Electromagnetically induced transparency and lasing without population inversion in semiconductor quantum wells

In this paper, we review our recent experimental studies on electromagnetically induced transparency (EIT) from electron spin coherences in semiconductor quantum wells. Coherent Raman resonances, manifestations of EIT from electron spin coherences at relatively low pump intensities, were demonstrated in both V-type and Λ-type three-level systems via heavy-hole exciton and trion transitions in undoped and doped quantum wells, respectively. Coherent Raman resonances from electron spin coherences via light-hole transitions were also demonstrated in a waveguide geometry that enables a long optical interaction length as well as a large absorption coefficient. Experimental approaches that can avoid or reduce detrimental many-body effects in quantum wells are suggested for the realization of nearly ideal EIT processes.

In this paper, we present an analytical solution to the Maxwell–Bloch equations of the two-level semiconductor quantum well, G a A s / A l G a A s . In addition, we discuss the effects of coherent Rabi oscillations Ω ( t ) and the frequency of the semiconductor system ν ( t ) on atomic occupation probabilities, ρ 11 ( t ) and ρ 22 ( t ) , population inversion, ρ z ( t ) , and information entropies, H ( σ x ) , H ( σ y ) , and H ( σ z ) . We observe clearly the emergence of long-lived quantum coherence and the decay in curves for some special cases of Ω ( t ) and ν ( t ) . Also, we show that the dynamic nonlinear properties of the system can be controlled by changing the values of the coherent Rabi oscillations Ω ( t ) and the frequency of the semiconductor system ν ( t ) . Due to the lack of mathematical treatment of such systems, our study promises significant advantages for a large number of nonlinear dynamic systems, opening up a wide range of applications for semiconductor quantum wells.

The dependence of the excitonic two-photon absorption on the quantum correlations (entanglement) of exciting biphotons by a semiconductor quantum well is studied. We show that entangled photon absorption can display very unusual features depending on space-time-polarization biphoton parameters and absorber density of states for both bound exciton states as well as for unbound electron-hole pairs. We report on the connection between biphoton entanglement, as quantified by the Schmidt number, and absorption by a semiconductor quantum well. Comparison between frequency-anti-correlated, unentangled and frequency-correlated biphoton absorption is addressed. We found that exciton oscillator strengths are highly increased when photons arrive almost simultaneously in an entangled state. Two-photon-absorption becomes a highly sensitive probe of photon quantum correlations when narrow semiconductor quantum wells are used as two-photon absorbers.

Optical excitation and control of electron spins in semiconductor quantum wells

A new technique for the measurement of the intersubband lifetime in semiconductor quantum wells is demonstrated. Electrons are optically excited from the ground state to the first excited state of a doped quantum well. From measurements of the absorption cross section between excited states, we find a lifetime equal to τs=0.65±0.15 ps for a 85 Å GaAs quantum well and τs=0.8±0.2 ps for a 100 Å Ga0.47In0.53As quantum well, in good agreement with the theoretical predictions of Ferreira and Bastard [Phys. Rev. B 40, 1074 (1989)]. In addition, our experiments unambiguously show that the intersubband absorption line is homogeneously broadened at cryogenic temperatures (≤100 K).

We examine theoretically the intersubband transitions induced by laser beams of light with orbital angular momentum (twisted light) in semiconductor quantum wells at normal incidence. These transitions become possible in the absence of gratings thanks to the fact that collimated laser beams present a component of the light’s electric field in the propagation direction. We derive the matrix elements of the light–matter interaction for a Bessel type twisted light beam represented by its vector potential in the paraxial approximation. Then, we consider the dynamics of photoexcited electrons making intersubband transitions between the first and second subbands of a standard semiconductor quantum well. Finally, we analyze the light–matter matrix elements in order to evaluate which transitions are more favorable for a given orbital angular momentum of the light beam in the case of small semiconductor structures.

Intersubband absorption in highly photoexcited semiconductor quantum wells

Based on a microscopic many-particle theory, we predict large optical gain in the probe and background-free four-wave mixing directions caused by excitonic instabilities in semiconductor quantum wells. For a single quantum well with radiative-decay limited dephasing in a typical pump-probe setup we discuss the microscopic driving mechanisms and polarization and frequency dependence of these instabilities.

The magnetotransport experiments based on the weak antilocalization (WAL) effect have confirmed the common belief that the Rashba spin-orbit coupling (SOC) of two-dimensional (2D) holes in semiconductor quantum wells (QWs) is a $k$-cubic term as the lowest order with negligible linear terms. However, an emerging finite linear Rashba SOC was recently found in 2D holes by semiempirical pseudopotential method (SEPM) due to the direct dipolar coupling of an external electric field to the valence subbands in the presence of heavy-hole--light-hole (HH-LH) mixing. Here, we resolve this discrepancy by illustrating that the hole densities in the experiments are so high that the emerging linear term becomes undetectable since its strength declines substantially as increasing the wavevector $k$. Taking the example of a strained $\mathrm{Ge}/{\mathrm{Si}}_{0.5}{\mathrm{Ge}}_{0.5}$ QW utilized in the experiment [Phys. Rev. Lett. 113, 086601 (2014)], we demonstrate that the hole density must be reduced by a factor of 5 to below $2.1\ifmmode\times\else\texttimes\fi{}{10}^{11}{\text{cm}}^{\ensuremath{-}2}$ in order to probe the $k$-linear term. We also evaluate the possibility to achieve WAL at low hole densities in order to measure SOC. These findings shed new light on the experimental measurement of Rashba SOC.

Four-wave mixing via electron spin coherence in a quantum well waveguide

The dynamics of the coherent superposition of exciton states in a semiconductor quantum well excited by the joint action of two successive light pulses with the time interval between them t12 has been theoretically studied. The dependences of the amplitude and initial phase of the quantum bits on t12 have been found. It has been shown that the time dependence of the Kerr rotation of the reflected probe pulse is determined not only by the dynamics of the excited state, but also by the optical properties of the heterostructure containing the quantum well. The dependence of the decay rate of the excited state on t12 has been predicted.

We provide a microscopic theory for the Doppler velocimetry of spin\npropagation in the presence of spatial inhomogeneity, driving electric field\nand the spin orbit coupling in semiconductor quantum wells in a wide range of\ntemperature regime based on the kinetic spin Bloch equation. It is analytically\nshown that under an applied electric field, the spin density wave gains a\ntime-dependent phase shift $\\phi(t)$. Without the spin-orbit coupling, the\nphase shift increases linearly with time and is equivalent to a normal Doppler\nshift in optical measurements. Due to the joint effect of spin-orbit coupling\nand the applied electric field, the phase shift behaviors differently at the\nearly and the later stages. At the early stage, the phase shifts are the same\nwith or without the spin-orbit coupling. While at the later stage, the phase\nshift deviates from the normal Doppler one when the spin-orbit coupling is\npresent. The crossover time from the early normal Doppler behavior to the\nanomalous one at the later stage is inversely proportional to the spin\ndiffusion coefficient, wave vector of the spin density wave and the spin-orbit\ncoupling strength. In the high temperature regime, the crossover time becomes\nlarge as a result of the decreased spin diffusion coefficient. The analytic\nresults capture all the quantitative features of the experimental results,\nwhile the full numerical calculations agree quantitatively well with the\nexperimental data obtained from the Doppler velocimetry of spin propagation\n[Yang {\\it et al.}, Nat. Phys. {\\bf 8}, 153 (2012)]. We further predict that\nthe coherent spin precession, originally thought to be broken down at high\ntemperature, is robust up to the room temperature for narrow quantum wells. We\npoint out that one has to carry out the experiments longer to see the effect of\nthe coherent spin precession at higher temperature due to the larger crossover\ntime.\n

A new form of the Hamiltonian and a boundary condition on the derivatives of the wave function are presented for use in the Schr\"odinger wave equation to calculate the energy eigenvalues in semiconductor quantum wells. This fourth-order Hamiltonian allows the use of a constant effective mass for the electron, and accounts for the effect of band nonparabolicity on the energy eigenvalues in a simple way. Calculations show that nonparabolicity contributes only a small effect for quantum wells grown in the material systems ${\mathrm{Al}}_{0.35}$${\mathrm{Ga}}_{0.65}$As/GaAs and InP/${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}$As. Larger effects are predicted in the [111] crystal-growth direction than the [100] direction.

The persistent spin helix (PSH) state in III--V semiconductor quantum wells (QWs) is a promising candidate for spin-based applications because the PSH state realizes controllable spin orientation with long spin lifetime. Although the cubic Dresselhaus spin-orbit (SO) interaction is known for breaking the PSH state in both (001)-oriented and (110)-oriented QWs, it is not well understood how the distinct symmetry of cubic Dresselhaus terms ${\ensuremath{\beta}}_{3}$ between (001) and (110) QWs affects the robustness of the PSH state. Here we investigate robustness of the PSH state between (001) and (110) QWs under various strengths of cubic Dresselhaus SO interaction based on numerical Monte Carlo approach and magnetoconductance simulation, respectively, representing optical spin excitation/detection and weak localization/weak antilocalization in magnetotransport. For electron spins initialized along $z\ensuremath{\parallel}[001]$ in a (001) QW and $x\ensuremath{\parallel}[001]\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}y\ensuremath{\parallel}[1\overline{1}0]$ in a (110) QW, where the spin distribution is developed with the helical spin mode, a (001) QW shows a more robust PSH state against the increase of ${\ensuremath{\beta}}_{3}$ than does a (110) QW. This phenomenon is contrary to numerically computed magnetoconductance, where weak localization is maintained on the variation of ${\ensuremath{\beta}}_{3}$ in a (110) QW, whereas weak antilocalization appears in a (001) QW. By deriving the spin lifetime of the PSH state in a (110) QW from a diffusion equation using a random-walk approach, we demonstrate that such a difference arises directly from the magnitude and orientation of third angular harmonics in cubic Dresselhaus fields for (001) and (110) QWs.

Taking as a starting point the Liouville equation for the one-body density matrix operator, a general expression for the third-order nonlinear current density responsible for the optical Kerr effect associated with intersubband transitions in a quantum well is derived by use of the perturbative expansion method. The nonlinear current density is related to the local field inside the quantum well via a nonlocal relation. By combining the field-induced nonlinear part of the current density with the Maxwell equation, a nonlinear integral equation for the local field is established. For a two-level quantum well, the integral equation is solved exactly. The nonlinear optical reflectivity, transmittance, and absorbance of the quantum well in turn are obtained. Numerical calculations of the light-induced change of the optical spectra are presented for a Al0.5Ga0.5As/GaAs/Al0.5Ga0.5 As quantum well. The numerical results show that the optical reflectivity and absorbance decrease, and the transmittance increases as the optical intensity of the incident light is increased. In the case where the quantum-well structure is heavily doped, a notable light-induced red-shift of the location of the resonance peak in the optical spectra stemming from the combined local-field effect and field-induced population redistribution is predicted.