Abstract

We investigate stimulated four-wave mixing (FWM) in the 6S1/2–6P3/2–8S1/2 open transition of a warm 133Cs atomic ensemble. Despite the absence of the two-photon cycling transition, we measure high-contrast FWM signals in the 6P3/2–8S1/2 transition between the upper excited states according to the frequency detuning and powers of the coupling and driving lasers. The FWM light generation in the upper excited states is interpreted as the FWM phenomena induced by the driving laser of the 6S1/2–6P3/2 transition from the cascade-type two-photon coherent atomic ensemble with the coupling and pump lasers. We believe that this work can contribute to the development of hybrid photonic quantum networks between photonic quantum states generated from different atomic systems.

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

1. Introduction

Quantum photonic sources (QPSs) generated from atomic ensembles [113] are the key components of long-distance quantum communications and quantum networks based on atom–photon interactions [1417]. In this regard, the four-wave mixing (FWM) process in atomic media lies at the heart of QPS generation from atomic ensembles [1821]. For application to quantum memory and quantum repeaters, when compared with QPSs generated via spontaneous parametric down-conversion (SPDC) with nonlinear crystals, QPSs based on atom–photon interactions are preferred [1416] because they offer the advantages of a narrow photon bandwidth for interactions with atoms. Therefore, understanding the FWM process in a variety of atomic configurations of different atoms is necessary for quantum optics applications based on atom–photon interactions [1821].

To date, FWM has been achieved in K, Na, Rb, and Cs atoms in cascade-type and double-Λ-type atomic configurations [1832]. The strong correlation due to nature of FWM is used for the photon pair and quantum-correlated twin beams generations [112,2534]. Moreover, quantum imaging, slow light, and light storage have been experimentally generated based on the FWM process in double-Λ-type atomic configurations of alkali vapors [2737]. Recently, the high-performance, spontaneous-FWM-based generation of correlated photon pairs from Rb atomic vapor cells via has been experimentally demonstrated with the use of a simple experimental setup [1013].

Interestingly, the wavelength of the 6P3/2–8S1/2 transition between the upper excited states of the 133Cs atom is close to that of the D1 line of the 87Rb atom, which provides a potential resource for interface between the photon pairs from Cs and Rb atoms. This work is important for hybrid photonic quantum network between the photonic quantum states generated from different atomic systems, such as Rb and Cs atoms. In the 6S1/2–6P3/2–8S1/2 transition of 133Cs atom, the phenomena of electromagnetically induced transparency (EIT) and two-photon absorption (TPA) have been studied [3839]. However, there are experimental difficulties in obtaining enhanced FWM nonlinearity for this transition with the Cs vapor cell because of the two-photon Doppler-shift due to the wavelength difference between the 6S1/2–6P3/2 (852 nm) and the 6P3/2–8S1/2 (795 nm) transitions as well as the absence of the two-photon cycling transition.

In this paper, we report on stimulated FWM corresponding to the 6S1/2–6P3/2–8S1/2 open transition with the use of a warm 133Cs atomic vapor cell. We examine the dependence of the FWM spectrum on the frequency detunings and powers of the coupling and driving lasers.

2. Experimental configuration for FWM generation from Cs atomic vapor

Figure 1(a) shows the energy-level diagram of the 6S1/2–6P3/2–8S1/2 transition of 133Cs atoms for FWM generation from the 6P3/2–8S1/2 transition between the upper excited states. The natural linewidths of the 6P3/2 and 8S1/2 states are 5.22 MHz and 2.18 MHz, respectively [4041]. The pump and driving lasers interact with the 6S1/2(F = 4)–6P3/2(F′ = 5) transition, and the coupling laser interacts with the 6P3/2(F′ = 5)–8S1/2(F′′ = 4) transition. Parameters δp, δd, and δc denote the detuning frequencies of the pump, driving, and coupling lasers, respectively. FWM light is induced by the driving laser under the phase-matching condition.

 figure: Fig. 1.

Fig. 1. Experimental configuration for FWM generation from the cascade-type atomic system of 133Cs atoms. (a) Energy-level diagram of the 6S1/2–6P3/2–8S1/2 transition of 133Cs atoms and experimental configuration for FWM in the cascade-type atomic system interacting with the pump, coupling, and driving lasers. (b) Experimental configuration for FWM generation under the phase-matching condition corresponding to the energy and wave-vector conservations of the contributing lasers. (c) Calculated phase-matching function as a function of the tilt angle.

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It is well known that the cascade-type two-photon resonance condition of the pump and coupling lasers should be satisfied to generate a cascade-type FWM signal because the FWM process is strongly correlated with the two-photon coherence between the two states interacting with the pump and coupling lasers [2021]. However, upon comparing this transition in Fig. 1(a) with the 5S1/2–5P3/2–5D5/2 transition of 87Rb [1921], it is found that the FWM signal for this transition with the Cs vapor cell is significantly weak because of the following reasons: First, the two-photon cycling transition, such as the 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F′′ = 4) transition of 87Rb, can be used to treat the three-level atomic systems without considering the decay channel of the 6P3/2 state [42]. The FWM signal can be significantly enhanced in the atomic medium with the pure two-photon coherence in a simple three-level atomic system. But, the 6S1/2(F = 4)–6P3/2(F′ = 5)–8S1/2(F′′ = 4) transition is not a two-photon cycling transition. Second, the wavelength difference between the 6S1/2–6P3/2 and the 6P3/2–8S1/2 transitions of 133Cs is larger than that between the 5S1/2–5P3/2 and 5P3/2–5D5/2 transitions of 87Rb. The enhanced FWM is due to the coherent contributions from nearly all the velocity classes in the Doppler-broadened atomic ensemble [43]. When the wavelength difference between the pump and coupling lasers is very small, the two-photon resonant condition for the atoms interacting with the counterpropagating pump and coupling lasers can be Doppler-free in the cascade-type configuration. In our experiment, the two-photon Doppler broadening (Δωtwo) for the 852-nm coupling laser and the 795-nm pump laser in the warm Cs vapor cell can be expressed as

$$\Delta {\omega _{two}} = ({k_p} - {k_c}) \cdot \Delta v,$$
where kp and kc denote the wave vectors of the pump and coupling lasers, respectively, and Δv the width of the atom velocity distribution. The value of Δωtwo was estimated to be 2π×20.5 MHz at Δv = 241 m/s, which is 9.4 times greater than the natural linewidth (2.18 MHz) of the 8S1/2 state. Therefore, in the 6S1/2–6P3/2–8S1/2 transition, the atoms of velocity classes contributing to the FWM process in the Doppler-broadened atomic ensemble significantly decreases.

An FWM signal (blue dashed line) is generated for the 6P3/2–8S1/2 transition under the phase-matching condition corresponding to the energy and wave-vector conservations of the contributing lasers, as shown in Fig. 1(b). Upon the interaction of the driving laser with the counterpropagating pump and coupling lasers at a certain tilt angle, the FWM light is induced along this angle relative to the pump laser direction. In our experiment, the generated FWM light was counterpropagated relative to the driving laser in the phase-matched direction.

The phase-matching function is related to the tilt angle (θ) of the generated FWM. The phase-matching function [7], $\varphi (\theta )$, can be expressed as

$$\varphi (\theta ) = \textrm{sinc}\left( {\frac{{\Delta k(\theta )L}}{2}} \right),$$
where Δk denotes the wave-vector mismatch of the four fields, i.e., $\Delta k(\theta ) = |{{k_p} + {k_c}} |- |{{k_d} + {k_F}} |\cos \theta$, with ${k_{p,c,d,F}}$ denoting the wave vectors, respectively, of the pump, coupling, driving, and FWM fields; and L the length of the 87Rb vapor cell.

Figure 1(c) shows the calculated phase-matching function as a function of the tilt angle. From Fig. 1(c), we note that the acceptance tilt angle is estimated to be ∼1.5°. Although the wavelength difference between the pump and coupling lasers is large, we confirm that it is possible to experimentally obtain FWM signals using the experimental configuration corresponding to Figs. 1(a) and (b).

Our experimental setup is shown in Fig. 2, and it is similar to that described in a previous study on the generation of FWM light from the cascade-type atomic system of a Rb atomic vapor cell [21]. The pump and coupling lasers are counterpropagated through a 50-mm-long vapor cell containing the 133Cs atoms and spatially overlapped completely with identical 1/e2 beam diameters of 2.2 mm. In our experiment, the laser systems consisted of two external cavity diode lasers (ECDLs). The two ECDLs were operated independently at wavelengths of 852 nm (for the pump and driving lasers) and 795 nm (for the coupling laser). The pump and driving lasers are separated from the single ECDL (852 nm). The linewidths of both ECDLs were estimated to be <1 MHz. The power of the three laser beams was adjusted by using a half-wave plate and polarizing beam splitter (PBS), and the temperature of the vapor cell was set to 37 °C. The vapor cell was housed in a three-layer µ-metal chamber to reduce interference from external magnetic fields. The FWM signals were measured with the use of an avalanche photodiode (APD: Hamamatsu C12703-01). In our experiment, we selectively measured the mutually orthogonal polarized FWM signal with the driving field by the PBS. The same polarization component of FWM signal is not measured by the APD. The driving laser was aligned at 1° relative to the pump and coupling lasers to ensure maximal FWM generation.

 figure: Fig. 2.

Fig. 2. Experimental schematic for FWM generation from 133Cs atomic vapor cell (PBS: polarizing beam splitter; APD: avalanche photodiode; BS: beam splitter; M: mirror).

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3. Experimental results and discussion

The FWM process is strongly correlated with two-photon coherence because of the possibility of nonlinear optical process enhancement via two-photon coherence [19]. Figure 3(a) shows the transmittance (blue curve) and FWM (red curve) signals for the 6S1/2(F = 4)–6P3/2(F′ = 3, 4, 5)–8S1/2(F′′ = 4) transition as a function of the detuning frequencies (δp and δd) of the pumping and driving lasers, where the gray-colored spectrum denotes the saturated absorption spectrum (SAS) of the pump laser for the 6S1/2(F = 4)–6P3/2 transition. The transmittance spectrum of the pump was measured by using a photodetector (PD) without the driving laser. The powers of the coupling and pump lasers were 4.5 mW and 1.0 mW, respectively, and the beam diameters of these two lasers were 2.2 mm, corresponding to beam intensities of 1.2 mW/mm2 and 0.26 mW/mm2, respectively. The coupling polarization was linearly polarized perpendicular to the pump polarization.

 figure: Fig. 3.

Fig. 3. (a) FWM (red curve) and DROP (blue curve) spectra as functions of the detuning frequencies δp and δd of the pump and driving lasers, respectively. (b) FWM spectra according to −δc (coupling laser detuning), where the gray curve denotes the saturated absorption spectrum (SAS) of the pump (driving) laser.

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In the 6S1/2(F = 4)–6P3/2(F′ = 3, 4, 5)–8S1/2(F′′ = 4) transition, the transmittance signal is mainly due to the double resonance optical pumping (DROP) effect, which corresponds to the optical pumping process via two-step excitation, including the decay channels from an excited state to the other ground state of 6S1/2(F = 3) [44]. Although the DROP peak on two-photon resonance is a high-contrast one, the two-photon coherence effect in this transition is remarkably weak because of the DROP process.

Nevertheless, when a driving laser with a power of 1.0 mW is added, we can clearly observe the FWM signal, as indicated by the red curve in Fig. 3(a). The observed FWM spectrum between the upper excited states of the 6P3/2–8S1/2 transition is background-free from the fluorescence between the upper excited states. The FWM signal in this transition can be understood as being stimulated via the interaction of the driving laser with the atomic medium under the weak residual pure two-photon coherence. We can see the spectral feature due to the ac Stark effect owing to the strong coupling laser and the three-photon atomic coherence considering the driving laser [20]. We next discuss in detail the observed dip in the FWM spectrum by investigating the FWM spectra according to the detuning conditions of the two-photon resonance.

The detuning frequencies (δc, δp, and δd) of the lasers interacting with the atomic medium affect the FWM nonlinearity in the coherent atoms with two-photon coherence. We investigated the FWM signals as a function of parameters δp and δd of the pump and driving lasers according to the detuning frequency (–δc) of the coupling laser in the range from −273 MHz to 300 MHz, as shown in Fig. 3(b). The FWM magnitude according to δC is symmetrically changed at the center of the two-photon resonance for the 6S1/2(F = 4)–6P3/2(F′ = 5)–8S1/2(F′′ = 4) transition. The main cause of this change in the FWM magnitude according to δc is the cycling transition of 6S1/2(F = 4)–6P3/2(F′ = 5). We cannot observe an FWM signal corresponding to the 6P3/2(F′ = 3 and 4) states even though there is a two-photon transition of 6S1/2(F = 4)–6P3/2(F′ = 3 and 4)–8S1/2(F′′ = 4). This is why the two-photon coherence is considerably weaker owing to the decay from the 6P3/2(F′ = 3 and 4) states to the other ground state of 6S1/2(F = 3).

As shown in Fig. 3(a), the frequency of the dip in the FWM spectrum corresponds to that of the DROP peak for the 6S1/2(F = 4)–6P3/2(F′ = 5)–8S1/2(F′′ = 4) transition. The dip in the FWM spectrum is due to the suppression of FWM by the EIT and DROP effect [21]. However, the center of the FWM spectrum is not the same as the dip in the FWM spectrum because the FWM light is induced by the driving laser for the 6S1/2(F = 4)–6P3/2(F′ = 3, 4, 5) transition. Although the cycling transition dominantly contributes to the two-photon coherence, other hyperfine states, except those of the cycling transition, affect the FWM generation induced by the driving laser. Therefore, the asymmetry of the FWM spectra changes according to the detuning frequency. At –δc = 143 MHz, when the pump and driving lasers are nearly resonant on the 6S1/2(F = 4)–6P3/2(F′ = 4) transition, we note that the FWM spectrum strongly tends to a symmetrical shape.

Figure 4 shows the FWM (red curve) and Doppler-free DROP (blue curve) signals corresponding to the 6S1/2(F = 4)–6P3/2(F′ = 3, 4, 5)–8S1/2(F′′ = 4) transition as a function of the detuning frequency (δc) of the coupling laser. Parameters δp and δd were fixed at the 6S1/2(F = 4)–6P3/2(F′ = 5) hyperfine transition, while δC was scanned in the vicinity of the 6P3/2(F′ = 5)–8S1/2(F′′ = 4) transition. The scanning of δC corresponds to the scanning of the two-photon detuning (δtwo = δc + δp). Although the FWM spectrum of Fig. 4 was measured by scanning of δc, we can illustrate the FWM signal as a function of δtwo because the cascade-type two-photon resonance condition should be satisfied to generate a cascade-type FWM signal.

 figure: Fig. 4.

Fig. 4. FWM (red curve) and DROP (blue curve) spectra as functions of the detuning frequency (δC) of the coupling laser.

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The DROP, rather than the two-photon coherence, dominantly contributes to the transmittance signal in this transition, as shown in the blue curve of Fig. 4. The DROP signal is due to the two-photon coherence with population changes between the 6S1/2 and 8S1/2 states. Although the DROP effect is not due to pure two-photon coherence, there is residual two-photon coherence. Here, we note the possibility of generating FWM light in this transition owing to the residual two-photon coherence in the DROP process.

Next, we investigated the FWM spectra as a function of the powers of the coupling and driving lasers. Figure 5(a) shows the FWM spectra according to the coupling power in the range from 0.1 mW to 4.8 mW when the pump and driving powers are fixed at 1.0 mW and 1.0 mW, respectively. As the coupling power increases, the spectral shape of the FWM changes from narrow to broad, and the dip in the FWM spectrum increases. The dip in the FWM spectrum is due to the suppression of FWM generation by the EIT and DROP effect. The observed FWM spectral broadening can be understood as an increase in the ac Stark splitting due to the strong coupling laser. However, the magnitude of the FWM signal is nearly saturated from the coupling power of 2.0 mW onward because of the DROP effect. In our experiment, the pump and driving powers were not sufficiently weak, and the change in population was non-negligible. As mentioned above, the 6S1/2(F = 4)–6P3/2(F′ = 5)–8S1/2(F′′ = 4) transition is a non-two-photon cycling transition. Therefore, as the coupling power increases, the populations of the 6S1/2(F = 4) state decrease owing to the DROP effect, and the magnitude of the FWM signal does not significantly change.

 figure: Fig. 5.

Fig. 5. FWM spectra according to (a) coupling power and (b) driving power from Doppler-broadened cascade-type atomic ensemble.

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Figure 5(b) shows the generated FWM signals according to the driving power when the pump and coupling laser powers are fixed at 1.0 mW and 4.0 mW, respectively. As the driving power increases from 0.1 mW to 4.0 mW, the FWM spectral shape exhibits broadening. Because the driving laser is resonant on the 6S1/2(F = 4)–6P3/2(F′ = 3, 4, 5) transition, optical pumping from the 6S1/2(F = 4) state to the 6S1/2(F = 3) occurs in response to increments in the driving power. Therefore, when the driving laser is strong, FWM signal generation may be suppressed because of the optical pumping.

The asymmetry of the FWM spectra changes according to the driving power. We note that the FWM spectrum is strongly symmetric at a driving power of 0.5 mW. This symmetric FWM spectrum at weak driving powers indicates that the FWM signal is mainly generated during the 6S1/2(F = 4)–6P3/2(F′ = 5)–8S1/2(F′′ = 4) transition without the effects of other hyperfine states of 6P3/2(F′ = 3 and 4). Although the hyperfine states of 6P3/2(F′ = 3 and 4) do not contribute to two-photon coherence, they affect the FWM process induced by the driving laser.

To elucidate the spectral feature of the FWM signals, we can theoretically investigate these phenomena in the simple four-level diamond configuration of Fig. R3 which includes the effects of hyperfine structure and Doppler broadening. For the sake of simplicity, we treat the realistic atom as a combination of four-level systems. This can be understood as a superposition of FWM signals due to other hyperfine states. Each set of four-level system can be characterized by different dipole moments and different hyperfine detunings.

Figure 6 shows a four-level atomic model with two degenerate intermediate states ($|2 \rangle$ and $|3 \rangle$). The density matrix equation of motion can be expressed as

$$\frac{{\partial {\rho _{ij}}}}{{\partial t}} ={-} \frac{1}{\hbar }\sum\limits_k {[{H_{ik}}{\rho _{kj}} - {\rho _{ik}}{H_{kj}}]} - {\Gamma _{ij}}{\rho _{ij}},$$
where the subscript indices i and j indicate the $|i \rangle$ and $|j \rangle$ states, respectively. ${\rho _{ij}}$ is a density-matrix element and ${H_{ij}}$ is the effective interaction Hamiltonian, which is composed of the atomic and interaction Hamiltonians. Further, ${\Gamma _{ij}}$ is the relaxation term describing all relaxation processes, including spontaneous transfer of the excited-state coherence to ground-state coherence. The electric-field amplitude of the generated FWM signal is proportional to the coherence ${\rho _{34}}$. Here, the detuning frequencies of Ωp, Ωd, and Ωc are ${\delta _p}$, ${\delta _d}$, and ${\delta _C}$, respectively. The decay rates of the intermediate and excited states were 5.2 MHz (Γ12 = Γ13 = 2.6 MHz) and 2.2 MHz (Γ24 = Γ34 = 1.1 MHz), respectively.

 figure: Fig. 6.

Fig. 6. Four-level atomic model for FWM generation, consisting of ground state ($|1 \rangle$), degenerate intermediate states ($|2 \rangle$ and $|3 \rangle$), and excited state ($|4 \rangle$).

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Considering the optical pumping effect on the other ground state via the branching ratio of each transition, the branching ratios (b1 and b2) of the intermediate and excited states depend on the transition routes, as governed by the selection rule. Therefore, we can illuminate the variance of the FWM signal according to the transition between the hyperfine states. We numerically investigated the spectral features of the FWM using the density matrix equation of Eq. (3) and incorporating the Maxwell–Boltzmann velocity distribution, in order to consider the case of a Doppler-broadened atomic medium.

Figure 7 shows the calculated FWM spectrum in the four-level atomic model. For the 6S1/2(F = 4)–6P3/2(F′ = 5, 4, 3)–8S1/2(F′′ = 4) transition, the branching ratios were set to b1 = 1, 0.5, 0.5 and b2 = 0.23, 0.10, 0.04, considering the decay channel of the 6P1/2, 7P1/2, and 7P3/2 state, respectively. The Rabi frequencies of Ωp, Ωd, and ΩC were set to 5 MHz, 5 MHz, and 15 MHz, respectively. The calculated FWM spectrum (black curve) is added the three FWM spectra (blue, red, and green curves) for the 6P3/2(F′ = 5, 4, 3) states. The spectral shape of the experimental FWM spectrum of Fig. 4 has asymmetry of the FWM spectrum. Similarly, the calculated FWM of Fig. 7 has an asymmetric structure spectral shape. Although the simple atomic model used for FWM analysis in this study differs from a real atomic system with hyperfine structures and Zeeman sublevels, the calculated ladder-type FWM spectrum is in an agreement with the observed FWM signal of this transition shown in Fig. 4.

 figure: Fig. 7.

Fig. 7. Numerically calculated FWM spectrum (black) in four-level atomic model. Composition of three FWM spectra (blue, red, and green curves) for the 6S1/2(F = 4)–6P3/2(F′ = 5, 4, 3)–8S1/2(F′′ = 4) transition according to the three 6P3/2(F′ = 5, 4, and 3) hyperfine states.

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4. Conclusion

In conclusion, we clearly observed the cascade-type FWM spectrum corresponding to the 6S1/2–6P3/2–8S1/2 transition of 133Cs atoms under the experimental condition of the small coupling and pump beams powers. In case of the 6S1/2–6P3/2–8S1/2 transition, the two-photon coherence is considerably weak owing to the decay from the 6P3/2(F′ = 3 and 4) states to the other ground state of 6S1/2(F = 3). The DROP effect corresponds to the optical pumping process via two-step excitation, including the decay channels from an excited state to the other ground state of 6S1/2(F = 3). Nevertheless, in this non-two-photon cycling transition, we could clearly observe the FWM signal owing to the residual two-photon coherence. The dip in the FWM spectrum according to the detuning frequency of the coupling laser corresponds to the DROP peak. The main cause of the dip in the FWM spectrum is the suppression of FWM generation by the EIT and DROP effect. Furthermore, we investigated the FWM spectra according to the coupling and driving powers. As the coupling power increased, the populations of the 6S1/2(F = 4) state decreased because of the DROP effect, and the magnitude of the FWM signal did not significantly change because most atoms excited to the 6P3/2(F′ = 3, 4) intermediate state spontaneously transferred to another 6S1/2(F = 3) ground state. On the other hand, the driving laser induced FWM light from the atomic system with two-photon coherence. We found that the asymmetry of the FWM spectra changed according to the driving power. This result indicates that the hyperfine states of 6P3/2(F′ = 3 and 4) affect the FWM process induced by the driving laser, even though they do not contribute to two-photon coherence. We believe that our findings can aid in providing a better understanding of the FWM process in a variety of atomic configurations of different atoms, which is necessary for quantum optics applications based on atom–photon interactions.

Funding

National Research Foundation of Korea (NRF) (2018R1A2A1A19019181, 2020M3E4A1080030); Ministry of Science and ICT, South Korea under the ITRC support program (IITP-2020-0-01606).

Disclosures

The authors declare no conflicts of interest.

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21. J. Park and H. S. Moon, “Stimulated emission from ladder-type two-photon coherent atomic ensemble,” Opt. Express 26(11), 14461–14471 (2018). [CrossRef]  

22. D. S. Glassner and R. J. Knize, “Reduced angular dependence for degenerate four-wave mixing in potassium vapor by including nitrogen buffer gas,” Appl. Phys. Lett. 66(13), 1593–1595 (1995). [CrossRef]  

23. M. Y. Lanzerotti, R. W. Schirmer, and A. L. Gaeta, “High-reflectivity, wide-bandwidth optical phase conjugation via four-wave mixing in potassium vapor,” Appl. Phys. Lett. 69(9), 1199–1201 (1996). [CrossRef]  

24. K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008). [CrossRef]  

25. C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007). [CrossRef]  

26. 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]  

27. V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003). [CrossRef]  

28. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985). [CrossRef]  

29. R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from nondegenerate four-wave mixing in an atomic vapor: The D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17(19), 16722 (2009). [CrossRef]  

30. 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]  

31. B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13(1), 015205 (2016). [CrossRef]  

32. R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017). [CrossRef]  

33. R. Ma, W. Liu, Z. Qin, X. Su, X. Jia, J. Zhang, and J. Gao, “Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor,” Opt. Lett. 43(6), 1243–1246 (2018). [CrossRef]  

34. M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013). [CrossRef]  

35. B. Zlatković, M. M. Ćurčić, I. S. Radojičić, D. Arsenović, A. J. Krmpot, and B. M. Jelenković, “Slowing probe and conjugate pulses in potassium vapor using four wave mixing,” Opt. Express 26(26), 34266–34273 (2018). [CrossRef]  

36. 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]  

37. R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009). [CrossRef]  

38. Y.-H. Chen, T.-W. Liu, C.-M. Wu, C.-C. Lee, C.-K. Lee, and W.-Y. Cheng, “High-resolution 133Cs 6S–6D, 6S–8S two-photon spectroscopy using an intracavity scheme,” Opt. Lett. 36(1), 76–78 (2011). [CrossRef]  

39. Z.-S. He, J.-Y. Su, H.-R. Chen, W.-F. Chen, M.-H. Sie, J.-Y. Ye, and C.-C. Tsai, “Low-light-level ladder-type electromagnetically induced transparency and two-photon absorption,” J. Opt. Soc. Am. B 31(10), 2485–2490 (2014). [CrossRef]  

40. G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977). [CrossRef]  

41. M. Tanasittikosol, C. Carr, C. S. Adams, and K. J. Weatherill, “Subnatural linewidths in two-photon excited-state spectroscopy,” Phys. Rev. A 85(3), 033830 (2012). [CrossRef]  

42. H.-R. Noh and H. S. Moon, “Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system,” Opt. Express 19(12), 11128–11137 (2011). [CrossRef]  

43. Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble,” Phys. Rev. A 96(6), 063832 (2017). [CrossRef]  

44. H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance optical pumping spectrum and its application for frequency stabilization of a laser diode,” Appl. Phys. Lett. 85(18), 3965–3967 (2004). [CrossRef]  

References

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  1. V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
    [Crossref]
  2. P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
    [Crossref]
  3. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
    [Crossref]
  4. S. Du, J. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
    [Crossref]
  5. B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
    [Crossref]
  6. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
    [Crossref]
  7. D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment,” Opt. Express 20(10), 11433–11444 (2012).
    [Crossref]
  8. D.-S. Ding, W. Zhang, S. Shi, Z.-Y. Zhou, Y. Li, B.-S. Shi, and G.-C. Guo, “Hybrid-cascaded generation of tripartite telecom photons using an atomic ensemble and a nonlinear waveguide,” Optica 2(7), 642–645 (2015).
    [Crossref]
  9. 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]
  10. C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
    [Crossref]
  11. Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Highly bright photon-pair generation in Doppler-broadened ladder-type atomic system,” Opt. Express 24(24), 28083–28091 (2016).
    [Crossref]
  12. J. Park, H. Kim, and H. S. Moon, “Polarization-entangled photons from a warm atomic ensemble,” Phys. Rev. Lett. 122(14), 143601 (2019).
    [Crossref]
  13. T. Jeong and H. S. Moon, “Temporal- and spectral-property measurements of narrowband photon pairs from warm double-(-type atomic ensemble,” Opt. Express 28(3), 3985–3994 (2020).
    [Crossref]
  14. Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
    [Crossref]
  15. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
    [Crossref]
  16. Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
    [Crossref]
  17. J. Park, H. Kim, and H. S. Moon, “Entanglement Sweeping with Polarization-Entangled Photon-Pairs from Warm Atomic Ensemble,” Opt. Lett. 45(8), 2403–2406 (2020).
    [Crossref]
  18. P. S. Hsu, A. K. Patnaik, and G. R. Welch, “Controlled parametric generation in a double-ladder system via all-resonant four-wave mixing,” Opt. Lett. 33(4), 381–383 (2008).
    [Crossref]
  19. Y.-S. Lee and H. S. Moon, “Atomic coherence effects in four-wave mixing process of a ladder-type atomic system,” Opt. Express 24(10), 10723–10732 (2016).
    [Crossref]
  20. Y.-S. Lee and H. S. Moon, “Doppler-free three-photon coherence in Doppler-broadened ladder-type atomic system,” Opt. Express 25(5), 5316–5326 (2017).
    [Crossref]
  21. J. Park and H. S. Moon, “Stimulated emission from ladder-type two-photon coherent atomic ensemble,” Opt. Express 26(11), 14461–14471 (2018).
    [Crossref]
  22. D. S. Glassner and R. J. Knize, “Reduced angular dependence for degenerate four-wave mixing in potassium vapor by including nitrogen buffer gas,” Appl. Phys. Lett. 66(13), 1593–1595 (1995).
    [Crossref]
  23. M. Y. Lanzerotti, R. W. Schirmer, and A. L. Gaeta, “High-reflectivity, wide-bandwidth optical phase conjugation via four-wave mixing in potassium vapor,” Appl. Phys. Lett. 69(9), 1199–1201 (1996).
    [Crossref]
  24. K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008).
    [Crossref]
  25. C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
    [Crossref]
  26. 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]
  27. V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003).
    [Crossref]
  28. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
    [Crossref]
  29. R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from nondegenerate four-wave mixing in an atomic vapor: The D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17(19), 16722 (2009).
    [Crossref]
  30. 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]
  31. B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13(1), 015205 (2016).
    [Crossref]
  32. R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017).
    [Crossref]
  33. R. Ma, W. Liu, Z. Qin, X. Su, X. Jia, J. Zhang, and J. Gao, “Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor,” Opt. Lett. 43(6), 1243–1246 (2018).
    [Crossref]
  34. M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013).
    [Crossref]
  35. B. Zlatković, M. M. Ćurčić, I. S. Radojičić, D. Arsenović, A. J. Krmpot, and B. M. Jelenković, “Slowing probe and conjugate pulses in potassium vapor using four wave mixing,” Opt. Express 26(26), 34266–34273 (2018).
    [Crossref]
  36. 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]
  37. R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
    [Crossref]
  38. Y.-H. Chen, T.-W. Liu, C.-M. Wu, C.-C. Lee, C.-K. Lee, and W.-Y. Cheng, “High-resolution 133Cs 6S–6D, 6S–8S two-photon spectroscopy using an intracavity scheme,” Opt. Lett. 36(1), 76–78 (2011).
    [Crossref]
  39. Z.-S. He, J.-Y. Su, H.-R. Chen, W.-F. Chen, M.-H. Sie, J.-Y. Ye, and C.-C. Tsai, “Low-light-level ladder-type electromagnetically induced transparency and two-photon absorption,” J. Opt. Soc. Am. B 31(10), 2485–2490 (2014).
    [Crossref]
  40. G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977).
    [Crossref]
  41. M. Tanasittikosol, C. Carr, C. S. Adams, and K. J. Weatherill, “Subnatural linewidths in two-photon excited-state spectroscopy,” Phys. Rev. A 85(3), 033830 (2012).
    [Crossref]
  42. H.-R. Noh and H. S. Moon, “Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system,” Opt. Express 19(12), 11128–11137 (2011).
    [Crossref]
  43. Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble,” Phys. Rev. A 96(6), 063832 (2017).
    [Crossref]
  44. H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance optical pumping spectrum and its application for frequency stabilization of a laser diode,” Appl. Phys. Lett. 85(18), 3965–3967 (2004).
    [Crossref]

2020 (2)

2019 (1)

J. Park, H. Kim, and H. S. Moon, “Polarization-entangled photons from a warm atomic ensemble,” Phys. Rev. Lett. 122(14), 143601 (2019).
[Crossref]

2018 (3)

2017 (3)

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble,” Phys. Rev. A 96(6), 063832 (2017).
[Crossref]

R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017).
[Crossref]

Y.-S. Lee and H. S. Moon, “Doppler-free three-photon coherence in Doppler-broadened ladder-type atomic system,” Opt. Express 25(5), 5316–5326 (2017).
[Crossref]

2016 (4)

Y.-S. Lee and H. S. Moon, “Atomic coherence effects in four-wave mixing process of a ladder-type atomic system,” Opt. Express 24(10), 10723–10732 (2016).
[Crossref]

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13(1), 015205 (2016).
[Crossref]

C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Highly bright photon-pair generation in Doppler-broadened ladder-type atomic system,” Opt. Express 24(24), 28083–28091 (2016).
[Crossref]

2015 (1)

2014 (2)

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]

Z.-S. He, J.-Y. Su, H.-R. Chen, W.-F. Chen, M.-H. Sie, J.-Y. Ye, and C.-C. Tsai, “Low-light-level ladder-type electromagnetically induced transparency and two-photon absorption,” J. Opt. Soc. Am. B 31(10), 2485–2490 (2014).
[Crossref]

2013 (2)

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013).
[Crossref]

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref]

2012 (3)

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]

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment,” Opt. Express 20(10), 11433–11444 (2012).
[Crossref]

M. Tanasittikosol, C. Carr, C. S. Adams, and K. J. Weatherill, “Subnatural linewidths in two-photon excited-state spectroscopy,” Phys. Rev. A 85(3), 033830 (2012).
[Crossref]

2011 (2)

2010 (1)

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[Crossref]

2009 (2)

2008 (6)

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]

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
[Crossref]

K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008).
[Crossref]

S. Du, J. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
[Crossref]

P. S. Hsu, A. K. Patnaik, and G. R. Welch, “Controlled parametric generation in a double-ladder system via all-resonant four-wave mixing,” Opt. Lett. 33(4), 381–383 (2008).
[Crossref]

2007 (2)

Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
[Crossref]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[Crossref]

2006 (2)

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
[Crossref]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[Crossref]

2005 (1)

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref]

2004 (1)

H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance optical pumping spectrum and its application for frequency stabilization of a laser diode,” Appl. Phys. Lett. 85(18), 3965–3967 (2004).
[Crossref]

2003 (1)

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003).
[Crossref]

2001 (1)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref]

1996 (1)

M. Y. Lanzerotti, R. W. Schirmer, and A. L. Gaeta, “High-reflectivity, wide-bandwidth optical phase conjugation via four-wave mixing in potassium vapor,” Appl. Phys. Lett. 69(9), 1199–1201 (1996).
[Crossref]

1995 (1)

D. S. Glassner and R. J. Knize, “Reduced angular dependence for degenerate four-wave mixing in potassium vapor by including nitrogen buffer gas,” Appl. Phys. Lett. 66(13), 1593–1595 (1995).
[Crossref]

1985 (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref]

1977 (1)

G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977).
[Crossref]

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]

Adams, C. S.

M. Tanasittikosol, C. Carr, C. S. Adams, and K. J. Weatherill, “Subnatural linewidths in two-photon excited-state spectroscopy,” Phys. Rev. A 85(3), 033830 (2012).
[Crossref]

Alessandretti, G.

G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977).
[Crossref]

Arimondo, E.

Arsenovic, D.

Balic, V.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref]

Becerra, F. E.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[Crossref]

Belthangady, C.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
[Crossref]

Boyer, V.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from nondegenerate four-wave mixing in an atomic vapor: The D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17(19), 16722 (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).
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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, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
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Braje, D. A.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
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Bramati, A.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003).
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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).
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Camacho, R. M.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
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T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[Crossref]

Chapman, M. S.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[Crossref]

Chen, H.-R.

Chen, P.

C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

Chen, S.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
[Crossref]

Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
[Crossref]

Chen, W.-F.

Chen, Y.-A.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
[Crossref]

Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
[Crossref]

Chen, Y.-H.

Cheng, W.-Y.

Chiarini, F.

G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977).
[Crossref]

Chng, B.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref]

Chow, T. K. A.

C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

Cirac, J. I.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref]

Curcic, M. M.

Dantan, A.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003).
[Crossref]

Ding, D.-S.

Du, S.

C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

S. Du, J. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
[Crossref]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
[Crossref]

Duan, L.-M.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref]

Embrey, C. S.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013).
[Crossref]

Gaeta, A. L.

M. Y. Lanzerotti, R. W. Schirmer, and A. L. Gaeta, “High-reflectivity, wide-bandwidth optical phase conjugation via four-wave mixing in potassium vapor,” Appl. Phys. Lett. 69(9), 1199–1201 (1996).
[Crossref]

Gao, J.

R. Ma, W. Liu, Z. Qin, X. Su, X. Jia, J. Zhang, and J. Gao, “Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor,” Opt. Lett. 43(6), 1243–1246 (2018).
[Crossref]

R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017).
[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]

Giacobino, E.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003).
[Crossref]

Glassner, D. S.

D. S. Glassner and R. J. Knize, “Reduced angular dependence for degenerate four-wave mixing in potassium vapor by including nitrogen buffer gas,” Appl. Phys. Lett. 66(13), 1593–1595 (1995).
[Crossref]

Gorini, G.

G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977).
[Crossref]

Gulati, G. K.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref]

Guo, G.-C.

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]

Harada, K.

K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008).
[Crossref]

Harris, S. E.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
[Crossref]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref]

Hayashi, N.

K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008).
[Crossref]

He, Z.-S.

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref]

Howell, J. C.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Hsu, P. S.

Jelenkovic, B. M.

B. Zlatković, M. M. Ćurčić, I. S. Radojičić, D. Arsenović, A. J. Krmpot, and B. M. Jelenković, “Slowing probe and conjugate pulses in potassium vapor using four wave mixing,” Opt. Express 26(26), 34266–34273 (2018).
[Crossref]

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13(1), 015205 (2016).
[Crossref]

Jenkins, S. D.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[Crossref]

Jeong, T.

Jia, X.

R. Ma, W. Liu, Z. Qin, X. Su, X. Jia, J. Zhang, and J. Gao, “Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor,” Opt. Lett. 43(6), 1243–1246 (2018).
[Crossref]

R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017).
[Crossref]

Jones, K. M.

Josse, V.

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003).
[Crossref]

Kennedy, T. A. B.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[Crossref]

Kim, H.

J. Park, H. Kim, and H. S. Moon, “Entanglement Sweeping with Polarization-Entangled Photon-Pairs from Warm Atomic Ensemble,” Opt. Lett. 45(8), 2403–2406 (2020).
[Crossref]

J. Park, H. Kim, and H. S. Moon, “Polarization-entangled photons from a warm atomic ensemble,” Phys. Rev. Lett. 122(14), 143601 (2019).
[Crossref]

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble,” Phys. Rev. A 96(6), 063832 (2017).
[Crossref]

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Highly bright photon-pair generation in Doppler-broadened ladder-type atomic system,” Opt. Express 24(24), 28083–28091 (2016).
[Crossref]

Kim, J. B.

H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance optical pumping spectrum and its application for frequency stabilization of a laser diode,” Appl. Phys. Lett. 85(18), 3965–3967 (2004).
[Crossref]

Knize, R. J.

D. S. Glassner and R. J. Knize, “Reduced angular dependence for degenerate four-wave mixing in potassium vapor by including nitrogen buffer gas,” Appl. Phys. Lett. 66(13), 1593–1595 (1995).
[Crossref]

Koch, M.

Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
[Crossref]

Kolchin, P.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
[Crossref]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref]

Krmpot, A. J.

B. Zlatković, M. M. Ćurčić, I. S. Radojičić, D. Arsenović, A. J. Krmpot, and B. M. Jelenković, “Slowing probe and conjugate pulses in potassium vapor using four wave mixing,” Opt. Express 26(26), 34266–34273 (2018).
[Crossref]

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13(1), 015205 (2016).
[Crossref]

Kurtsiefer, C.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref]

Kuzmich, A.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[Crossref]

Lanzerotti, M. Y.

M. Y. Lanzerotti, R. W. Schirmer, and A. L. Gaeta, “High-reflectivity, wide-bandwidth optical phase conjugation via four-wave mixing in potassium vapor,” Appl. Phys. Lett. 69(9), 1199–1201 (1996).
[Crossref]

Lee, C.-C.

Lee, C.-K.

Lee, L.

H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance optical pumping spectrum and its application for frequency stabilization of a laser diode,” Appl. Phys. Lett. 85(18), 3965–3967 (2004).
[Crossref]

Lee, S. M.

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble,” Phys. Rev. A 96(6), 063832 (2017).
[Crossref]

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Highly bright photon-pair generation in Doppler-broadened ladder-type atomic system,” Opt. Express 24(24), 28083–28091 (2016).
[Crossref]

Lee, W. K.

H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance optical pumping spectrum and its application for frequency stabilization of a laser diode,” Appl. Phys. Lett. 85(18), 3965–3967 (2004).
[Crossref]

Lee, Y.-S.

Lett, P. D.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from nondegenerate four-wave mixing in an atomic vapor: The D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17(19), 16722 (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]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[Crossref]

Li, Y.

Liu, T.-W.

Liu, W.

R. Ma, W. Liu, Z. Qin, X. Su, X. Jia, J. Zhang, and J. Gao, “Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor,” Opt. Lett. 43(6), 1243–1246 (2018).
[Crossref]

R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017).
[Crossref]

Loy, M. M. T.

C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

Lukin, M. D.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[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, R.

R. Ma, W. Liu, Z. Qin, X. Su, X. Jia, J. Zhang, and J. Gao, “Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor,” Opt. Lett. 43(6), 1243–1246 (2018).
[Crossref]

R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017).
[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]

Marino, A. M.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013).
[Crossref]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from nondegenerate four-wave mixing in an atomic vapor: The D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17(19), 16722 (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]

Maslennikov, G.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref]

Matsukevich, D.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref]

Matsukevich, D. N.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[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. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[Crossref]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
[Crossref]

Mitsunaga, M.

K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008).
[Crossref]

Moon, H. S.

J. Park, H. Kim, and H. S. Moon, “Entanglement Sweeping with Polarization-Entangled Photon-Pairs from Warm Atomic Ensemble,” Opt. Lett. 45(8), 2403–2406 (2020).
[Crossref]

T. Jeong and H. S. Moon, “Temporal- and spectral-property measurements of narrowband photon pairs from warm double-(-type atomic ensemble,” Opt. Express 28(3), 3985–3994 (2020).
[Crossref]

J. Park, H. Kim, and H. S. Moon, “Polarization-entangled photons from a warm atomic ensemble,” Phys. Rev. Lett. 122(14), 143601 (2019).
[Crossref]

J. Park and H. S. Moon, “Stimulated emission from ladder-type two-photon coherent atomic ensemble,” Opt. Express 26(11), 14461–14471 (2018).
[Crossref]

Y.-S. Lee and H. S. Moon, “Doppler-free three-photon coherence in Doppler-broadened ladder-type atomic system,” Opt. Express 25(5), 5316–5326 (2017).
[Crossref]

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble,” Phys. Rev. A 96(6), 063832 (2017).
[Crossref]

Y.-S. Lee and H. S. Moon, “Atomic coherence effects in four-wave mixing process of a ladder-type atomic system,” Opt. Express 24(10), 10723–10732 (2016).
[Crossref]

Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Highly bright photon-pair generation in Doppler-broadened ladder-type atomic system,” Opt. Express 24(24), 28083–28091 (2016).
[Crossref]

H.-R. Noh and H. S. Moon, “Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system,” Opt. Express 19(12), 11128–11137 (2011).
[Crossref]

H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance optical pumping spectrum and its application for frequency stabilization of a laser diode,” Appl. Phys. Lett. 85(18), 3965–3967 (2004).
[Crossref]

Mori, K.

K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008).
[Crossref]

Noh, H.-R.

Okuma, J.

K. Harada, K. Mori, J. Okuma, N. Hayashi, and M. Mitsunaga, “Parametric amplification in an electromagnetically-induced-transparency medium,” Phys. Rev. A 78(1), 013809 (2008).
[Crossref]

Orozco, L. A.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[Crossref]

Pan, J.-W.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
[Crossref]

Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
[Crossref]

Park, J.

Patnaik, A. K.

Petrov, P. G.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013).
[Crossref]

Petrucci, F.

G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977).
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Wen, J.

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R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
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C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
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P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
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Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
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R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
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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).
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Zhang, W.

Zhao, B.

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
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Zhao, Y.

Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
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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).
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Zhou, Z.-Y.

Zhu, G.-J.

Z.-S. Yuan, Y.-A. Chen, S. Chen, B. Zhao, M. Koch, T. Strassel, Y. Zhao, G.-J. Zhu, J. Schmiedmayer, and J.-W. Pan, “Synchronized Independent Narrow-Band Single Photons and Efficient Generation of Photonic Entanglement,” Phys. Rev. Lett. 98(18), 180503 (2007).
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C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
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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).
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B. Zlatković, M. M. Ćurčić, I. S. Radojičić, D. Arsenović, A. J. Krmpot, and B. M. Jelenković, “Slowing probe and conjugate pulses in potassium vapor using four wave mixing,” Opt. Express 26(26), 34266–34273 (2018).
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B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13(1), 015205 (2016).
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Appl. Phys. Lett. (3)

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J. Opt. Soc. Am. B (2)

Laser Phys. Lett. (1)

B. Zlatković, A. J. Krmpot, N. Šibalić, M. Radonjić, and B. M. Jelenković, “Efficient parametric non-degenerate four-wave mixing in hot potassium vapor,” Laser Phys. Lett. 13(1), 015205 (2016).
[Crossref]

Nat. Commun. (1)

C. Shu, P. Chen, T. K. A. Chow, L. Zhu, Y. Xiao, M. M. T. Loy, and S. Du, “Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell,” Nat. Commun. 7(1), 12783 (2016).
[Crossref]

Nat. Photonics (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Nature (2)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref]

Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, “Experimental demonstration of a BDCZ quantum repeater node,” Nature 454(7208), 1098–1101 (2008).
[Crossref]

Opt. Commun. (1)

G. Alessandretti, F. Chiarini, G. Gorini, and F. Petrucci, “Measurement of the Cs 8S-level lifetime,” Opt. Commun. 20(2), 289–291 (1977).
[Crossref]

Opt. Express (9)

H.-R. Noh and H. S. Moon, “Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system,” Opt. Express 19(12), 11128–11137 (2011).
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T. Jeong and H. S. Moon, “Temporal- and spectral-property measurements of narrowband photon pairs from warm double-(-type atomic ensemble,” Opt. Express 28(3), 3985–3994 (2020).
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Y.-S. Lee and H. S. Moon, “Atomic coherence effects in four-wave mixing process of a ladder-type atomic system,” Opt. Express 24(10), 10723–10732 (2016).
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Y.-S. Lee and H. S. Moon, “Doppler-free three-photon coherence in Doppler-broadened ladder-type atomic system,” Opt. Express 25(5), 5316–5326 (2017).
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J. Park and H. S. Moon, “Stimulated emission from ladder-type two-photon coherent atomic ensemble,” Opt. Express 26(11), 14461–14471 (2018).
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Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Highly bright photon-pair generation in Doppler-broadened ladder-type atomic system,” Opt. Express 24(24), 28083–28091 (2016).
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D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment,” Opt. Express 20(10), 11433–11444 (2012).
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Opt. Lett. (5)

Optica (1)

Phys. Rev. A (8)

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88(3), 033845 (2013).
[Crossref]

R. Ma, W. Liu, Z. Qin, X. Jia, and J. Gao, “Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor,” Phys. Rev. A 96(4), 043843 (2017).
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Y.-S. Lee, S. M. Lee, H. Kim, and H. S. Moon, “Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble,” Phys. Rev. A 96(6), 063832 (2017).
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M. Tanasittikosol, C. Carr, C. S. Adams, and K. J. Weatherill, “Subnatural linewidths in two-photon excited-state spectroscopy,” Phys. Rev. A 85(3), 033830 (2012).
[Crossref]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[Crossref]

Phys. Rev. Lett. (9)

V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett. 91(10), 103601 (2003).
[Crossref]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55(22), 2409–2412 (1985).
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J. Park, H. Kim, and H. S. Moon, “Polarization-entangled photons from a warm atomic ensemble,” Phys. Rev. Lett. 122(14), 143601 (2019).
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B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94(18), 183601 (2005).
[Crossref]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: use of a single driving laser,” Phys. Rev. Lett. 97(11), 113602 (2006).
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Science (1)

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Figures (7)

Fig. 1.
Fig. 1. Experimental configuration for FWM generation from the cascade-type atomic system of 133Cs atoms. (a) Energy-level diagram of the 6S1/2–6P3/2–8S1/2 transition of 133Cs atoms and experimental configuration for FWM in the cascade-type atomic system interacting with the pump, coupling, and driving lasers. (b) Experimental configuration for FWM generation under the phase-matching condition corresponding to the energy and wave-vector conservations of the contributing lasers. (c) Calculated phase-matching function as a function of the tilt angle.
Fig. 2.
Fig. 2. Experimental schematic for FWM generation from 133Cs atomic vapor cell (PBS: polarizing beam splitter; APD: avalanche photodiode; BS: beam splitter; M: mirror).
Fig. 3.
Fig. 3. (a) FWM (red curve) and DROP (blue curve) spectra as functions of the detuning frequencies δp and δd of the pump and driving lasers, respectively. (b) FWM spectra according to −δc (coupling laser detuning), where the gray curve denotes the saturated absorption spectrum (SAS) of the pump (driving) laser.
Fig. 4.
Fig. 4. FWM (red curve) and DROP (blue curve) spectra as functions of the detuning frequency (δC) of the coupling laser.
Fig. 5.
Fig. 5. FWM spectra according to (a) coupling power and (b) driving power from Doppler-broadened cascade-type atomic ensemble.
Fig. 6.
Fig. 6. Four-level atomic model for FWM generation, consisting of ground state ($|1 \rangle$), degenerate intermediate states ($|2 \rangle$ and $|3 \rangle$), and excited state ($|4 \rangle$).
Fig. 7.
Fig. 7. Numerically calculated FWM spectrum (black) in four-level atomic model. Composition of three FWM spectra (blue, red, and green curves) for the 6S1/2(F = 4)–6P3/2(F′ = 5, 4, 3)–8S1/2(F′′ = 4) transition according to the three 6P3/2(F′ = 5, 4, and 3) hyperfine states.

Equations (3)

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Δ ω t w o = ( k p k c ) Δ v ,
φ ( θ ) = sinc ( Δ k ( θ ) L 2 ) ,
ρ i j t = 1 k [ H i k ρ k j ρ i k H k j ] Γ i j ρ i j ,

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