  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.
