## Quantum correlated light beams from non-degenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of ^{85}Rb and ^{87}Rb

Optics Express, Vol. 17, Issue 19, pp. 16722-16730 (2009)

http://dx.doi.org/10.1364/OE.17.016722

Acrobat PDF (256 KB)

### Abstract

We present experimental results showing that quantum correlated light can be produced using non-degenerate, off-resonant, four-wave mixing (4WM) on both the D1 (795 nm) and D2 (780 nm) lines of ^{85}Rb and ^{87}Rb, extending earlier work on the D1 line of ^{85}Rb. Using this 4WM process in a hot vapor cell to produce bright twin beams, we characterize the degree of intensity-difference noise reduction below the standard quantum limit for each of the four systems. Although each system approximates a double-lambda configuration, differences in details of the actual level structure lead to varying degrees of noise reduction. The observation of quantum correlations on light produced using all four of these systems, regardless of their substructure, suggests that it should be possible to use other systems with similar level structures in order to produce narrow frequency, non-classical beams at a particular wavelength.

© 2009 OSA

## 1. Introduction

^{85}Rb closely approximates an ideal double-lambda system [12

12. 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]

13. J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, “Experimental investigation of amplitude and phase quantum correlations in a type II optical parametric oscillator above threshold: from nondegenerate to degenerate operation,” Opt. Lett. **30**(10), 1177–1179 (2005). [CrossRef] [PubMed]

14. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. **100**(3), 033602 (2008). [CrossRef] [PubMed]

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

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

17. 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] [PubMed]

^{85}Rb and show that quantum noise reduction can also be obtained at the D2 line in

^{85}Rb as well as at the D1 and D2 lines in

^{87}Rb. Under the circumstances we have investigated, the D2 lines appear a less favorable choice than the D1 lines, showing evidence of competing effects beyond 4WM. Still, the levels of quantum noise reduction using the D2 lines are comparable to the levels achieved with other atom-based noise reduction schemes [2

2. A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. **36**(2), 93–98 (1996). [CrossRef]

18. E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. **33**(11), 1213–1215 (2008). [CrossRef] [PubMed]

^{87}Rb are complicated by residual

^{85}Rb in the cell, which produces extra absorption for one of the light beams. Even with this extra absorption, the present

^{87}Rb cell can be used to produce high levels of quantum correlations. These results strongly suggest that the same method for generating nonclassical light, namely off-resonant, non-degenerate 4WM in a double-lambda system, will be useful in other systems with similar level structures.

## 2. Experiment

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

19. C. M. Caves, “Quantum Limits on Noise in Linear-Amplifiers,” Phys. Rev. D Part. Fields **26**(8), 1817–1839 (1982). [CrossRef]

^{85}Rb, 6.835 GHz for

^{87}Rb). Adjustments of the phase delay in the microwave interferometer provide fine-tuning of the two-photon detuning,

^{85}Rb where

^{85}Rb D1 line, at least for an analysis frequency of 1 MHz where we were working. For all of the data in this paper we used the two frequency-locked lasers since this method could be used for both

^{85}Rb and

^{87}Rb.

^{85}Rb. To that end we have started with parameters previously established to lead to high squeezing levels for the D1 line of

^{85}Rb and then made small adjustments. Thus our results establish squeezing levels which can be obtained in practice, but do not necessarily represent the absolute best possible values which can be obtained by a full optimization of all parameters for each case. In addition to intrinsic effects due to the atomic level structure, the measured squeezing level is also affected by technical limitations in the apparatus such as losses on the vapor cell windows, the efficiency of the photodetectors, and the quality of polarization filtering to remove pump light. These effects are not very sensitive to the precise laser wavelengths and so are effectively constant for the four systems studied here.

^{85}Rb [12

12. 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]

^{85}Rb D1 line, the one-photon detuning, Δ, was set to be about 0.8 GHz blue of the indicated transition (see Fig. 1). The two-photon detuning, δ, was adjusted to give 4WM gain. The exact value depends on the pump laser power and detuning due to AC Stark shifts. The highest squeezing does not generally correspond to the laser tunings that give the highest 4WM gain. Small adjustments of Δ and δ were made to find the highest squeezing. Typically the value of δ for the highest squeezing is a few MHz larger than the value for the highest gain. Once the point of highest squeezing was determined, the value of δ was left fixed and Δ was varied. Thus our data represents one cut through a multidimensional parameter space. In switching from

^{85}Rb to

^{87}Rb we also changed the pump power and cell temperature, as discussed below.

12. 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]

*N*) of ideal amplifier gain (each with a gain

*g*slightly greater than 1) interspersed with

*N*beamsplitters (each with a transmission

*t*slightly less than 1). Since loss is modeled by beamsplitters which add only vacuum noise, this model represents a minimal extension of the ideal lossless phase insensitive amplifier model. Given values of

*g*and

*t*the model calculates the power ratios (probe out)/(probe in) and (conjugate out)/(probe in) and the intensity-difference squeezing. To determine

*g*and

*t*we adjust their values until the model reproduces the two measured power ratios. Since there are two adjustable parameters, we can always find values that simultaneously reproduce both measured ratios. Given that the choice of

*N*is arbitrary (as long as it is large), we report below the total inferred gain,

*G=g*and the total inferred probe transmission,

^{N},*T=t*of the entire system, rather than

^{N},*g*and

*t*themselves. Determining

*g*and

*t*(done from the power measurements alone) also determines the expected level of intensity-difference squeezing. After adjusting the predicted level of intensity-difference squeezing for detection efficiency we can compare it to the experimentally measured value. More detail can be found in [12

**78**(4), 043816 (2008). [CrossRef]

## 3. Observed quantum noise reduction

### 3.1 ^{85}Rb D1 line

^{85}Rb. A more extensive discussion of the intensity-difference noise reduction using this line can be found in [12

**78**(4), 043816 (2008). [CrossRef]

^{85}Rb, the excited state hyperfine structure is not resolved and thus Δ is measured from the peak of the Doppler broadened line originating on the F

_{1}= 2 ground state level (see Fig. 1). The optimal pump power is a function of other parameters. Depending on the detuning Δ self-focusing/defocusing effects in the non-linear medium can become important. We found empirically that 400 mW, with a waist of 550 μm (1/e

^{2}intensity radius) in the cell, worked well.

^{85}Rb D1 line agree well with the levels predicted from the gain and transmission inferred from the probe and conjugate powers.

### 3.2 ^{85}Rb D2 line

^{85}Rb also shows quantum noise reduction below the SQL. Although the level of noise reduction is not as impressive as that observed using the D1 line, the levels seen here are comparable to the best levels of quantum noise reduction observed in other atomic 4WM experiments. The best squeezing is observed for a pump detuning ≈1.5 times larger than that for the D1 line.

^{85}Rb D1 line, the observed probe and conjugate powers cannot be reconciled with the observed squeezing levels simply by invoking loss on the probe. The numerical values of the gain and transmission calculated from the model thus cannot be considered reliable; the value of the model is to show that there is a qualitative difference between the D2 and D1 lines.

### 3.3 ^{87}Rb D1 line

^{87}Rb, the hyperfine splitting in the ground state is larger (

^{85}Rb (

^{85}Rb for the same pump power [22

22. M. D. Lukin, A. B. Matsko, Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. **82**(9), 1847–1850 (1999). [CrossRef]

^{85}Rb) to 700 mW, the maximum power available, and also raised the cell temperature. Under these conditions we measure a gain [simple (probe power out)/(probe power in), not the gain inferred from the model] of

^{85}Rb, and

^{87}Rb when the laser tunings are optimized for the best noise reduction in each case. In

^{87}Rb the excited state hyperfine structure is partially resolved and thus Δ is measured from the peak of the Doppler broadened

^{85}Rb but the value of Δ where the probe transmission becomes high is significantly larger for

^{87}Rb than

^{85}Rb, even though the Doppler widths of the

^{87}Rb and

^{85}Rb lines are nearly identical. This increased absorption at small Δ turns out to have a technical origin: although the Rb cell nominally contains only

^{87}Rb, there is a few percent of residual

^{85}Rb present. The relative positions of the absorption lines are such that the

^{85}Rb introduces extra absorption for the probe. Figure 4 shows the probe transmission as a function of frequency. The 4WM gain feature occurs in a spectral region where there is significant absorption by

^{85}Rb. As the pump is tuned further blue, the 4WM feature also moves blue, i.e. away from the

^{85}Rb absorption. Presumably the need to move the 4WM peak away from the

^{85}Rb absorption is the main reason that the optimum squeezing here requires a significantly larger Δ than in

^{85}Rb. If a pure

^{87}Rb cell were available, the optimum squeezing level could be obtained for a smaller Δ with reduced pump power. While it would obviously be advantageous to work with a higher purity sample, even with the level of

^{85}Rb contamination found in our current cell one can select laser parameters which produce high levels of quantum noise reduction.

^{85}Rb, the data in the region of good squeezing is well described by the model. Although we have changed parameters to adjust the gain, we see no evidence of a qualitative difference between the

^{85}Rb and

^{87}Rb D1 lines.

### 3.4 ^{87}Rb D2 line

^{87}Rb D2 line, the noise reduction is the lowest of the four studied cases. As was seen with

^{85}Rb, the D2 line requires a larger detuning than the D1 line. As for

^{85}Rb D2, the probe absorption inferred from the model is significant even at these large detunings. Again, the squeezing levels predicted by the model are significantly higher than the observed levels, signaling that an additional noise mechanism is at work.

## 4. Discussion

26. F. Renzoni, W. Maichen, L. Windholz, and E. Arimondo, “Coherent population trapping with losses observed on the Hanle effect of the D1 sodium line,” Phys. Rev. A **55**(5), 3710–3718 (1997). [CrossRef]

*et al.*[27

27. I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “ Comparison of ^{87}Rb N-resonances for D1 and D2 transitions, ” Opt. Lett. **31**(15), 2353 (2006). [CrossRef] [PubMed]

28. A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A **65**(4), 043817 (2002). [CrossRef]

## 5. Conclusion

^{85}Rb and

^{87}Rb using both the D1 and D2 transition lines. With some adjustments in parameters the same basic laser tuning scheme works for all four systems. The optimum choice of pump laser tuning is a balance between the need to tune close to the atomic line in order to have gain and the need to tune away from the line to reduce probe losses. A minimal extension of the ideal amplifier model, allowing for imperfect transmission of the probe beam in the gain medium, shows good agreement with the observations for the D1 lines but not for the D2 lines, pointing to an additional source of noise for the D2 lines. Despite competing effects, there is a range of parameters over which each system approximates, to a greater or lesser degree, an ideal double-lambda 4WM system. We believe that these results are general enough to suggest that applying the same methodology to other systems with similar level structure would result in quantum noise reduction as well.

## Acknowledgements

## References and links

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. |

2. | A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. |

3. | D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. |

4. | B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature |

5. | I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. |

6. | K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. |

7. | G. Hètet, B. C. Buchler, O. Glöeckl, M. T. L. Hsu, A. M. Akulshin, H. A. Bachor, and P. K. Lam, “Delay of squeezing and entanglement using electromagnetically induced transparency in a vapour cell,” Opt. Express |

8. | G. Hétet, O. Glockl, K. A. Pilypas, C. C. Harb, B. C. Buchler, H. A. Bachor, and P. K. Lam, “Squeezed light for bandwidth-limited atom optics experiments at the rubidium D1 line,” J. Phys. B |

9. | S. W. Du, J. M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B |

10. | S. A. Haine and J. J. Hope, “Outcoupling from a Bose-Einstein condensate with squeezed light to produce entangled-atom laser beams,” Phys. Rev. A |

11. | P. D. Lett, “Correlated photons for correlated atoms,” J. Mod. Opt. |

12. | 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 |

13. | J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, “Experimental investigation of amplitude and phase quantum correlations in a type II optical parametric oscillator above threshold: from nondegenerate to degenerate operation,” Opt. Lett. |

14. | H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. |

15. | A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature |

16. | R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. |

17. | V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science |

18. | E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. |

19. | C. M. Caves, “Quantum Limits on Noise in Linear-Amplifiers,” Phys. Rev. D Part. Fields |

20. | M. S. Shahriar and P. R. Hemmer, “Generation of squeezed states and twin beams via non-degenerate four-wave mixing in a Λ system,” Opt. Commun. |

21. | M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. |

22. | M. D. Lukin, A. B. Matsko, Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. |

23. | M.D. Lukin, P.R. Hemmer, and M.O. Scully, “Resonant nonlinear optics in phase coherent media,” in Advances in Atomic, Molecular, and Optical Physics |

24. | M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, “Coherent population trapping resonances in thermal |

25. | D. A. Steck, “Rubidium 85 D line data,”, http://steck.us/alkalidata (revision 0.2 1 September 2008); D.A. Steck, “Rubidium 87 D line data,” http://steck.us/alkalidata (revision 2.1, 1 September 2008). |

26. | F. Renzoni, W. Maichen, L. Windholz, and E. Arimondo, “Coherent population trapping with losses observed on the Hanle effect of the D1 sodium line,” Phys. Rev. A |

27. | I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “ Comparison of |

28. | A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A |

**OCIS Codes**

(230.4320) Optical devices : Nonlinear optical devices

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 22, 2009

Revised Manuscript: August 21, 2009

Manuscript Accepted: August 25, 2009

Published: September 3, 2009

**Citation**

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, "Quantum correlated light beams from non-degenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of ^{85}Rb and ^{87}Rb," Opt. Express **17**, 16722-16730 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16722

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### References

- 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] [PubMed]
- A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36(2), 93–98 (1996). [CrossRef]
- D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004). [CrossRef] [PubMed]
- B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004). [CrossRef] [PubMed]
- I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, “Optimal control of light pulse storage and retrieval,” Phys. Rev. Lett. 98(24), 243602 (2007). [CrossRef] [PubMed]
- K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008). [CrossRef] [PubMed]
- G. Hètet, B. C. Buchler, O. Glöeckl, M. T. L. Hsu, A. M. Akulshin, H. A. Bachor, and P. K. Lam, “Delay of squeezing and entanglement using electromagnetically induced transparency in a vapour cell,” Opt. Express 16(10), 7369–7381 (2008). [CrossRef] [PubMed]
- G. Hétet, O. Glockl, K. A. Pilypas, C. C. Harb, B. C. Buchler, H. A. Bachor, and P. K. Lam, “Squeezed light for bandwidth-limited atom optics experiments at the rubidium D1 line,” J. Phys. B 40(1), 221–226 (2007). [CrossRef]
- S. W. Du, J. M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25(12), C98 (2008). [CrossRef]
- S. A. Haine and J. J. Hope, “Outcoupling from a Bose-Einstein condensate with squeezed light to produce entangled-atom laser beams,” Phys. Rev. A 72(3), 033601 (2005). [CrossRef]
- P. D. Lett, “Correlated photons for correlated atoms,” J. Mod. Opt. 51, 1817 (2004).
- 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]
- J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, “Experimental investigation of amplitude and phase quantum correlations in a type II optical parametric oscillator above threshold: from nondegenerate to degenerate operation,” Opt. Lett. 30(10), 1177–1179 (2005). [CrossRef] [PubMed]
- H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100(3), 033602 (2008). [CrossRef] [PubMed]
- A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature 457(7231), 859–862 (2009). [CrossRef] [PubMed]
- R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103(1), 010501 (2009). [CrossRef] [PubMed]
- 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] [PubMed]
- E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. 33(11), 1213–1215 (2008). [CrossRef] [PubMed]
- C. M. Caves, “Quantum Limits on Noise in Linear-Amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982). [CrossRef]
- M. S. Shahriar and P. R. Hemmer, “Generation of squeezed states and twin beams via non-degenerate four-wave mixing in a Λ system,” Opt. Commun. 158(1-6), 273–286 (1998). [CrossRef]
- M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, “Resonant enhancement of parametric processes via radiative interference and induced coherence,” Phys. Rev. Lett. 81(13), 2675–2678 (1998). [CrossRef]
- M. D. Lukin, A. B. Matsko, Fleischhauer, and M. O. Scully, “Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence,” Phys. Rev. Lett. 82(9), 1847–1850 (1999). [CrossRef]
- M. D. Lukin, P. R. Hemmer, and M.O. Scully, "Resonant nonlinear optics in phase coherent media," in Advances in Atomic, Molecular, and Optical Physics 42, Elsevier (1999).
- M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, “Coherent population trapping resonances in thermal 85Rb vapor: D1 versus D2 line excitation,” Opt. Lett. 27(16), 1472–1474 (2002). [CrossRef]
- D. A. Steck, "Rubidium 85 D line data," http://steck.us/alkalidata (revision 0.2 1 September 2008); D. A. Steck, "Rubidium 87 D line data," http://steck.us/alkalidata (revision 2.1, 1 September 2008).
- F. Renzoni, W. Maichen, L. Windholz, and E. Arimondo, "Coherent population trapping with losses observed on the Hanle effect of the D1 sodium line," Phys. Rev. A 55(5), 3710-;3718 (1997). [CrossRef]
- I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “ Comparison of 87Rb N-resonances for D1 and D2 transitions,” Opt. Lett. 31(15), 2353 (2006). [CrossRef] [PubMed]
- A. S. Zibrov, C. Y. Ye, Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, “Observation of a three-photon electromagnetically induced transparency in hot atomic vapor,” Phys. Rev. A 65(4), 043817 (2002). [CrossRef]

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