## Electromagnetically induced transparency via electron spin coherence in a quantum well waveguide

Optics Express, Vol. 11, Issue 24, pp. 3298-3303 (2003)

http://dx.doi.org/10.1364/OE.11.003298

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### Abstract

We propose and analyze a novel scheme to realize electromagnetically induced transparency (EIT) via robust electron spin coherence in semiconductor quantum wells. This scheme uses light hole transitions in a quantum well waveguide to induce electron spin coherence in the absence of an external magnetic field. For certain polarization configurations, the light hole transitions form a crossed double-V system. EIT in this system is strongly modified by a coherent wave mixing process induced by the electron spin coherence.

© 2003 Optical Society of America

1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today **50**(7), 36–42 (1997). [CrossRef]

4. example For a recent review see forM. D. Lukin, “Trapping and manipulating photons in an atomic ensembles,” Rev. Mod. Phys. **75**, 457 (2003). See also the extensive references cited there. [CrossRef]

1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today **50**(7), 36–42 (1997). [CrossRef]

5. R. Binder and M. Lindberg, “Ultrafast adiabatic population transfer in p-doped semiconductor quantum wells,” Phys. Rev. Lett. **81**, 1477 (1998). [CrossRef]

6. M. Phillips and H. Wang, “Spin coherence and electromagnetically induced transparency via exciton correlations,” Phys. Rev. Lett. **89**, 186401 (2002). [CrossRef] [PubMed]

8. M. 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]

9. J. M. Kikkawa, I. P. Smorchkova, N. Samarth, and D. D. Awschalom, “Room-temperature spin memory in two-dimensional electron gases,” Science **277**, 1284 (1997). [CrossRef]

10. For a recent review, see J. M. Kikkawa and D. D. Awschalom, “Electron spin and optical coherence in semiconductors,” Phys. Today **52**(6), 33 (1999). [CrossRef]

*ρ*, induced through the |b>-to-|a> and |b>- to-|d> transitions can interact with a σ+ polarized control field via the |b>-to-|d> transition. The resulting

_{ad}*ρ*leads to the usual EIT in a single-V system. This spin coherence, however, can also couple to a σ- polarized control field via the |c>-to-|a> transition. The resulting

_{ab}*ρ*oscillates at a frequency of 2ν-ν

_{dc}_{1}(ν and ν

_{1}are the frequency of the control and probe beams, respectively). For convenience, we refer to this second process as a coherent wave mixing process.

*H*=

*H*

_{0}+

*V*, where

*H*is the unperturbed Hamiltonian and

_{0}*V*is the Hamiltonian for the relevant dipole optical interaction within the rotating wave approximation, can be written in the form:

_{1}| denotes the Rabi frequency of the probe field and |Ω

_{+}| and |Ω

_{-}| denote those of the coupling field: Ω∝

*E*with

*E*being the complex electric field amplitude. For the linear polarized control field, |Ω

_{+}|=|Ω

_{-}|. To include the coherent wave mixing process, we write the relevant density matrix elements, up to the first order in the probe field, as follows:

_{1}). In contrast to the conventional population pulsation process, population pulsation in the crossed double-V system arises from electron spin coherence and does not occur in the first order of the probe field. Effects of population pulsation thus do not contribute up to the first order of the probe field.

*γ*is the decay rate for the spin coherence, Γ is the recombination rate for upper states |a> and |d>, and Δ

_{ad}_{1}=ω-ν

_{1}with ω being the lh transition frequency. We take ω=ν although a generalization to nonzero detuning for the control field is straightforward. We have also assumed that all the dipole transitions involved have the same decoherence rate,

*γ*. Note that the symmetry of the optical transitions involved implies that

*A’*=

*A*,

*B’*=

*B*,

*C’*=

*C*,

*Y*=

*X**,

*ρ*=

_{bb}*ρ*, and

_{cc}*ρ*=

_{aa}*ρ*.

_{dd}*I*=|Ω

_{+}|

^{2}/

*γ*Γ is the normalized saturation intensity. Note that

*B*

^{(1)}depends on the phase difference Δϕ=2ϕ-ϕ

_{1}where ϕ and ϕ

_{1}are the phase of the control and probe field, respectively. As can be seen from Eqs. (3), (11) and (12),

*A*

^{(1)}leads to a polarization at the same frequency and wave vector as the probe field. In comparison,

*B*

^{(1)}, which arises from the coherent wave mixing process discussed earlier, leads to a polarization at frequency 2ν-ν

_{1}and wave vector

**2k-k**

_{1}where

**k**and

**k**

_{1}are the wave vector for the control and probe beams, respectively.

*N*is an effective density averaged over the cross-section of the probe beam and

*µ*is the dipole matrix element for the z-component of the lh transition.

*χ*(

*ν*

_{1}) is the susceptibility that contains contributions from absorption saturation and the usual EIT process.

*(*χ ¯

*ν*

_{1}) is the susceptibility associated with the coherent wave mixing process.

_{1}) as a function of the probe detuning in Fig. 2 and those of

*(*χ ¯

*ν*

_{1}) in Fig. 3. For a qualitative illustration of absorption and dispersion characteristics, we take γ=10

^{12}Hz, Γ=10

^{8}Hz, γ

_{ad}=10Γ, Δϕ=0, and the Rabi frequency for the control field to be |Ω

_{+}|=|Ω

_{-}|=10

^{11}Hz. Figure 2 shows a sharp absorption dip in Im[χ(ν

_{1})] and a steep variation in Re[χ(ν

_{1})] near zero detuning. Both of these features result directly from the long-lived electron spin coherence and are characteristic of EIT in ordinary V-type three-level systems. It can be shown that the double V-system modifies the details of χ(ν

_{1}) and that it enhances the transparency governed by Imχ(ν

_{1}=ν). The susceptibility,

*(*χ ¯

*ν*

_{1}), plotted in Fig. 3 also displays sharp spectral features near zero detuning with a magnitude comparable to that for χ(ν

_{1}), indicating that the coherent wave mixing process is as strong as the usual EIT process. This is expected since both processes arise from the electron spin coherence.

_{1}), the nonlinear polarization induced by the usual EIT process and that by the coherent wave mixing process have the same frequency (see Eq. (3)). The complete propagation characterics, however, are difficult to determine since at finite control-probe detuning, the polarizations induced by the usual EIT and the coherent wave mixing processes feature different frequencies and wave vectors. Solutions to Maxwell’s wave equations including contributions from both polarizations are needed and will be discussed in a future publication.

**k**

_{1}(counter-propagating with respect to the probe). This is due to the fact that only the in-plane component of the wave vector needs to be conserved for phase matching since the motion of carriers are confined to the plane of the QW.

## References and links

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

2. | M. O. Scully and M. S. Zubairy, |

3. | E. Arimondo, “Coherent population trapping in laser spectroscopy,” Progress in Optics |

4. | example For a recent review see forM. D. Lukin, “Trapping and manipulating photons in an atomic ensembles,” Rev. Mod. Phys. |

5. | R. Binder and M. Lindberg, “Ultrafast adiabatic population transfer in p-doped semiconductor quantum wells,” Phys. Rev. Lett. |

6. | M. Phillips and H. Wang, “Spin coherence and electromagnetically induced transparency via exciton correlations,” Phys. Rev. Lett. |

7. | M. Phillips and H. Wang, “Electromagnetically induced transparency due to intervalence band coherence in a GaAs quantum well,” Opt. Lett. |

8. | M. Phillips, H. Wang, I. Rumyantsev, N.H. Kwong, R. Takayama, and R. Binder, “Electromagnetically induced transparency in semiconductors via biexciton coherence,” Phys. Rev. Lett. |

9. | J. M. Kikkawa, I. P. Smorchkova, N. Samarth, and D. D. Awschalom, “Room-temperature spin memory in two-dimensional electron gases,” Science |

10. | For a recent review, see J. M. Kikkawa and D. D. Awschalom, “Electron spin and optical coherence in semiconductors,” Phys. Today |

11. | A. P. Heberle, W. W. Ruhle, and K. Ploog, “Quantum beats of electron Larmor precession in GaAs wells”, Phys. Rev. Lett. |

12. | A. Imamoglu, “Electromagnetically induced transparency with two dimensional electron spins,” Opt. Comm. |

**OCIS Codes**

(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW

(270.1670) Quantum optics : Coherent optical effects

**ToC Category:**

Research Papers

**History**

Original Manuscript: October 23, 2003

Revised Manuscript: November 17, 2003

Published: December 1, 2003

**Citation**

Tao Li, Hailin Wang, N. Kwong, and R. Binder, "Electromagnetically induced transparency viaelectron spin coherence in a quantum wellwaveguide," Opt. Express **11**, 3298-3303 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-24-3298

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### References

- S. E. Harris, �??Electromagnetically induced transparency,�?? Phys. Today 50(7), 36-42 (1997). [CrossRef]
- M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge Univ. Press, Cambridge, 1997).
- E. Arimondo, �??Coherent population trapping in laser spectroscopy,�?? Progress in Optics 35, 257 (1996). [CrossRef]
- For a recent review see for example, M. D. Lukin, �??Trapping and manipulating photons in an atomic ensembles,�?? Rev. Mod. Phys. 75, 457 (2003). See also the extensive references cited there. [CrossRef]
- R. Binder and M. Lindberg, "Ultrafast adiabatic population transfer in p-doped semiconductor quantum wells," Phys. Rev. Lett. 81, 1477 (1998). [CrossRef]
- M. Phillips and H. Wang, �??Spin coherence and electromagnetically induced transparency via exciton correlations,�?? Phys. Rev. Lett. 89, 186401 (2002). [CrossRef] [PubMed]
- M. Phillips and H. Wang, �??Electromagnetically induced transparency due to intervalence band coherence in a GaAs quantum well,�?? Opt. Lett. 28, 831 (2003). [CrossRef] [PubMed]
- M. 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]
- J. M. Kikkawa, I. P. Smorchkova, N. Samarth, D. D. Awschalom, �??Room-temperature spin memory in twodimensional electron gases,�?? Science 277, 1284 (1997). [CrossRef]
- For a recent review, see J. M. Kikkawa, and D. D. Awschalom, �??Electron spin and optical coherence in semiconductors,�?? Phys. Today 52(6), 33 (1999). [CrossRef]
- A. P. Heberle, W. W. Ruhle, and K. Ploog, �??Quantum beats of electron Larmor precession in GaAs wells�??, Phys. Rev. Lett. 72, 3887 (1994). [CrossRef] [PubMed]
- A. Imamoglu, �??Electromagnetically induced transparency with two dimensional electron spins,�?? Opt. Comm. 179, 179 (2000). [CrossRef]

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