Transition to a Bose-Einstein condensate of excitons at sub-Kelvin temperatures

Abstract

Bose-Einstein condensation (BEC) is a quantum mechanical phenomenon directly linked to the quantum statistics of bosons. While cold atomic gases provide a new arena for exploring the nature of BEC, a long-term quest to confirm BEC of excitons, quasi-Bose particles formed as a bound state of an electron-hole pair, has been underway since its theoretical prediction in the 1960s. Ensembles of electrons and holes are complex quantum systems with strong Coulomb correlations; thus, it is non-trivial whether nature chooses a form of exciton BEC. Various systems have been examined in bulk and two-dimensional semiconductors and also exciton-photon hybrid systems. Among them, the 1s paraexciton state in a single crystal of Cu2O has been a prime candidate for realizing three-dimensional BEC. The large binding energy and long lifetime enable preparation of cold excitons in thermal equilibrium with the lattice and decoupled from the radiation field. However, collisional loss severely limits the conditions for reaching BEC. Such a system with a large inelastic cross section is excluded in atomic BEC experiments, where a small inelastic scattering rate and efficient elastic scattering are necessary for evaporative cooling. Here we demonstrate that it is nevertheless possible to achieve BEC by cooling paraexcitons to sub-Kelvin temperatures in a cold phonon bath. Emission spectra from paraexcitons in a three-dimensional trap show an anomalous distribution in a threshold-like manner at the critical number of BEC expected for ideal bosons. Bosonic stimulated scattering into the condensate and collisional loss compete and limit the condensate to a fraction of about 1%. This observation adds a new class of experimentally accessible BEC for exploring a rich variety of matter phases of electron-hole ensembles.