A pr 1 99 7 Critical velocities in exciton superfluidity

The presence of exciton phonon interactions is shown to play a key role in the exciton superfluidity. We apply the Landau criterion for an exciton-phonon condensate moving uniformly at zero temperature. It turns out that there are essentially two critical velocities in the theory. Within the range of these velocities the condensate can exist only as a bright soliton. The excitation spectrum and differential equations for the wave function of this condensate are derived. The problem of critical velocities in the theory of superfluidity arose a long time ago when the experiments with the liquid He showed a substantial discrepancy with quantum-mechanical predictions. Later, the effect was analyzed and its phenomenological description was given (e.g. see [1]). The fact that the liquid He could not be treated as a weakly non-ideal Bose gas was believed to be the main reason for inconsistency of microscopic theory with experimental data. For a long time He has been the only substance where the superfluidity can be observed. The recent experiments with the dilute gas of excitons [2], [3] provide new possibilities for studying different types of superfluidity. In this series of experiments the Cu 2 O crystal was irradiated with laser light pulses of several ns duration. At low intensities of the laser beam (low concentration of excitons) the system revealed a typical diffusive behavior of exciton gas. Once the intensity of the beam exceeds some value, the majority of particles move together in the packet. Their common propagation velocity is close to the longitudinal sound velocity, and the packet evolves as a bright soliton. Some alternative explanations of the phenomena are known. One of them [2] implies that the bright soliton is a one-dimensional traveling wave which satisfies the Gross-Pitaevsky (nonlinear Schrödinger) equation [5] for the Bose-condensate wave function Ψ(x, t) i¯ h ∂Ψ ∂t = − ¯ h 2 2m ∆Ψ + νΨ * Ψ 2 (1) with attractive potential of exciton-exciton interaction ν < 0.