## Intensity-dependent effects on four-wave mixing based on electromagnetically induced transparency |

Optics Express, Vol. 19, Issue 22, pp. 21614-21619 (2011)

http://dx.doi.org/10.1364/OE.19.021614

Acrobat PDF (861 KB)

### Abstract

We extend the study on a four-wave mixing (FWM) scheme of contiuous-wave lasers in a hot rubidium vapor when the probe and coupling fields work in the electromagnetically induced transparency (EIT) regime while the pump and signal fields work in the two-photon Raman regime. Our experimental results show that the generated signal field is well contained in an EIT dip of the incident probe field as a result of efficient FWM. We find, in particular, that an optimal FWM process can only be attained when the coupling and pump fields are well matched in intensity. If the probe intensity is far beyond the EIT condition, however, the nonlinear efficiency of energy transfer from the probe field to the signal field will be greatly reduced.

© 2011 OSA

## 1. Introduction

1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today **50**, 36–42 (1997) [CrossRef]

2. M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of absorptive photon switching by quantum interference,” Phys. Rev. A **64**, 041801(R) (2001) [CrossRef]

3. D. A. Braje, V. Balic̈, G. Y. Yin, and S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A **68**, 041801(R) (2003) [CrossRef]

4. H. Kang and Y. F. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. **91**, 093601 (2003) [CrossRef] [PubMed]

5. Y. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. **21**, 1064–1066 (1996) [CrossRef] [PubMed]

6. A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. **84**, 5308–5311 (2000) [CrossRef] [PubMed]

7. 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**, 183601 (2004) [CrossRef] [PubMed]

8. S. A. Babin, S. I. Kablukov, U. Hinze, E. Tiemann, and B. Wellegehausen, “Level-splitting effects in resonant four-wave mixing,” Opt. Lett. **26**, 81–83 (2000) [CrossRef]

9. H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A **70**, 061804(R) (2004) [CrossRef]

10. Y. Wu and X. X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A **70**, 053818 (2004) [CrossRef]

11. B. X. Fan, Z. L. Duan, L. Zhou, C. L. Yuan, Z. Y. Ou, and W. P. Zhang, “Generation of a single-photon source via a four-wave mixing process in a cavity,” Phys. Rev. A **80**, 063809 (2009) [CrossRef]

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

13. 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**, 010501 (2009) [CrossRef] [PubMed]

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

15. Y. W. Lin, W. T. Liao, T. Peters, H. C. Chou, J. S. Wang, H. W. Cho, P. C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. **102**, 213601 (2009) [CrossRef] [PubMed]

16. J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett. **102**, 063602 (2009) [CrossRef] [PubMed]

17. J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliunas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. **104**, 033903 (2010) [CrossRef] [PubMed]

18. G. Wang, Y. Xue, J. H. Wu, Z. H. Kang, Y. Jiang, S. S. Liu, and J. Y. Gao, “Efficient frequency conversion induced by quantum constructive interference,” Opt. Lett. **35**, 3778–3780 (2010) [CrossRef] [PubMed]

## 2. Coherently enhanced four-wave mixing

*S*

_{1/2},

*F*= 2〉 ↔ |5

*P*

_{1/2},

*F*′ = 2〉 and acts as the coupling field of Rabi frequency Ω

_{1}; an external cavity diode laser-ECDL1 (DL100) is tuned to transition |5

*S*

_{1/2},

*F*= 1〉 ↔ |5

*P*

_{1/2},

*F*′ = 2〉 and acts as the probe field of Rabi frequency Ω

*; another external cavity diode laser-ECDL2 (DL100) is tuned to transition |5*

_{p}*S*

_{1/2},

*F*= 2〉 ↔ |5

*P*

_{3/2}〉 and acts as the pump field of Rabi frequency Ω

_{2}. In this case, a signal field of Rabi frequency Ω

*may be generated on transition |5*

_{s}*S*

_{1/2},

*F*= 1〉 ↔ |5

*P*

_{3/2}〉 as a result of FWM. The coupling, probe, and pump beams of linear polarizations (either horizontal or vertical) propagate collinearly into a temperature-stabilized vapor cell with the help of a beam splitter (BS), a λ/2 wave plate, and a polarization beam splitter (PBS1). The vapor cell of

^{87}

*Rb*atoms has a sample length of

*L*= 3.0cm and an volume density of

*N*= 2.2 × 10

^{11}cm

^{−3}at the temperature of

*T*= 62 °

*C*. After the vapor cell, the probe field Ω

*and the pump field Ω*

_{p}_{2}of horizontal polarizations pass through another polarization beam splitter (PBS2) to arrive in a grating (G1) while the coupling field Ω

_{1}and the signal field Ω

*of vertical polarizations are reflected by PBS2 to another grating (G2). The grating G1 (G2) with a groove density of 1200 lines/mm can spatially separate the probe (coupling) field Ω*

_{s}*(Ω*

_{p}_{1}) of 795 nm and the pump (signal) field Ω

_{2}(Ω

*) of 780 nm. Photodiodes D1 and D2 are used to monitor intensities of the probe field Ω*

_{s}*and the signal field Ω*

_{p}*, respectively.*

_{s}*I*∝ |Ω

_{s}*|*

_{s}^{2}) as a function of the probe detuning Δ

*when the coupling field has a vanishing detuning Δ*

_{p}_{1}= 0.0MHz. As we can see from the black curves, the signal field is not generated in the absence of the pump field (Ω

_{2}= 0) and a typical EIT dip centered at Δ

*= 0.0MHz is observed on the Doppler broadened spectrum of probe absorption. On the other hand, the red curves clearly show that the signal field is generated inside the EIT dip when the pump filed of detuning Δ*

_{p}_{2}= −400MHz is turned on (Ω

_{2}≠ 0). We also find that the EIT dip becomes much shallower due to the nonlinear energy transfer from the probe field to the signal field along the closed pathway |5

*S*

_{1/2},

*F*= 1〉 → |5

*P*

_{1/2},

*F*′ = 2〉 → |5

*S*

_{1/2},

*F*= 2〉 → |5

*P*

_{3/2}〉 → |

*S*

_{1/2},

*F*= 1〉. We have set Δ

_{1}= 0.0MHz for the coupling field while Δ

_{2}= −400MHz for the pump field, which is critical for achieving an optimal FWM process with Doppler broadening. This specific choice has two advantages in improving the FWM efficiency with a remarkable Doppler broadening present: I) to well suppress the energy dissipation in FWM processes due to spontaneous emissions from state |5

*P*

_{1/2},

*F*′ = 2〉 and state |5

*P*

_{3/2}〉; II) to ensure the existence of constructive quantum interference between two competitive FWM processes [18

18. G. Wang, Y. Xue, J. H. Wu, Z. H. Kang, Y. Jiang, S. S. Liu, and J. Y. Gao, “Efficient frequency conversion induced by quantum constructive interference,” Opt. Lett. **35**, 3778–3780 (2010) [CrossRef] [PubMed]

*I*

_{1}∝ |Ω

_{1}|

^{2}) for four different values of the pump intensity (

*I*

_{2}∝ |Ω

_{2}|

^{2}). It is clear that, for a given pump intensity, the signal intensity first quickly increases to a maximum and then slowly decreases after this maximum when the coupling field becomes stronger and stronger. Moreover, for a larger (smaller) pump intensity, the maximal signal intensity always corresponds to a larger (smaller) coupling intensity. This means that the maximal signal field can only be attained when the coupling field and the pump field are well matched in intensity. To have a deeper insight, we further plot the pump intensity as a function of the coupling intensity when the maximal signal intensity is attained (see the black curve in Fig. 4). It is clear that there exists a linear relationship between the pump intensity and the coupling intensity for achieving the optimal FWM process. This is a direct evidence for the necessary condition of intensity matching between the pump field and the coupling field. If the intensity matching condition is not fully satisfied, the energy transfer from the probe field to the signal field will be reversed a little so that the signal intensity is reduced to certain extent. In Fig. 4, we also plot the maximal signal intensity as a function of the coupling intensity (see the red curve), where the maximal signal intensity has a largest value when the coupling intensity is 170mW/cm

^{2}and the pump intensity is 172mW/cm

^{2}.

*≪ Ω*

_{p}_{1}and Δ

*= Δ*

_{p}_{1}≈ 0.0 MHz. Now we begin to examine how the probe intensity

*I*influences the signal intensity

_{p}*I*and thus the FWM efficiency defined as η =

_{s}*I*/

_{s}*I*. In Fig. 5, the probe intensity is increased from 0.3mW/cm

_{p}^{2}to 10.8mW/cm

^{2}for the fixed and matched coupling and pump intensities 170 mW/cm

^{2}and 172 mW/cm

^{2}. We find that the FWM efficiency is almost a constant (about 0.32) and the signal intensity increases linearly with the probe intensity when it is smaller than 1.5mW/cm

^{2}. In this case, the EIT condition Ω

*≪ Ω*

_{p}_{1}is well satisfied. As the probe intensity goes beyond the condition Ω

*≪ Ω*

_{p}_{1}, however, the FWM efficiency gradually falls down to a very low level (less than 0.08) and the signal intensity reaches its maximal value at

*I*≈ 7.5mW/cm

_{p}^{2}. Thus we may conclude that EIT plays an essential role in achieving the maximal FWM efficiency and the optimal energy transfer from the probe field to the signal field. Finally, we note that the maximal FWM efficiency could be dramatically improved if a longer Rb vapor cell or a denser atomic sample is employed [18

18. G. Wang, Y. Xue, J. H. Wu, Z. H. Kang, Y. Jiang, S. S. Liu, and J. Y. Gao, “Efficient frequency conversion induced by quantum constructive interference,” Opt. Lett. **35**, 3778–3780 (2010) [CrossRef] [PubMed]

9. H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A **70**, 061804(R) (2004) [CrossRef]

19. S. Babin, U. Hinze, E. Tiemann, and B. Wellegehausen, “Continuous resonant four-wave mixing in double-Λ level configurations of Na_{2},” Opt. Lett. **21**, 1186–1188 (1996) [CrossRef] [PubMed]

20. B. L. Lü, W. H. Burkett, and Min Xiao, “Nondegenerate four-wave mixing in a double-Λ system under the influence of coherent population trapping,” Opt. Lett. **23**, 804–806 (1998) [CrossRef]

**35**, 3778–3780 (2010) [CrossRef] [PubMed]

9. H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A **70**, 061804(R) (2004) [CrossRef]

19. S. Babin, U. Hinze, E. Tiemann, and B. Wellegehausen, “Continuous resonant four-wave mixing in double-Λ level configurations of Na_{2},” Opt. Lett. **21**, 1186–1188 (1996) [CrossRef] [PubMed]

20. B. L. Lü, W. H. Burkett, and Min Xiao, “Nondegenerate four-wave mixing in a double-Λ system under the influence of coherent population trapping,” Opt. Lett. **23**, 804–806 (1998) [CrossRef]

## 3. Summary

**35**, 3778–3780 (2010) [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | S. E. Harris, “Electromagnetically induced transparency,” Phys. Today |

2. | M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of absorptive photon switching by quantum interference,” Phys. Rev. A |

3. | D. A. Braje, V. Balic̈, G. Y. Yin, and S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A |

4. | H. Kang and Y. F. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. |

5. | Y. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. |

6. | A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. |

7. | 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. |

8. | S. A. Babin, S. I. Kablukov, U. Hinze, E. Tiemann, and B. Wellegehausen, “Level-splitting effects in resonant four-wave mixing,” Opt. Lett. |

9. | H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A |

10. | Y. Wu and X. X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A |

11. | B. X. Fan, Z. L. Duan, L. Zhou, C. L. Yuan, Z. Y. Ou, and W. P. Zhang, “Generation of a single-photon source via a four-wave mixing process in a cavity,” Phys. Rev. A |

12. | R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics |

13. | 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. |

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

15. | Y. W. Lin, W. T. Liao, T. Peters, H. C. Chou, J. S. Wang, H. W. Cho, P. C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett. |

16. | J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett. |

17. | J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliunas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett. |

18. | G. Wang, Y. Xue, J. H. Wu, Z. H. Kang, Y. Jiang, S. S. Liu, and J. Y. Gao, “Efficient frequency conversion induced by quantum constructive interference,” Opt. Lett. |

19. | S. Babin, U. Hinze, E. Tiemann, and B. Wellegehausen, “Continuous resonant four-wave mixing in double-Λ level configurations of Na |

20. | B. L. Lü, W. H. Burkett, and Min Xiao, “Nondegenerate four-wave mixing in a double-Λ system under the influence of coherent population trapping,” Opt. Lett. |

**OCIS Codes**

(020.1670) Atomic and molecular physics : Coherent optical effects

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(270.4180) Quantum optics : Multiphoton processes

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: August 23, 2011

Revised Manuscript: September 13, 2011

Manuscript Accepted: September 13, 2011

Published: October 18, 2011

**Citation**

Gang Wang, Lin Cen, Yi Qu, Yan Xue, Jin-Hui Wu, and Jin-Yue Gao, "Intensity-dependent effects on four-wave mixing based on electromagnetically induced transparency," Opt. Express **19**, 21614-21619 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21614

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### References

- S. E. Harris, “Electromagnetically induced transparency,” Phys. Today50, 36–42 (1997) [CrossRef]
- M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of absorptive photon switching by quantum interference,” Phys. Rev. A64, 041801(R) (2001) [CrossRef]
- D. A. Braje, V. Balic̈, G. Y. Yin, and S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A68, 041801(R) (2003) [CrossRef]
- H. Kang and Y. F. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett.91, 093601 (2003) [CrossRef] [PubMed]
- Y. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett.21, 1064–1066 (1996) [CrossRef] [PubMed]
- A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett.84, 5308–5311 (2000) [CrossRef] [PubMed]
- 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, 183601 (2004) [CrossRef] [PubMed]
- S. A. Babin, S. I. Kablukov, U. Hinze, E. Tiemann, and B. Wellegehausen, “Level-splitting effects in resonant four-wave mixing,” Opt. Lett.26, 81–83 (2000) [CrossRef]
- H. Kang, G. Hernandez, and Y. F. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A70, 061804(R) (2004) [CrossRef]
- Y. Wu and X. X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A70, 053818 (2004) [CrossRef]
- B. X. Fan, Z. L. Duan, L. Zhou, C. L. Yuan, Z. Y. Ou, and W. P. Zhang, “Generation of a single-photon source via a four-wave mixing process in a cavity,” Phys. Rev. A80, 063809 (2009) [CrossRef]
- R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics3, 103–106 (2009) [CrossRef]
- R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett.103, 010501 (2009) [CrossRef] [PubMed]
- A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature457, 859–862 (2009) [CrossRef] [PubMed]
- Y. W. Lin, W. T. Liao, T. Peters, H. C. Chou, J. S. Wang, H. W. Cho, P. C. Kuan, and I. A. Yu, “Stationary light pulses in cold atomic media and without Bragg gratings,” Phys. Rev. Lett.102, 213601 (2009) [CrossRef] [PubMed]
- J. Otterbach, R. G. Unanyan, and M. Fleischhauer, “Confining stationary light: Dirac dynamics and Klein tunneling,” Phys. Rev. Lett.102, 063602 (2009) [CrossRef] [PubMed]
- J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliunas, and M. Fleischhauer, “Effective magnetic fields for stationary light,” Phys. Rev. Lett.104, 033903 (2010) [CrossRef] [PubMed]
- G. Wang, Y. Xue, J. H. Wu, Z. H. Kang, Y. Jiang, S. S. Liu, and J. Y. Gao, “Efficient frequency conversion induced by quantum constructive interference,” Opt. Lett.35, 3778–3780 (2010) [CrossRef] [PubMed]
- S. Babin, U. Hinze, E. Tiemann, and B. Wellegehausen, “Continuous resonant four-wave mixing in double-Λ level configurations of Na2,” Opt. Lett.21, 1186–1188 (1996) [CrossRef] [PubMed]
- B. L. Lü, W. H. Burkett, and Min Xiao, “Nondegenerate four-wave mixing in a double-Λ system under the influence of coherent population trapping,” Opt. Lett.23, 804–806 (1998) [CrossRef]

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