# Quantum vortex dynamics in two-dimensional neutral superfluids

## TL;DR

This paper develops a quantum theory of vortex dynamics in two-dimensional superfluids, deriving an effective action that includes vortex mass, Magnus force, and dissipation effects, with implications for optical lattice experiments.

## Contribution

It introduces a comprehensive quantum model for vortex motion, extending previous classical descriptions by including environmental quantum fluctuations and their dissipative effects.

## Key findings

- Vortex Magnus force confirmed in the adiabatic limit.
- Vortex mass expression derived from effective action.
- Dissipation in vortex motion can be tuned in optical lattices.

## Abstract

We derive an effective action for the vortex position degree-of-freedom in a superfluid by integrating out condensate phase and density fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius $R$, or the typical distance between vortices, is very much larger than the coherence length $\xi$. We go beyond the adiabatic approximation numerically, accounting for the quantum dynamics of environmental modes and capturing their dissipative coupling to condensate dynamics. For the case of an optical-lattice superfluid we demonstrate that vortex motion damping can be adjusted by tuning the ratio between the tunneling energy $J$ and the on-site interaction energy $U$. We comment on the possibility of realizing vortex Landau level physics.