Rate Equations for Sympathetic Cooling of Trapped Bosons or Fermions

Details Rate Equations for Sympathetic Cooling of Trapped Bosons or Fermions Rate Equations for Sympathetic Cooling of Trapped Bosons or Fermions

2001-06-20

arxiv.org/abs/cond-mat/0106418v1

Phys. Rev. A. 65 (2002) 043601

Physics

Condensed Matter

Soft Condensed Matter

36 pages, 4 EPS-figures

Scientific paper

10.1103/PhysRevA.65.043601

We derive two different sets of rate equations for sympathetic cooling of harmonically trapped Bosons or Fermions. The rate equations are obtained from a master equation derived earlier by Lewenstein et al. [Phys. Rev. A 51 (1995) 4617] by means of decoherence and ergodicity arguments. We show analytically that the thermal equilibrium state is a stationary solution of our rate equation. We present analytical results for the rate coefficients which are needed to solve the rate equations, and we give approximate formulae that permit their computation in practice. We solve the two sets of rate equations numerically and compare the results. The cooling times obtained in both approaches agree very well. The equilibration rates show fair agreement.

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