XBEC · Exploring Bose-Einstein Condensation of Excitons and Related Quantum Phases

Exploring Bose-Einstein Condensation of Excitons and Related Quantum Phases

The X-BEC project envisioned a route to provide unambiguous signatures for excitons Bose-Einstein condensation. Excitons are composite bosons made of an electron and hole bound by Coulomb attraction. Their condensation was originally proposed in the 1960's, and excitons were actually initially considered very promising candidates because they benefit from a light effective mass leading to a cryogenically accessible critical temperature for the condensation, i.e. of around 1 Kelvin. However, excitons Bose-Einstein condensation had since then a rather controversial history, made of claims and denials, whereas atomic gases could remarkably demonstrate Bose-Einstein condensation in tour-de-force experiments where vapors are laser cooled to nano-Kelvin temperatures under ultra-high vacuum conditions. To reveal Bose-Einstein condensation the project has emphasized so-called spatially indirect excitons engineered in double GaAs quantum wells, where electrons and holes are spatially separated. As a result, indirect excitons benefit from a long effective lifetime, greater than 100 ns, allowing them to reach thermodynamic equilibrium. Also, indirect excitons experience repulsive dipolar interactions that prevent a collapse of cold phases in an electron-hole plasma. Importantly, within the course of the project we have developed model electrostatic traps, where cold exciton gases are deterministically confined. Such traps are directly obtained by depositing an array of metallic electrodes at the surface of a device embedding a double quantum well. Thus, relying on the interaction between the excitons dipole and the applied field, arbitrary trap geometries are realized. Within X-BEC we have mostly studied parabolic confinement profiles, of around 10 microns dimensions. Thus, in a series of experiments started in 2015-2016 we have provided unambiguous signatures for excitons quantum condensation and subsequent superfluidity. At first we have evidenced that the photoluminescence radiated by a trapped exciton gas darkens below a critical temperature of about 1K, and for a narrow range of densities only. This striking behavior actually marks a quantum statistical population of excitons in the lowest energy states, where Bose-Einstein condensation is expected, and which are optically dark. This occupation is then non-classical because the energy splitting between bright and dark states amounts to only a few micro-eV in double quantum wells, i.e. at least 10 times less than the thermal energy at 1K. According to theoretical models that have been carried out within the project, the darkening of the photoluminescence emission shall actually signal the buildup of a so-called gray condensate of excitons, where a dominant fraction of dark excitons is coherently coupled to a weaker population of bright excitons. The latter component of the condensate is then of crucial importance, because it radiates the photoluminescence that carries the quantum signatures of the many-body state. The gray nature of the condensation, i.e. the coherent coupling between dark and bright excitons, has then been confirmed using spatial interferometry. Thus, we have shown that the weak photoluminescence radiated in the regime of quantum darkening exhibits macroscopic (quantum) spatial coherence, below the same critical temperature of about 1 K and for the same narrow density range. Finally, by analyzing the spatial profile of the photoluminescence and its spatial coherence, we have detected quantized vortices in the regime where a trapped gas has undergone quantum condensation. Remarkably, this observation provides a direct signature for a superfluid character of the exciton condensate, and paves the way towards studies of many-body problems well beyond the original proposal, for instance the study of the Berezinskii-Kosterlitz-Thouless crossover in the solid-state, i.e. the singular nature of the superfluid transition for two-dimensional systems.

Data: CORDIS, © European Union