Quantum nucleation of phase slips in Bose-Einstein condensates

We present a theoretical study of quantum fluctuations in a Bose-Einstein condensate confined within a thin cylindrical trap and perturbed by a moving impurity. We derive an effective action which maps the problem to that of a massive particle with damping in a periodic potential. Quantum fluctuations lead to a finite nucleation rate of phase slips and we make use of known results in our determination of the transport characteristic. Real Bose-Einstein condensate are finite systems and exhibit interesting effects depending on topology: in superfluid rings we obtain a critical velocity below which the nucleation rate is quenched. In a cigar shaped condensate the low-energy action is equivalent to that of a capacitively shunted Josephson junction. The state with a well defined phase difference across the impurity then is unstable towards a decoupled state with a fixed number of particles on either side of the impurity.