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Physical Review B

Optically mediated coherent population trapping in asymmetric semiconductor quantum wells

J. F. Dynes, Mark D. Frogley, J. Rodger, Chris C. Phillips

Published Aug 9, 2005• 126 citations
Publisher

Abstract

A quantum well (QW), with only three transitions, which are all dipole allowed because of the QW asymmetry, is investigated when driven coherently by two infrared optical fields. One field couples the $\ensuremath{\mid}1⟩\ensuremath{-}\ensuremath{\mid}2⟩$ and $\ensuremath{\mid}2⟩\ensuremath{-}\ensuremath{\mid}3⟩$ transitions simultaneously, while a second field couples the $\ensuremath{\mid}1⟩\ensuremath{-}\ensuremath{\mid}3⟩$ transition. The absorption linear response is computed allowing the illustration of some features due to quantum coherence. Without the second field, the absorption of a weak probe is that of a strongly saturated system. As the coupling strength of the second field is increased the absorption strength of a weak probe increases, by over an order of magnitude factor in absorption strength compared to the case in the absence of the second field. The results are shown to be due to an optically mediated, coherent population trapping effect.

DOI
10.1103/physrevb.72.085323

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A quantum well (QW), with only three transitions, which are all dipole allowed because of the QW asymmetry, is investigated when driven coherently by two infrared optical fields. One field couples the \ensuremath∣1⟩\ensuremath−\ensuremath∣2⟩\ensuremath{\mid}1⟩\ensuremath{-}\ensuremath{\mid}2⟩\ensuremath∣1⟩\ensuremath−\ensuremath∣2⟩ and \ensuremath∣2⟩\ensuremath−\ensuremath∣3⟩\ensuremath{\mid}2⟩\ensuremath{-}\ensuremath{\mid}3⟩\ensuremath∣2⟩\ensuremath−\ensuremath∣3⟩ transitions simultaneously, while a second field couples the \ensuremath∣1⟩\ensuremath−\ensuremath∣3⟩\ensuremath{\mid}1⟩\ensuremath{-}\ensuremath{\mid}3⟩\ensuremath∣1⟩\ensuremath−\ensuremath∣3⟩ transition. The absorption linear response is computed allowing the illustration of some features due to quantum coherence. Without the second field, the absorption of a weak probe is that of a strongly saturated system. As the coupling strength of the second field is increased the absorption strength of a weak probe increases, by over an order of magnitude factor in absorption strength compared to the case in the absence of the second field. The results are shown to be due to an optically mediated, coherent population trapping effect.
We investigate the conduction intersubband linear response of a n-type quantum well driven by one or two infrared optical fields with arbitrary strengths. The fields couple the third subband to the second energy subband and the ground subband, forming a Λ system. We investigate the dependences of the absorption spectrum on the pump field strengths. The results for the equal Rabi frequencies can be understood in terms of quantum coherence processes of the intersubband transitions, such as coherent population trapping, and electromagnetically induced transparency. The effects of different Rabi frequencies on the absorption spectrum due to fields are also discussed.
A strong infrared field tuned in resonance with dipole-allowed intersubband transitions in quantum-well conduction bands can act to coherently mix or dress the resonant states. The effects of dressing two excited conduction subbands on the linear response of a weak probe field nearly resonant with one of the excited subbands and the partially occupied ground subband is theoretically treated to arbitrary order in the coupling-field strength. Three critical coupling-field strengths are identified that demark: (i) the minimum coupling required to observe changes in the linear response, (ii) the onset of a resolvable doublet in the response, and (iii) the strong-coupling limit in which the line doubling is fully developed. Analytic expressions for these three critical fields are obtained in terms of the Rabi frequency and the phenomenological damping parameters associated with states in the three subbands.
The phenomenon of electromagnetically induced quantum coherence is demonstrated between three confined electron subband levels in a quantum well which are almost equally spaced in energy. Applying a strong coupling field, two-photon resonant with the 1-3 intersubband transition, produces a pronounced narrow transparency feature in the 1-2 absorption line. This result can be understood in terms of all three states being simultaneously driven into "phase-locked" quantum coherence by a single coupling field. We describe the effect theoretically with a density matrix method and an adapted linear response theory.
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.
Density-matrix equations for electrons in laser-coupled quantum wells are derived in second quantization, including an off-diagonal radiative-decay coupling between a pair of electron transitions. Calculations of spontaneous photoluminescence and time-resolved optical absorption for the probe field are formulated. The zero absorption of the pump-laser field within an overlapping region between two absorption peaks is found in a resonant asymmetric double-quantum-well system and explained as the quantum interference between two nearly degenerate electron transitions. Quantum interference is clearly demonstrated through phase cancellation between the two statistically averaged transition dipole moments. The laser frequency for zero absorption can be tuned within a tunneling gap by applying a small dc bias field. The ${k}_{\ensuremath{\Vert}}$-dependent energy-level separation is found to be a crucial factor for destroying quantum interference. The optical gain of the probe field is seen as a hole in the weak absorption peak for the resonant asymmetric double quantum wells selectively coupled by a laser field and shown to be a result of the partial inversion of the electron occupation probabilities in momentum space after laser excitation. The probe-field gain increases with the strength of the pump laser. The effects of transition blocking, induced quantum coherence, and off-diagonal radiative-decay coupling are quantitatively analyzed for this gain.
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.