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Physical review. B, Condensed matter

Gain without inversion in interband transitions of semiconductor quantum wells from a single-particle perspective

Dong‐Seon Lee, Kevin J. Malloy

Published Jun 15, 1996• 10 citations
Publisher

Abstract

The quantum interferences arising in three-level atomic systems are investigated in analogous asymmetric semiconductor quantum well structures. These investigations lead to the conditions necessary for induced zero absorption and gain without population inversion in interband transitions. Asymmetric quantum well configurations are proposed and analyzed for induced zero absorption and gain without inversion using a single-particle density-matrix approach. This density-matrix approach is described and shown to give the steady-state solutions for absorption and gain without the approximations required for perturbative or iterative methods. Both excitonic and continuum transitions are examined using typical semiconductor parameters with excitonic transitions contributing the largest fraction of gain without inversion. While interband transitions differ from intraband and atomic transitions, results for the proposed quantum well configurations validate the basic concept of inversionless gain in semiconductors and point the way to ultralow threshold semiconductor microlasers. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.15749

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The quantum interferences arising in three-level atomic systems are investigated in analogous asymmetric semiconductor quantum well structures. These investigations lead to the conditions necessary for induced zero absorption and gain without population inversion in interband transitions. Asymmetric quantum well configurations are proposed and analyzed for induced zero absorption and gain without inversion using a single-particle density-matrix approach. This density-matrix approach is described and shown to give the steady-state solutions for absorption and gain without the approximations required for perturbative or iterative methods. Both excitonic and continuum transitions are examined using typical semiconductor parameters with excitonic transitions contributing the largest fraction of gain without inversion. While interband transitions differ from intraband and atomic transitions, results for the proposed quantum well configurations validate the basic concept of inversionless gain in semiconductors and point the way to ultralow threshold semiconductor microlasers. \textcopyright{} 1996 The American Physical Society.
Mechanisms for reduced interband absorption using intersubband coherence or intersubband coupling in semiconductor quantum wells are analyzed by exactly solving the density matrix equation. By placing some mild limitations on the diagonal density matrix elements, general analytic solutions are obtained without weak-field restrictions. Our solutions demonstrate reduced absorption, various nonlinear processes, and coupling-field-modulation of interband transitions. Our results agree well with previous results for three-level atomic systems, give insights into nonlinear mechanisms, and point out the importance of nonperturbative approaches to this class of problems.>
This paper presents the current results of field-induced quantum interference in semiconductor quantum wells. Three-level systems with two conduction subbands in single and double quantum wells coupled by a resonant field are studied. We investigate effects of the Coulomb and field-induced electronic renormalizations of the energy subbands and steady eigenstates of electrons. The random-phase and ladder approximations have been used to calculate the linear interband and intersubband optical absorptions and refractive indices. The effect of collective dipole moment on the nonlinear susceptibility has been incorporated into the study by using a local-field approach. Lasing without population inversion, electromagnetically induced transparency, and enhanced nonlinearity with reduced absorption inside the intersubband-coupled single quantum well and dc-field coupled double quantum wells are found.
We propose a new class of intersubband lasers and amplifiers that achieve net gain without population inversion. The laser scheme is based on a unipolar semiconductor double quantum- well structure where gain occurs at a transition between conduction band subbands. In order to achieve net gain without inversion, we utilize Fano-type interferences. The semiconductor laser scheme that we are considering is analogous to the atomic lambda system that has been extensively analyzed in the context of electromagnetically induced transparency and lasing without inversion. A coherent coupling field however, is not required in the present scheme. The electronic coherence necessary for Fano-type interferences is established by resonant tunneling. For nonlinear optics applications, the asymmetry of the structure allows for (chi) (2) processes and therefore higher conversion efficiency or parametric gain.
The absorption and stimulated emission of coherent electromagnetic radiation tuned close to an autoionizing state is investigated with the aim of clarifying some of the aspects behind the proposals of inversionless gain involving such atomic configurations. This is carried out within the framework of individual atomic evolution rather than by the use of density matrix equations, thus providing better insight into the fundamental processes of absorption and emission. In particular, we find that stimulated emission does not overcome absorption in spite of quantum interference of the Fano type being present. It is also shown that gain, in this configuration, although it can take place without population inversion between the involved levels, requires in any case a strong departure from thermal equilibrium conditions. Thereby a strong pumping mechanism, or equivalently a strong excitation power, is needed to reach the lasing threshold. This raises some questions on the relevance of the population inversion indicator of efficient gain implicitly assumed in similar configurations and in many related works.
In a self-consistent field formalism we investigated the weak-probe optical intersubband response of a three-subband semiconductor quantum well pumped by a strong coherent laser beam. We showed that, when the pumping photon energy is somewhat above the energy separation between the two lowest subbands, a combination of hole-burning effects and coherent pump–probe wave interactions can lead to both optical gain without population inversion and an Autler–Townes-like doublet in the probe optical spectrum. These two absorption peaks, whose positions are blueshifted as the pump intensity is increased, are due to the two-photon absorption process and light-induced intersubband transitions between the two upper states. It is also demonstrated that, in a stepwise two-photon pumping scheme, the optical gain with population inversion can also occur in the quantum-well system when a modestly strong pump field is present.
Optical interband excitonic absorption of semiconductor quantum wells (QW’s) driven by a coherent pump field is investigated on the basis of semiconductor Bloch equations. The pump field has a photon energy close to the intersubband spacing between the first two conduction subbands in the QW’s. An external weak optical field probes the interband transition. The excitonic effects and pump-induced population redistribution within the conduction subbands in the QW system are included. When the density of the electron–hole pairs in the QW structure is low, the pump field induces an Autler–Townes splitting of the exciton absorption spectrum. The split size and the peak positions of the absorption doublet depend not only on the pump frequency and intensity but also on the carrier density. As the density of the electron–hole pairs is increased, the split contrast (the ratio between the maximum and the minimum values) is decreased, because the exciton effect is suppressed at higher densities owing to the many-body screening.