OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 24 — Dec. 1, 2003
  • pp: 3298–3303
« Show journal navigation

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

Tao Li, Hailin Wang, N.H. Kwong, and R. Binder  »View Author Affiliations


Optics Express, Vol. 11, Issue 24, pp. 3298-3303 (2003)
http://dx.doi.org/10.1364/OE.11.003298


View Full Text Article

Acrobat PDF (87 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

Electromagnetically induced transparency (EIT) exploits destructive quantum interference associated with a nonradiative coherence to make an otherwise opaque medium transparent [1

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

4

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]

]. Optical processes underlying EIT can also lead to remarkable phenomena including lasing without inversion, slow and stopped light, and stimulated Raman adiabatic passage [1

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

5

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

]. The tremendous success of EIT studies in atomic and atomic-like systems has stimulated considerable interest in extending these studies to semiconductor systems, both for a better understanding of nonradiative quantum coherences in semiconductors and for possible applications ranging from classical to quantum information processing.

While EIT in interband optical transitions in semiconductors have been demonstrated via the use of a variety of nonradiative quantum coherences including exciton spin coherence, biexciton coherence, and intervalence band coherence [6

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

8

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]

], these coherences are extremely fragile against both carrier-phonon and carrier-carrier scattering. These studies have all been carried out with ultrafast pulses at low temperature. It is very difficult, if possible at all, to extend these approaches to elevated temperatures.

Recent studies of optical spin manipulations in semiconductor have shown that electron spin coherence, as a form of nonradiative quantum coherence, is exceptionally robust. Electron spin coherence can be preserved over remarkably long time and length scales and especially can persist to room temperature [9

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

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]

]. Destructive quantum interference associated with the robust electron spin coherence thus provides a promising avenue for realizing room temperature EIT in semiconductors.

Interband dipole optical transitions near the band edge of semiconductors such as a GaAs quantum well (QW) are characterized by transitions between the doubly degenerate conduction bands with S z=1/2 and -1/2 and the doubly degenerate heavy-hole (hh) and light hole (lh) valence bands with J z=±3/2 and ±1/2, respectively. The two hh transitions share no common states. No electron spin coherence can be induced via hh transitions in the absence of an external magnetic field. The spin coherence, however, can be induced in the presence of an external magnetic field in the Voigt configuration, as shown in earlier experimental studies [9

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]

11

11. 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 recent theoretical proposal on EIT via electron spin coherence in a QW has also required the presence of a strong external magnetic field [12

12. A. Imamoglu, “Electromagnetically induced transparency with two dimensional electron spins,” Opt. Comm. 179, 179 (2000). [CrossRef]

].

In this paper we propose and analyze an EIT scheme that exploits polarization selection rules for the lh transition to induce electron spin coherence in the absence of an external magnetic field. As shown in Fig. 1(a), the two electron spin states can couple to a common lh valence band state. To induce electron spin coherence, the relevant dipole optical transitions need to be driven by two optical fields, one of which is polarized along the z-axis (the growth direction). The other field can be either σ+ or σ- polarized. Note that the field polarized along the z-axis has to propagate in the x-y plane (the plane of the QW), which requires the use of a waveguide geometry. We assume the lateral extension of the waveguide to be much greater than both the quantum well thickness and the optical wavelength. We also assume that the fundamental waveguide mode, which we consider in this paper, can approximately be represented as a plane wave.

Fig. 1. (a) Polarization selection rule for the lh transition. (b) Polarization configuration for the EIT scheme. Both the control and the probe propagate in the QW waveguide along the y-axis.

To realize EIT via the electron spin coherence, we can use a probe beam polarized along the z-axis and a control beam polarized along the x-axis (see Fig. 1(b)). Both beams couple to respective lh transitions and propagate in the QW waveguide along the y-axis. Note that the nonradiative coherence between the two lh valence bands decays rapidly and features a decoherence time a few orders of magnitude shorter than that of the electron spin coherence. Effects of the hole spin coherence are thus negligible. In this limit, we can view the above EIT scheme as a crossed double-V system.

EIT in this crossed double-V system can differ significantly from ordinary V-type systems. For convenience, we label the four energy levels in the lh transition as |a>, |b>, |c>, and |d>, as shown in Fig. 1(a). The electron spin coherence, ρad, 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 ρab 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 ρdc oscillates at a frequency of 2ν-ν1 (ν and ν1 are the frequency of the control and probe beams, respectively). For convenience, we refer to this second process as a coherent wave mixing process.

For a more detailed analysis, we model the coherent optical interactions using the atomic-like 4-level system shown in Fig. 1(a). This model is of course oversimplified. A realistic quantitative description would need to include the influence of the interactions between carriers and also that of scatterings of the carriers by phonons and disorders. Nevertheless, the present model can provide a qualitative illustration of the special nonlinear optical processes in the crossed double-V system.

The Hamiltonian for the crossed double-V system, H=H 0+V, where H0 is the unperturbed Hamiltonian and V is the Hamiltonian for the relevant dipole optical interaction within the rotating wave approximation, can be written in the form:

H0=ħωaaa+ħωbbb+ħωccc+ħωddd,
(1)
ν=ħ[Ω12eiν1tab+Ω2eiνtac+Ω12eiν1tdc+Ω+2eiνtdb+h.c.],
(2)

where |Ω1| 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:

ρab=Aeiν1t+Bei(2νν1)t,ρdc=Aeiν1t+Bei(2νν1)t,
(3)
ρdb=Ceiνt,ρac=Ceiνt,
(4)
ρad=Xei(νν1)t+Yei(νν1)t,
(5)

where the complex amplitudes are slowly-varying functions of time.

The coherent wave mixing process discussed above can also lead to population pulsation. To the second order of the probe field, populations, as represented by the diagonal matrix elements, can oscillate with a beat frequency of ±2(ν-ν1). 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.

The equations of motion for the relevant populations and complex amplitudes, up to the first order in the probe field but to all orders of the control field, are given as (decay rates are added phenomenologically):

A˙(1)=(iΔ1+γ)A(1)iΩ12(ρaa(0)ρbb(0))iΩ+2X(1),
(6)
X˙(1)=(iΔ1+γad)X(1)+iΩ12C*(0)iΩ+2A(1)+iΩ2B*(1),
(7)
B˙(1)=(iΔ1γ)B(1)iΩ2X*(1),
(8)
C˙(0)=γC(0)iΩ+2(ρdd(0)ρbb(0)),
(9)
ρ˙aa(0)=Γρaa(0)iΩ2(C(0)C*(0)),
(10)

where γad is the decay rate for the spin coherence, Γ is the recombination rate for upper states |a> and |d>, and Δ1=ω-ν1 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*, ρbb=ρcc, and ρaa=ρdd.

With continuous-wave control and probe fields, we obtained the steady-state solution for the above equations of motion:

A(1)=i(iΔ1+γ)Ω12(1+I){IΩ+24iΔ1+γad+(Ω+2+Ω2)4iΔ1+γ[1γ+1(iΔ1+γ)]},
(11)
B(1)=i(iΔ1γ)Ω1*2(1+I){ΩΩ+4iΔ1+γad+(Ω+2+Ω2)4iΔ1+γ[1γ+1(iΔ1+γ)]},
(12)

where I=|Ω+|2/γΓ is the normalized saturation intensity. Note that B (1) depends on the phase difference Δϕ=2ϕ-ϕ1 where ϕ and ϕ1 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-ν1 and wave vector 2k-k 1 where k and k 1 are the wave vector for the control and probe beams, respectively.

To describe the propagation of the probe in the crossed double-V system, we define two susceptibilities:

χ(ν1)=[A(1)(ν1)+A(1)(ν1)]Nμ2ħΩ1(ν1),
(13)
χ¯(ν1)=[B(1)(ν1)+B(1)(ν1)Nμ2]ħΩ1*(ν1),
(14)

where 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.

We plot both real and imaginary parts of χ(ν1) 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=1012 Hz, Γ=108 Hz, γad=10Γ, Δϕ=0, and the Rabi frequency for the control field to be |Ω+|=|Ω-|=1011 Hz. Figure 2 shows a sharp absorption dip in Im[χ(ν1)] and a steep variation in Re[χ(ν1)] 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(ν1) and that it enhances the transparency governed by Imχ(ν1=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(ν1), 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.

Fig. 2. The susceptibility associated with the usual EIT process as a function of probe detuning. Solid line: imaginary part; dashed line: real part.
Fig. 3. The susceptibility associated with the coherent wave mixing process as a function of probe detuning. The units are the same as in Fig. 2. Solid line: imaginary part; dashed line: real part.

The transmission, group velocity, and other propagation characteristics of a probe pulse near zero control-probe detuning are strongly modified by the coherent wave mixing process. At zero control-probe detuning (ν=ν1), 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.

A drawback of the proposed EIT scheme is that the control beam becomes strongly attenuated as it propagates along the QW waveguide. To avoid strong attenuation of the control, one can use a control beam that is still x-polarized but propagates along the z-axis (orthogonal to the probe) instead of the y-axis. This orthogonal geometry, however, can also lead to a peculiar behavior: the optical field induced by the coherent wave mixing process can propagate along the direction of -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.

In summary, we have proposed and analyzed a novel scheme to realize EIT via electron spin coherence in semiconductor QWs. This scheme uses lh transitions in a QW waveguide to induce electron spin coherence in the absence of an external magnetic field. EIT in this scheme is strongly modified by a coherent wave mixing process induced by the electron spin coherence. The present theoretical model oversimplifies optical interactions in a QW. For a more quantitative description, a microscopic many-body theory and solutions to Maxwell’s wave equations are needed and will be treated in future work. Given the robustness of electron spin coherence even at room temperature, the proposed EIT scheme can potentially lead to room temperature EIT operation in a semiconductor, opening up new avenues for applications of nonradiative quantum coherence and especially EIT processes.

This work is supported by ONR/DARPA-SpinS, ARO, NSF-DMR, and JSOP.

References and links

1.

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

2.

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge Univ. Press, Cambridge, 1997).

3.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Progress in Optics 35, 257 (1996). [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]

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]

7.

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]

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]

11.

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]

12.

A. Imamoglu, “Electromagnetically induced transparency with two dimensional electron spins,” Opt. Comm. 179, 179 (2000). [CrossRef]

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


Sort:  Journal  |  Reset  

References

  1. S. E. Harris, �??Electromagnetically induced transparency,�?? Phys. Today 50(7), 36-42 (1997). [CrossRef]
  2. M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge Univ. Press, Cambridge, 1997).
  3. E. Arimondo, �??Coherent population trapping in laser spectroscopy,�?? Progress in Optics 35, 257 (1996). [CrossRef]
  4. 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]
  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]
  7. 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]
  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, D. D. Awschalom, �??Room-temperature spin memory in twodimensional 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]
  11. 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]
  12. A. Imamoglu, �??Electromagnetically induced transparency with two dimensional electron spins,�?? Opt. Comm. 179, 179 (2000). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited