## Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment |

Optics Express, Vol. 20, Issue 10, pp. 11433-11444 (2012)

http://dx.doi.org/10.1364/OE.20.011433

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### Abstract

We experimentally generate a non-classical correlated two-color photon pair at 780 and 1529.4 nm in a ladder-type configuration using a hot ^{85}Rb atomic vapor with the production rate of ~10^{7}/s. The non-classical correlation between these two photons is demonstrated by strong violation of Cauchy-Schwarz inequality by the factor R = 48 ± 12. Besides, we experimentally investigate the relations between the correlation and some important experimental parameters such as the single-photon detuning, the powers of pumps. We also make a theoretical analysis in detail and the theoretical predictions are in reasonable agreement with our experimental results.

© 2012 OSA

## 1. Introduction

## 2. Experimental setup

## 3. Theoretical analysis

23. J. M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A **74**(2), 023808 (2006). [CrossRef]

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

*T*is temperature, and

*m*means the mass of the Rb atom. The above equation describes the two-color correlation function in the time domain, which consists of two parts: oscillation term and decay term. When τ≧0, Ξ(τ) = 1, and Ξ(τ) = 0 for τ<0. The decay term shows the width of correlation function, and the oscillation term describes oscillation phenomenon.

^{6}(s

^{−1}), 1 × 2π × 10

^{6}(s

^{−1}) and Ω

_{p1}= 60 × 2π × 10

^{6}(s

^{−1}), Δ

_{1}= 25 × 2π × 10

^{6}(s

^{−1}) (such parameters correspond to the resonance conditions in a cold atomic ensemble), we plot the correlation function shown in Fig. 3(a) . The oscillation phenomenon is from the interference of two types of photon pairs generated through two different SFWM processes in atomic-gas media, can be explained by the dressed-state picture [25

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

20. 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] [PubMed]

_{1}= 100 × 2π × 10

^{6}(s

^{−1}), Γ

_{1}= 210 × 2π × 10

^{6}(s

^{−1}), Δ

_{1}= 2.5 × 2π × 10

^{9}(s

^{−1}) are taken. Such parameters correspond to our experimental conditions. The numerical simulated result is shown in Fig. 3(b). We can see that the atomic decay rates affect the oscillation behavior, large decay rate induces the short dephasing time (of ~ns decay time), which causes the oscillations suppressed.

_{s1s2}

^{(2)}(τ) becomes large too. This is very reasonable because with the increase of the detuning, the transition probability between the states |1> and |3> becomes small, therefore the possibility exciting two atoms or more between the states |1> and |3> at the same time becomes small too, it reduces the possibility of multi-photon emission, which is a main noise factor. Figure 4(b) is the calculated correlation vs the transition coefficient A. From that we could see that with the decrease of the power of the Pump 2, the g

_{s1s2}

^{(2)}(τ) becomes large. This is also reasonable because with the decrease of the power of the Pump 2, the possibility exciting two atoms or more between the states |1> and |3> at the same time becomes small too, it also reduces the possible multi-photon emission and the noise caused by it.

## 4. Experimental results

_{s1,s2}(0) becomes larger with the increase of detuning of Pump 2, which is in agreement well with the theoretical prediction shown in Fig. 4(a).

_{s1,s2}(0) becomes weak, shown in Fig. 7(a). This is also in agreement well with our theoretical prediction shown in Fig. 4(b). If the power of pump 2 is fixed to be 16

*u*W, when we change the power of Pump 1, we find the correlation g

_{s1,s2}(0) becomes larger with the increase of the power of Pump 1, shown in Fig. 7(b). The reason is clear because with the increment of the power of the Pump 1, the transition probability between the states |3> to |4> becomes large. The atom on the state |3> excited from the state |1> by Pump 2 can be excited to the state |4> with higher probability, which increase the probability of emitting an infrared photon and a visible photon directly.

## 5. Conclusion

## Acknowledgments

## References and links

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19. | R. T. Willis, “Photon pair production from a hot atomic ensemble in the diamond configuration,” Ph. D. thesis, University of Maryland, College Park, (2009). |

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23. | J. M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A |

24. | C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A |

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

26. | R. W. Boyd, |

27. | D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S |

**OCIS Codes**

(190.7220) Nonlinear optics : Upconversion

(270.1670) Quantum optics : Coherent optical effects

(190.4223) Nonlinear optics : Nonlinear wave mixing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 9, 2012

Revised Manuscript: March 21, 2012

Manuscript Accepted: April 26, 2012

Published: May 4, 2012

**Citation**

Dong-Sheng Ding, Zhi-Yuan Zhou, Bao-Sen Shi, Xu-Bo Zou, and Guang-Can Guo, "Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment," Opt. Express **20**, 11433-11444 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11433

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### References

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