Dephasing of optically induced excitonic coherences in semiconductor heterostructures

Resonant optical excitation of a direct bandgap semiconductor below the band edge induces excitonic coherences. Experiments based on transient four-wave mixing or cw spectral-hole burning provide an excellent approach to eliminate inhomogeneous broadening and enable determination of the time scale and origin of the decay of the optically induced quantum coherence. Such measurements are of interest in basic physics since they reflect fundamental interactions between the exciton and the surrounding environment including, for example, lattice vibrations and interface fluctuations. They also relate to potential applications of these excitations such as in coherent control or quantum information processing. PACS: 71.35.-y; 78.47.+p; 39.30.+w Optical excitations near the bandedge of direct bandgap semiconductors and semiconductor heterostructures are dominated by the contributions from strong excitonic resonances that form just below the bandedge. In the absence of disorder leading to inhomogeneous broadening, the spectral linewidth of these resonances reflects the decay of optically induced quantum coherence due to dephasing. Understanding the physics of the dephasing process, which can be due to energy relaxation as well as pure dephasing, i.e., processes that lead to a loss of the coherence but with no changes in excitonic population, provides important information on interactions between the exciton and the surrounding environment including, for example, lattice vibrations and interface fluctuations. This information is not only of fundamental importance but also critical for many potential applications such as coherent control and quantum information processing proposed recently. Dephasing represents the decay of the phase correlation between two states that are prepared as a coherent superposition state, for example |Ψ 〉 = C1|1〉+C2 eiωt|2〉 where hω= E2 − E1. Dephasing can simply arise from a decay of the probability amplitude of one of the states due to population relaxation such as spontaneous emission. Such energy relaxation processes can also be observed in the time evolution of the population of the relevant state ∝ |Ci |2, which is phase insensitive. Measurement of the dephasing rate, however, follows from probing an observable that is sensitive to the relative phase between C1 and C2. Of particular interest to the focus of this paper, is the dephasing rate associated with the dipole coherence ∝ C1C∗ 2 e−iωt +cc. If the population decays at a rate, Γ , then the dipole coherence decays at a rate γ = Γ/2. Processes that lead to loss of coherence between C1 and C2 (dipole or other coherence) without a decay of the amplitude of either C1 or C2 are referred to as pure dephasing and result in a total dephasing rate of γ = Γ/2+γph with γph being the pure dephasing rate. Theories that have considered the complications of general dephasing processes for excitons at low temperature in semiconductors are in general more complex than those in simpler atomic type systems (see for example [1–5]). In a homogeneously broaden system, one can either measure the line shape of the dipole transition, which will yield a Lorentzian corresponding to the Fourier transform of decay of the dipole coherence, or directly probe the decay by time resolving the emitted coherent radiation following an impulse resonant excitation. Figure 1 shows as an example the time resolved free polarization decay (FPD) from homogeneously broadened exciton resonances in a bulk thin film of GaAs [6]. In this study, the sample was slightly strained to lift the heavy-hole (hh) and light-hole (lh) degeneracy. The FPD shows a simple exponential decay of the dipole induced coherence with a series of dipole coherence beats superimposed on the decay representing the interference of the coherent radiation emitted from the hh and lh excitons. In heterostructures such as quantum wells and quantum dots, the excitonic resonances as observed in photoluminescence (PL) or photoluminescence excitation (PLE) are broadened far beyond the fundamental linewidth from dephasing due to inhomogeneous broadening induced by interface disorder. Confinement of excitons by the potential barriers leads to a shift of the excitonic resonances from that expected in the ideal three dimensional case. Fluctuations in the well thickness, which are known to occur on various length scales, lead to spatially dependent shifts in the energy level struc-