Effects of classical noises on atom cooling and trapping

From a Fokker-Planck equation for the evolution of Wigner distribution func tion, the influence of classical noises, classified as additive noise and m ultiplicative noise, on the dynamics of atom in cooling and trapping proces ses is investigated. Our method permits an exact calculation for the case o f harmonic trap which includes dissipation and noises simultaneously. It is found that the average energy heated by the noises does not increase simpl y in an exponential manner as predicted by Savard et al. (T.A. Savard, K.M. O'Hara, J.E. Thomas, Phys. Rev. A 56 (1997) R1095) based on the quantum me chanical first-order time-dependent perturbation theory. For some noise str engths, the average energy can increase much faster, especially at the begi nning stage of evolution. We consider the disagreement between our results and theirs is due to the violation of the Virial theorem in the nonequilibr ium process. The previous treatment actually implies the Virial theorem. On the other hand, an estimate shows that a nonharmonic trap is more sensitiv e to classical noises than a harmonic one. Furthermore, it is found that th e atom momentum fluctuations in three directions can become correlated due to their coupling to the same noise reservoir. (C) 2001 Elsevier Science B. V. All rights reserved.