Nonlinear Optical Probe of Indirect Excitons

Studies of spatially indirect excitons (IX) in semiconductors have attracted considerable research efforts since early 1960’s, fueled by the prediction of the remarkable quantum properties. This resulted in recent demonstration of quantum coherent effects including spontaneous coherence [1–3], long-range spin currents and associated polarization textures [4, 5] of indirect excitons. An IX can be formed by an electron and a hole confined in separate coupled quantum wells (CQW). Application of the electric field across the CQWs bends the band structure so that the IX state became the ground state of the system [6, 7]. The spatial separation of electrons and holes within IX allows them to achieve long lifetimes, which may be orders of magnitude longer than the lifetimes of spatially direct excitons (DX). At the same time, the spatial separation of electrons and holes strongly reduces the oscillator strength of IXs,with respect to DXs. This determines the choice of the experimental methods for studies of these quasiparticles. The most frequently used optical methods are based on the emission (photoluminescence, PL) spectroscopy. The PL signal scales linearly with the emission rate in time-resolved experiments and is nearly independent on the emission rate in cw experiments for the samples with low nonradiative recombination. A set of the linear optics methods was employed for studies of IXs, including the imaging spectroscopy [8], the time-resolved imaging [9], the polarization-resolved imaging [4], and the first-order coherence measurements [1–3]. However, the powerful methods of nonlinear optics, which have been successfully applied for DXs in quantum wells (QW) [10], [11] remain unexplored in the studies of IXs. A nonlinear optical process, in its broadest definition, is a process in which the optical properties of the medium depend on the light field itself [12]. In the case of optical pumping in semiconductors, light-induced modifications of the optical properties of the medium can persist for a long time after the perturbing light is turned off. In this case, a pump-probe arrangement can be used, with pump and probe interactions separated in time [13]. This allows for time-resolved studies of optical and spin coherence in the medium. In semiconductor QWs resonant optical pumping of DX resonance with circularly polarized light, and subsequent detection of the pump-induced dispersive response is widely used to study exciton population and spin dynamics [14]. Experimentally, either modification of intensity (photoinduced reflectivity) or the rotation of the polarization plane of the linearly polarized probe pulse (photoinduced Kerr rotation) upon reflection from the sample are measured [15]. These signals are proportional to the square of the oscillator strength of the excitonic transition and have a pronounced resonant character [12]. Thus, because the oscillator strength of IX is orders of magnitude lower than for DX, it is impossible to simply transpose the ideas developed for nonlinear spectroscopy of DX to IX. In this paper, we show how IXs, despite their vanishing oscillator strengths, can induce measurable photoinduced reflectivity and Kerr rotation. Our proposal relies on two peculiar properties of the CQW structures. The first essential property is the spin conserving tunneling of electrons between the QWs [16]. It allows for substantial spin polarization of IX via optical orientation of DXs. This has been unambiguously demonstrated by polarization-resolved photoluminescence experiments [17]. Thus, optical pumping of IXs can de realized via the DX state. The second imporant effect is the spindependent coupling between DX and IX states. This coupling is quite strong in CQW, where each IX and each DX have either holes or electrons located in the same QW. This is why the presence of IX population in the structure alters DX resonance properties, mainly