## Electromagnetically induced transparency on GaAs quantum well to observe hole spin dephasing

Optics Express, Vol. 16, Issue 20, pp. 15728-15732 (2008)

http://dx.doi.org/10.1364/OE.16.015728

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### Abstract

Electromagnetically induced transparency (EIT) was observed with transient optical response of exciton correlation in GaAs/AlGaAs quantum well structure. Decoherence of EIT was increased with temperature (12–60 K), which could be simulated by increasing non-radiation decay rate between coherently coupled ground states in Bloch equation for Λ type three level. The non-radiation decay was mainly due to hole spin dephasing in the system for EIT via coulomb correlation. The hole spin dephasing rate was found with increasing lattice temperature and well accorded to the past results of time resolving method with n-doping material.

© 2008 Optical Society of America

## 1. Introduction

2. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature **397**, 594–598 (1999). [CrossRef]

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

4. H. Kang, G. Hernandez, and Y. Zhu, “Slow-Light Six-Wave Mixing at Low Light Intensities,” Phys. Rev. Lett. **93**, 073601 (2004). [CrossRef] [PubMed]

5. C. Ottaviani, S. Rebić, D. Vitali, and P. Tombesi, “Quantum phase-gate operation based on nonlinear optics: Full quantum analysis,” Phys. Rev. A **73**, 010301 (2006). [CrossRef]

10. J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. **67**, 3062–3065 (1991). [CrossRef] [PubMed]

11. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. **86**, 783–786 (2001). [CrossRef] [PubMed]

6. M. Phillips, H. Wang, M. C. Phillips, H. Wang, I. Rumyantsev, N. H. Kwong, R. Takayama, and R. Binder, “Electromagnetically Induced Transparency in Semiconductors via Biexciton Coherence,” Phys. Rev. Lett. **91**, 183602 (2003). [CrossRef] [PubMed]

## 2. Experiment and Calculation

_{0.35}Ga

_{0.65}As barriers. The absorption peaks corresponding to the heavy hole and the light hole exciton transitions were clearly observed from 11K up to room temperature [12

12. C. C. Byeon, M.-k. Oh, H. Kang, J. Su Kim, H.-G. Choi, M. S. Jeong, C.-s. Kee, D.-k. Ko, and J. Lee, “Coherent absorption spectroscopy with supercontinuum for semiconductor quantum well structure,” J. Opt. Soc. Ko. **11**, 138–141 (2007). [CrossRef]

*γ*

_{-+}) could be found by fitting calculation with Bloch equation to the observed EIT signal.

*ε*and probe laser field

_{c}*ε*was noted with

_{p}*ε*(

_{c}*ε*) was a strong coupling field (weak probe field) with center frequency

_{p}*ν*(

_{c}*ν*) and pulse envelope

_{p}*E*(

_{c}*E*). Rabi frequencies Ω

_{p}_{c}=

*µ*(

_{c}E_{c}*t*)/ħ and Ω

*=*

_{p}*µ*(

_{p}E_{p}*t*)/ħ were used for interaction picture, where µ is the dipole transition matrix element. The ground state (single exciton spin states),

_{--}is 1 with total population normalized. With the rotating wave approximation, the Bloch equations of the density matrices are

^{e+}(ρ

^{-+}) is the dipole coherence between biexciton and ground state

*δ*=

_{c}*ν*-

_{c}*ω*

_{-}and

*δ*=

_{p}*ν*-

_{p}*ω*

_{+}, where

*ω*

_{-}(

*ω*

_{+}) was the resonant frequency of exciton

*γ*was valued same at the temperature range (11~60 K) in our calculation. Meanwhile, the non radiative decoherence between ground states (

*γ*

_{-+}) with increasing temperature would be adjusted to fit the calculation to experimental EIT curve.

*γ*

_{-+}at each temperature (Fig. 3). The value of decoherence,

*γ*

_{-+}was decaying function with temperature and it was about 4 picoseconds at 11 K (Fig. 4).

## 3. Dephasing time

16. M. Gurioli, A. Vinattieri, M. Colocci, C. Deparis, J. Massies, G. Neu, A. Bosacchi, and S. Franchi, “Temperature dependence of the radiative and nonradiative recombination time in GaAs/Al_{x}Ga_{1-x}As quantum-well structures,” Phys. Rev. B **44**, 3115–3124 (1991). [CrossRef]

14. A. P. Heberle, W. W. Ruhle, and K. Ploog, Phys. Rev. Lett.72, 3887–3890 (1994). [CrossRef] [PubMed]

15. M. Syperek, D. R. Yakovlev, A. Greilich, J. Misiewicz, M. Bayer, D. Reuter, and A. D. Wieck, “Spin Coherence of Holes in GaAs/(Al,Ga)As Quantum Wells,” Phys. Rev. Lett. **99**, 187401 (2007) [CrossRef] [PubMed]

14. A. P. Heberle, W. W. Ruhle, and K. Ploog, Phys. Rev. Lett.72, 3887–3890 (1994). [CrossRef] [PubMed]

17. T. C. Damen, L. Viña, J. E. Cunningham, J. Shah, and L. J. Sham, “Subpicosecond spin relaxation dynamics of excitons and free carriers in GaAs quantum wells,” Phys. Rev. Lett. **67**, 3432–3435 (1991). [CrossRef] [PubMed]

18. B. Baylac, T. Amand, X. Marie, B. Dareys, M. Brousseau, G. Bacquet, and V. Thierry-Mieg, “Hole spin relaxation in n-modulation doped quantum wells,” Solid State Commun. **93**, 57–60 (1995). [CrossRef]

17. T. C. Damen, L. Viña, J. E. Cunningham, J. Shah, and L. J. Sham, “Subpicosecond spin relaxation dynamics of excitons and free carriers in GaAs quantum wells,” Phys. Rev. Lett. **67**, 3432–3435 (1991). [CrossRef] [PubMed]

17. T. C. Damen, L. Viña, J. E. Cunningham, J. Shah, and L. J. Sham, “Subpicosecond spin relaxation dynamics of excitons and free carriers in GaAs quantum wells,” Phys. Rev. Lett. **67**, 3432–3435 (1991). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgment

## References and links

1. | S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today |

2. | L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature |

3. | H. Kang and Y. Zhu, “Observation of large Kerr nonliearity at low light intensity,” Phys. Rev. Lett. |

4. | H. Kang, G. Hernandez, and Y. Zhu, “Slow-Light Six-Wave Mixing at Low Light Intensities,” Phys. Rev. Lett. |

5. | C. Ottaviani, S. Rebić, D. Vitali, and P. Tombesi, “Quantum phase-gate operation based on nonlinear optics: Full quantum analysis,” Phys. Rev. A |

6. | M. Phillips, H. Wang, M. C. Phillips, H. Wang, I. Rumyantsev, N. H. Kwong, R. Takayama, and R. Binder, “Electromagnetically Induced Transparency in Semiconductors via Biexciton Coherence,” Phys. Rev. Lett. |

7. | K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto, “Coherent Population Trapping of Electron Spins in a High-Purity |

8. | V. M. Axt and T. Kuhn, “Femtosecond spectroscopy in semiconductors: a key to coherences, correlations and quantum kinetics,” Rep. Prog. Phys. |

9. | C. Ku and C. J. Chang-Hasnain, “Slow light in semiconductor heterostructures,” S. L. Chuang, J. of Phys. D, Appl. Phys. |

10. | J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor,” Phys. Rev. Lett. |

11. | D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of Light in Atomic Vapor,” Phys. Rev. Lett. |

12. | C. C. Byeon, M.-k. Oh, H. Kang, J. Su Kim, H.-G. Choi, M. S. Jeong, C.-s. Kee, D.-k. Ko, and J. Lee, “Coherent absorption spectroscopy with supercontinuum for semiconductor quantum well structure,” J. Opt. Soc. Ko. |

13. | N. Peyghambarian, S. W. Koch, and A. Mysyrowicz, |

14. | A. P. Heberle, W. W. Ruhle, and K. Ploog, Phys. Rev. Lett.72, 3887–3890 (1994). [CrossRef] [PubMed] |

15. | M. Syperek, D. R. Yakovlev, A. Greilich, J. Misiewicz, M. Bayer, D. Reuter, and A. D. Wieck, “Spin Coherence of Holes in GaAs/(Al,Ga)As Quantum Wells,” Phys. Rev. Lett. |

16. | M. Gurioli, A. Vinattieri, M. Colocci, C. Deparis, J. Massies, G. Neu, A. Bosacchi, and S. Franchi, “Temperature dependence of the radiative and nonradiative recombination time in GaAs/Al |

17. | T. C. Damen, L. Viña, J. E. Cunningham, J. Shah, and L. J. Sham, “Subpicosecond spin relaxation dynamics of excitons and free carriers in GaAs quantum wells,” Phys. Rev. Lett. |

18. | B. Baylac, T. Amand, X. Marie, B. Dareys, M. Brousseau, G. Bacquet, and V. Thierry-Mieg, “Hole spin relaxation in n-modulation doped quantum wells,” Solid State Commun. |

**OCIS Codes**

(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW

(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: August 19, 2008

Revised Manuscript: September 15, 2008

Manuscript Accepted: September 16, 2008

Published: September 19, 2008

**Citation**

Hoonsoo Kang, Jong Su Kim, Sung In Hwang, Young Ho Park, Do-kyeong Ko, and Jongmin Lee, "Electromagnetically induced transparency on GaAs quantum well to observe hole spin dephasing," Opt. Express **16**, 15728-15732 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15728

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### References

- S. E. Harris, "Electromagnetically Induced Transparency," Phys. Today 50, 36-42 (1997).
- L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature 397, 594-598 (1999). [CrossRef]
- H. Kang and Y. Zhu, "Observation of large Kerr nonliearity at low light intensity," Phys. Rev. Lett. 91, 093601 (2003). [CrossRef] [PubMed]
- H. Kang, G. Hernandez, and Y. Zhu, "Slow-Light Six-Wave Mixing at Low Light Intensities," Phys. Rev. Lett. 93, 073601 (2004). [CrossRef] [PubMed]
- C. Ottaviani, S. Rebi?, D. Vitali, and P. Tombesi, "Quantum phase-gate operation based on nonlinear optics: Full quantum analysis," Phys. Rev. A 73, 010301 (2006). [CrossRef]
- M. Phillips and H. Wang, "Spin Coherence and Electromagnetically Induced Transparency via Exciton Correlations," Phys. Rev. Lett. 89, 186401 (2002), M. C. Phillips, H. Wang, I. Rumyantsev, N. H. Kwong, R. Takayama, and R. Binder, "Electromagnetically Induced Transparency in Semiconductors via Biexciton Coherence," Phys. Rev. Lett. 91, 183602 (2003). [CrossRef] [PubMed]
- K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto, "Coherent Population Trapping of Electron Spins in a High-Purity n-Type GaAs Semiconductor," Phys. Rev. Lett. 95, 187405 (2005). [CrossRef] [PubMed]
- V. M. Axt and T. Kuhn, "Femtosecond spectroscopy in semiconductors: a key to coherences, correlations and quantum kinetics," Rep. Prog. Phys. 67, 433-512 (2004). [CrossRef]
- C. Ku and C. J. Chang-Hasnain, "Slow light in semiconductor heterostructures," J. Phys. D, Appl. Phys. 40, R93-R107 (2007). [CrossRef]
- J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991). [CrossRef] [PubMed]
- D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, "Storage of Light in Atomic Vapor," We report an experiment in which a light pulse is effectively decelerated and trapped in a vapor of Rb atoms, stored for a controlled period of time, and then released on demand. We accomplish this "storage of light" by dynamically reducing the group velocity of the light pulse to zero, so that the coherent excitation of the light is reversibly mapped into a Zeeman (spin) coherence of the Rb vapor. Phys. Rev. Lett. 86, 783-786 (2001). [CrossRef] [PubMed]
- C. C. Byeon, M.-k. Oh, H. Kang, J. Su Kim, H.-G. Choi, M. S. Jeong, C.-s. Kee, D.-k. Ko, and J. Lee, "Coherent absorption spectroscopy with supercontinuum for semiconductor quantum well structure," J. Opt. Soc. Ko. 11, 138-141 (2007). [CrossRef]
- N. Peyghambarian, S. W. Koch, and A. Mysyrowicz, Introduction to Semiconductor Optics (Prentics-Hall International, Inc. 1993).
- A. P. Heberle, W. W. Ruhle, and K. Ploog, Phys. Rev. Lett. 72, 3887-3890 (1994). [CrossRef] [PubMed]
- M. Syperek, D. R. Yakovlev, A. Greilich, J. Misiewicz, M. Bayer, D. Reuter, and A. D. Wieck, "Spin Coherence of Holes in GaAs/(Al,Ga)As Quantum Wells," Phys. Rev. Lett. 99, 187401 (2007) [CrossRef] [PubMed]
- M. Gurioli, A. Vinattieri, M. Colocci, C. Deparis, J. Massies, G. Neu, A. Bosacchi, and S. Franchi, "Temperature dependence of the radiative and nonradiative recombination time in GaAs/AlxGa1-xAs quantum-well structures," Phys. Rev. B 44, 3115-3124 (1991). [CrossRef]
- T. C. Damen, L. Viña, J. E. Cunningham, J. Shah, and L. J. Sham, "Subpicosecond spin relaxation dynamics of excitons and free carriers in GaAs quantum wells," Phys. Rev. Lett. 67, 3432-3435 (1991). [CrossRef] [PubMed]
- B. Baylac, T. Amand, X. Marie, B. Dareys, M. Brousseau, G. Bacquet, and V. Thierry-Mieg, "Hole spin relaxation in n-modulation doped quantum wells," Solid State Commun. 93, 57-60 (1995). [CrossRef]

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