chekhova, “Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer,” Phys. Rev. Lett. 119(22), 223604 (2017).
[Crossref]

Other (1)

N. Prajapati and I. Novikova, “Polarization-Based Truncated SU(1,1) Interferometer based on Four-wave Mixing in Rb vapor,” arXiv:1906.07213 [physics, physics:quant-ph] ArXiv: 1906.07213 (2019).

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 (6)

Fig. 1.
Fig. 1. Experimental setup. Left: Simplified diagram of the atomic vapor cell (purple) and the relevant FWM beams (yellow: pumps, red: probe, blue: conjugate). Each beam travels from left to right within the cell. The blue cubes are polarizing beam splitters (PBS). Note that the beamsplitters are not necessary for the creation of a nonlinear interferometer, and are present simply to ease the alignment process for the four tightly-angled input beams. Right: Labeling scheme for probes (p $_{A/B}$ ; inserted and amplified), pumps (P $_{A/B}$ ; inserted and partially annihilated) and conjugates (c $_{A/B}$ ; generated) as seen from the input face of the second PBS, looking towards the cell. The dashed lines represent modes paired together by either the single-pump (purple) or the dual-pump (brown) FWM process.
Fig. 2.
Fig. 2. Signal of each output beam measured on a photodetector over 240 ms, with a 50 Hz signal applied to a piezoelectric mirror on probe B (before the cell). The power of probes A and B is approximately 10 $\mu \textrm {W}$ each. The probe detuning is 3.060 GHz. Note that the four scans were taken independently of one another and are not phase-synchronized. Non-zero signals on unseeded modes are due to spontaneous FWM as well as imperfect detector calibration and residual pump light. Red: cell seeded with probe A. Yellow: cell seeded with probe B. Blue: cell seeded with both probes.
Fig. 3.
Fig. 3. Signal fluctuations on conjugate B on detector as the power ratio between probes A and B is varied, when probe A only (red), probe B only (blue) or both probes A and B (orange) are inserted. In all cases, the probe detuning is 3.05 GHz and a 0-8V 100 Hz sine signal is applied to a piezoelectric mirror in the path of input probe B. Shaded error bars are calculated from 12 trials at each sampled power ratio. (Note that the “power ratio” does not take into account if the beams were blocked or unblocked, i.e. for the “Probe X only” cases.)
Fig. 4.
Fig. 4. Fluctuations in the signal of conjugate B as probe detuning (from the pump frequency) is varied, while a 0-8V 100 Hz sine signal is applied to a piezoelectric mirror in the path of input probe B. As before, the legend denotes which seed beams are inserted into the cell for each case. Shaded error bars are calculated from 12 trials at each sampled power ratio.
Fig. 5.
Fig. 5. Mean signal (left) and fluctuations (right) in probe A as a function of pump power ratio (P $_A$ /P $_B$ ). As before, the legend denotes which seed beams are inserted into the cell for each case. (Note that the false negative signal is due to detector calibration, i.e. darkness on the detector corresponds to a signal between 0 and -0.1 V, as seen in the “Probe B only” case on the left.) Shaded error bars for the fluctuations are calculated as in Fig. 3 (there are error bars for all three cases; however, the error bars are smaller than the data markers for the “Probe X only” cases).
Fig. 6.
Fig. 6. Noise power of probe A on a spectrum analyzer, with a 50 Hz signal applied to a piezo mirror in the path of probe B (before the cell). Yellow: detector noise, with no incident light. Red: both probes inserted into cell. Blue: probe A only. For both of the latter two cases, the minimum power on the detector was equal. RBW = 100 kHz; VBW = 1 kHz.

Metrics