Phenomenological Theory of Mode Collapse-revival in Confined Bose Gas

Abstract

A phenomenological theory of mode collapse-revival for a system with a weak nonlinearity is presented. The theory takes into account fluctuations of the number n of quanta of oscillations. The collapse time $τ_c ^{-1}$ for a mode of frequency $ω_0$ turns out to be $ω_0(\sqrt{n/2}\hbar ω_0 \mid ν\mid)$, where νis a coefficient in a nonlinear correction to the mode frequency with respect to the oscillation energy E. For a Bose gas in a harmonic trap $τ_c$ is order of $ω_0^{-1}\sqrt{μN/E\hbar ω_0}$. This value is order of 250 ms. for typical experimental conditions. The coefficient νis calculated for the breathing mode in an isotropic trap.