Observable signatures of Hall viscosity in lowest Landau level superfluids

TL;DR

This paper explores how Hall viscosity manifests in lowest Landau level superfluids, proposing observable effects in cold atom experiments and providing a microscopic derivation of their governing equations.

Contribution

It introduces the concept of Hall viscosity in LLL superfluids, linking it to observable phenomena and deriving the relevant equations microscopically.

Findings

Hall viscosity causes vortex dipole rotation.

Wave-speed corrections depend on wave vector.

Hall viscosity is nonuniversal in LLL superfluids.

Abstract

Hall viscosity is a nondissipative viscosity occurring in systems with broken time-reversal symmetry, such as quantum Hall phases and $p+ip$ superfluids. Despite Hall viscosity's expected ubiquity and past observations in: classical soft matter, optical, and graphene systems, it has yet to be measured experimentally in any macroscopic quantum state of matter. Toward this end, we describe the observable effects of Hall viscosity in a simple family of rotating Bose-Einstein condensates of electrically neutral bosons, in which all of the bosons condense into a single lowest Landau level (LLL) orbital. Such phases are accessible to current cold atom experiments, and we dub them LLL superfluids. We demonstrate that LLL superfluids possess a nonuniversal Hall viscosity, leading to a range of observable consequences such as rotation of vortex-antivortex dipoles and wave-vector dependent corrections to the speed of sound. Furthermore, using a coherent state path integral approach, we present a microscopic derivation of the Landau-Ginzburg equations of a LLL superfluid, showing explicitly how Hall viscosity enters.