Acceleration of quasi-particle modes in Bose-Einstein condensates

Phys. Lett. A 248, p. 290 (1998)     cond-mat/9807002    

Bose-Einstein condensates can well be described by a nonlinear Schrödinger equation. Once a special solution of this equation is known, one can introduce the concept of quasi-particle modes which are small perturbations around the original solution. The problem of determining their time evolution can - after some manipulations - be reduced to solving the equation

i df/dt = [p2 (c2 - V(x)/M) ]1/2 f(x,t)

where c denotes the sound velocity in the condensate, p = -i d/dx is a momentum operator, and V(x) is the potential confining the condensate.

In the special case that V(x) = -M a x is a linear potential one can expand the right-hand-side above in orders of the acceleration a. To first order one roughly finds

i df/dt = c |p| {1+ a x/(2 c2)} f(x,t)

The solution of this equation demonstrates that quasi-particles behave quite different from ordinary particles. In particular, we found that the acceleration affects the quasi-particle velocity only half as strong as usual. Even more remarkably is that the operator p is not shifted with time as usual [p(t) = p + M a t], but that it is subject to a squeezing transformation:

p(t) = p exp{at/(2c)}

Thus, quasi-particle wavepackets evolve quite different as ordinary wavepackets:

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