Quantum statistics of an ideal gas of Bose particles predicts a phase boundary for Bose-Einstein condensation. The expected relation for the saturated-gas density, n =CT 3/2 , is observed for an exciton gas in CU2O by time resolution of the energy spectrum.PACS numbers: 71.35. +Z, 05.30.-d, 67.90,+z, 78.47.+p More than sixty years after Einstein originally considered the case of an ideal gas of noninteracting Bose particles, 1 experimental verification of its quantumstatistical properties remains a challenging task. In such a system, consisting of free particles with integral spin, Bose-Einstein (BE) statistics requires an excited-state occupation number of the form f (E,p, y where E is the single-particle kinetic energy and T is the gas temperature. The chemical potential n is determined by the condition N=$~f (E,ii,T)D(E) xdE, where TV is the number of particles in excited states in volume K, and D(E)ocVE I/2 is the density of states. /1 is large and negative at low density, and approaches zero as the number of particles is increased. At a given T and V the number of particles in excited states cannot exceed a certain critical value, because the above integral is finite even at ju =0, the maximum allowable value. The critical density for this excited-state saturation at ju = 0 is given bywhere m is the particle mass and g is the spin degeneracy. According to Einstein, once the population of the excited states reaches this saturation condition, further addition of particles at constant T and V must be accommodated by the ground state-Bose-Einstein condensation (BEC). For some time it has been recognized that excitons in semiconductors may provide a test of BE quantum statistics. 2 " 4 The exciton, or bound electron-hole pair, has several desirable properties: (1) Its mass is much smaller than that of an atom or molecule, thus requiring much lower n c for a given T\ (2) the excitonic-gas density can be controlled over a wide range by changing opticalexcitation level; and (3) in many cases the excitonic gas emits a recombination luminescence which directly reflects the kinetic-energy distribution in the gas. Degenerate BE statistics have been reported for excitons in Ge 5 and biexcitons in CuCl. 6 In the latter case, a stable macroscopic occupation of low-energy states was observed by resonant pumping of these states above a critical threshold in excitation power.One of the most promising systems for the study of an ideal Bose gas involves excitons in CU20. 2 Hulin, Mysyrowicz, and BenoTt a la Guillaume 7 have reported a gradual transition from classical to degenerate Bose statistics for orthoexcitons in CU2O generated by a nonresonant laser, on the basis of a spectral analysis of the time-integrated luminescence from these excitons. With increasing laser intensity, both particle density and temperature of the excitonic gas increased, and the system appeared to approach n c (T) asymptotically.In this Letter, we report a study of time-and spaceresolved luminescence of orthoexcitons in CU2O. This technique pro...
