Long-range coherence of interacting Bose gas of dipolar excitons

Exciton condensation in quantum wells with defects of macroscopic sizes

Formation of the excitonic condensed phase in quantum wells with defects of macroscopic size is investigated in the case of a specific kind of defect arising in local areas of planar quantum wells where the wells are thicker or thinner by an atomic monolayer or two. The excitonic system in the wells is non-equilibrium as the excitons are constantly created by an irradiation and decay due to the finite lifetime. The condensation considered in the paper is not the Bose-Einstein condensation but rather the classical condensation due an interaction between excitons with additional peculiarities caused by non-equilibrium conditions. The main contribution to the exciton's energy in the defect's area comes from the energy of the exciton's confinement along the growth axis and the respective quantization of the exciton's levels. The condensation manifests itself by an enhancement the exciton accumulation in the defect's area with increasing pumping and by an appearance of different types of structures in the exciton density distribution when the defect's size is large. The condensed phase may appear in the form of islands or in the form of rings on the defect's boundary. It is shown, that the value of the exciton's lifetime plays an important role in the spatial distribution of the exciton density. The similarity and the difference of density structures for wells with the extra or lacking atomic monolayer in the defect's area are investigated. The specific features of the manifestation of the exciton luminescence at the condensation in the defect's region is analyzed.

Bose-Einstein condensation and indirect excitons: a review

We review recent progress on Bose-Einstein condensation (BEC) of semiconductor excitons. The first part deals with theory, the second part with experiments. This Review is written at a time where the problem of exciton Bose-Einstein condensation has just been revived by the understanding that the exciton condensate must be dark because the exciton ground state is not coupled to light. Here, we theoretically discuss this missed understanding before providing its experimental support through experiments that scrutinize indirect excitons made of spatially separated electrons and holes. The theoretical part first discusses condensation of elementary bosons. In particular, the necessary inhibition of condensate fragmentation by exchange interaction is stressed, before extending the discussion to interacting bosons with spin degrees of freedom. The theoretical part then considers composite bosons made of two fermions like semiconductor excitons. The spin structure of the excitons is detailed, with emphasis on the crucial fact that ground-state excitons are dark: indeed, this imposes the exciton Bose-Einstein condensate to be not coupled to light in the dilute regime. Condensate fragmentations are then reconsidered. In particular, it is shown that while at low density, the exciton condensate is fully dark, it acquires a bright component, coherent with the dark one, beyond a density threshold: in this regime, the exciton condensate is 'gray'. The experimental part first discusses optical creation of indirect excitons in quantum wells, and the detection of their photoluminescence. Exciton thermalisation is also addressed, as well as available approaches to estimate the exciton density. We then switch to specific experiments where indirect excitons form a macroscopic fragmented ring. We show that such ring provides efficient electrostatic trapping in the region of the fragments where an essentially-dark exciton Bose-Einstein condensate is formed at sub-Kelvin bath temperatures. The macroscopic spatial coherence of the photoluminescence observed in this essentially dark region confirms this conclusion.

Exciton phase transitions in semiconductor quantum wells with disc-shaped electrode

Phase transitions in a system of indirect excitons in semiconductor double quantum wells are studied for a set-up when one of the electrodes is of finite size and, in particular, has the shape of a disc. At voltage a region under the rim of the disc is created where excitons have lower energy, thus providing a macroscopic trap attractive for excitons while being repulsive for charged particles. The theory of the formation of patterns of the excitonic condensed phase under the disc is built based on the assumption of the existence of the inter-exciton range where the interaction between them is attractive. The finite value of the exciton lifetime is taken into account serving as a limiting factor for the size of the islands of the condensed phase. The calculations reveal complex restructuring of the patterns of the spatial distribution of exciton density with increasing pumping intensity: from the structureless gaseous phase to separate islands of the condensed phase within the gaseous phase, then to islands of the gaseous phase in the bulk of the condensed phase and finally to the continuous condensed phase.

Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipole systems

The superfluid to normal fluid transition of dipolar bosons in two dimensions is studied in a broad density range by using path integral Monte Carlo simulations and summarized in the phase diagram. While at low densities we find good agreement with the universal results depending only on the scattering length a{s}, at moderate and high densities the transition temperature is strongly affected by interactions and the excitation spectrum of quasiparticles. The results are expected to be of relevance to dipolar atomic and molecular systems and indirect excitons in quantum wells.

Ordered structures of exciton condensed phases in the presence of an inhomogeneous potential

A theory of the separation of a system of indirect excitons into a condensed and a gaseous phase with the formation of regular patterns of alternating phases in inhomogeneous external fields is developed. The model of spinodal decomposition of phase transitions, generalized for systems of unstable particles, is used. The theory is applied to the study of the non-uniform distribution of the exciton density in a double quantum well under a slot cut in a metallic electrode. It is shown that in a certain range of exciton generation rates a chain of light-emitting islands periodically localized along the slot is developed. With increasing width of the slot, the chain splits into two parallel chains shifted by a half period with respect to each other. By creating a biased external potential along the slot, the periodical pattern could be forced to move along the slot. The effect of the motion of the islands should manifest itself as time oscillations of the intensity of the light emitted from a fixed point.

Gauge-field rotation of an electrically polarized bose condensate by a radial magnetic field

Here it is shown that a condensate of electrically polarized bosons subject to a radial magnetic field must rotate due to the Aharonov-Bohm effect. As in mechanically rotated superfluids, rotation is accompanied by penetration of vortices into the condensate at some critical magnetic field. In the case of a Bose-condensed exciton cloud in a double-quantum well, a necessary electric polarization is provided with spatial separation of electrons and holes forming excitons. Penetration of vortices strongly affects the intensity and the angular distribution of photoluminescence from the exciton cloud. This effect can be used for an experimental manifestation of exciton Bose condensation.