Quantum dynamics of evaporatively cooled Bose-Einstein condensates

Evaporative cooling has been successfully used to produce Bose-Einstein condensates ~BEC’s! inside magnetooptic traps with neutral atoms @1#. A number of questions arise as to the quantum state that is achieved, since this involves both the dynamics of the cooling process and the applicability of the ergodic hypothesis. Atom-atom interactions have a strong influence on the cooling process and the final state in these experiments. Quantum fluctuations are important in determining atom laser coherence properties @2#, especially since the experimental systems do not have as large a particle number as traditional condensed matter experiments. However, there is no guarantee that a canonical ensemble will result from evaporative cooling, as the observations are made in a transient, nonequilibrium phase. Thus, conventional canonical methods may not be applicable to these experiments. In this paper, we report the use of phase-space methods for direct quantum-dynamical calculations of the cooling and formation of Bose-Einstein condensates on a threedimensional lattice. The results are restricted as yet to small condensates, due to the large numbers of modes involved. The computational results are very similar to those observed experimentally. In particular, we find quantum evaporative cooling, followed by a clear transition to a condensate. This is strongly influenced by nonclassical features of the quantum dynamics. The calculations indicate additional structure, which we interpret as spontaneous formation of vortices—a process of much wider interest in other fields of physics @3#. These appear to originate in the residual orbital angular momentum of the trapped atoms, which was neglected in previous studies, and would provide a significant test of the present theory. Earlier calculations of cooling dynamics have usually treated the cooling process either classically @4,5#, or have used various additional assumptions about the quantum states involved. This leads to the question of how to handle the transition to the final quantum dominated condensate, which is often assumed to be a canonical ensemble at a temperature estimated from the classical theory. The final ensemble behavior is then usually calculated from the meanfield Gross-Pitaevskii equations @6#, although some attempts have been made to go beyond this @7#, including treatment of the kinetics of condensation @8,9# based on a master equation. However, small atom traps are neither in the thermodynamic limit, nor necessarily in a steady state. A firstprinciples theory is really needed, to provide a benchmark