Berry Phase Effects on the Dynamics of Quasiparticles in a Superfluid with a Vortex

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms’ momentum distribution around a vortex.

Figure 1

Thermal-atom momentum distribution around a trapped vortex. Length scales are in units of $l=0.73\mu \mathrm{m}$ for a ${\mathrm{Rb}}^{87}$ BEC in a trap specified in the text. (a) A schematic plot of experimental geometry. Measurement of thermal-atom momentum distribution is to be made in a region $S$ at 100 unit lengths away from the vortex center with a radius of 20 unit lengths. This region contains about 9740 condensate and 1650 thermal atoms. (b) Condensate atom density (multiplied by the interaction strength $g$) in the presence of a trapped vortex. (c) Density of states for quasiparticles in the measurement region $S$ as a function of quasiparticle momentum $q_c$ along the circulation flow. (d) Momentum distribution of thermal atoms in the measurement region $S$. Dotted and dashed lines correspond to our Eq. (14) and the naive expression ${\int }_{S}d{\mathbf{r}}_c\rho /[\exp (\frac{{\omega }_c+{\mathbf{q}}_c·\nabla \theta }{k_{B}T})-1]$, respectively. For reference, the momentum of condensate atoms is indicated by the vertical solid line.