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Indirect excitons: Transport and thermalisation dynamics, photoluminescence patterns and blue shift

We study the dynamics of indirect excitons in coupled quantum wells (CQWs) at low bath temperatures.

In experiments, the spatial photoluminescence patterns originating from the optical decay of indirect excitons are known to reveal remarkable features and there has been much activity in this field over the last decade. We perform numerical simulations using models based on the transport and thermalisation of a two dimensional statistically-degenerate gas of dipolar excitons. Working in collaboration with the group of Leonid Butov at UCSD, we make quantitative comparisons between the results of experiments and theoretical modelling.

Indirect excitons (right) are created in CQW structures by optical excitation of the medium with an electric field applied perpendicular to the QW plane. Photo excited electron-hole pairs bind to form excitons and the electric field shifts the energy levels within the wells so that electrons and holes reside in adjacent layers. The resulting indirect excitons are dipole orientated structures and the spatial separation of the electron and hole wave functions greatly increases the exciton lifetime. The long exciton lifetime results in exciton transport over large distances and the built-in dipole moment enables transport to be controlled by externally applied electric potential landscapes. This system presents an opportunity to study the transport properties of a two dimensional degenerate Bose gas in solids.

We have studied the inner ring in the exciton emission pattern. This consists of a bright ring around a point laser excitation spot. Our model includes the fact that only excitons with small in-plane momentum are optically active. The inner ring is then well explained in terms of exciton transport and cooling; the laser induced heating at the excitation spot suppresses optical decay and only excitons which transport away from the excitation spot may cool to the low lattice temperature and decay optically. We have also studied the excitation energy dependence of the inner ring and the density dependence of the blue shift in the exciton spectrum which appears due to the dipole-dipole interaction of indirect excitons.

The temporal counterpart of the inner ring is an effect known as the PL-jump. This occurs immediately after termination of the laser. In the absence of heating, the entire exciton population is allowed to cool to the lattice temperature becoming optically active. This gives rise to a sharp increase in the photoluminescence signal as the exciton gas rapidly decays. The full dynamics of the simulated inner ring and PL-jump can be seen in the movie (left).

Indirect exciton transport may be controlled by potential landscapes created by patterned electrodes above the CQW structures. Although indirect excitons are electrically neutral overall, their well-defined dipole moment makes them susceptible to a spatially or time varying potential. Indirect excitons accumulate at potential minima which, for high enough densities, they can effectively screen due to the dipole-dipole repulsion. We studied ramps - linear potential gradients, and a conveyer - a moving lattice created by a set of electrodes at ac voltages.

In the electrostatic exciton conveyer (right), indirect excitons are localised to the potential minima of the lattice. Excitons are dragged along by the conveyer as it moves along the quantum well plane. Exciton transport via the conveyer decreases with increasing conveyer velocity as the conveyer motion allows insufficient time for excitons to transport to the potential minima. We also found that for a high exciton density, the conveyer potential is completely screened leading to transport in the opposite direction to conveyer motion.

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