Hydrodynamic collective modes for cold trapped gases

TL;DR

This paper explores how collective oscillation frequencies in cold trapped gases can serve as precise tests for quantum many-body theories, accounting for interactions, dimensionality, and thermal effects, with potential experimental applications.

Contribution

It provides a general framework to calculate collective modes for quantum gases with arbitrary equations of state in the hydrodynamic regime, including numerical methods and exact solutions.

Findings

Eigenvalues of a differential operator determine oscillation frequencies.

Exact solutions for harmonic traps and specific equations of state.

Method to excite and measure different eigenmodes experimentally.

Abstract

We suggest that collective oscillation frequencies of cold trapped gases can be used to test predictions from quantum many-body physics. Our motivation lies both in rigid experimental tests of theoretical calculations and a possible improvement of measurements of particle number, chemical potential or temperature. We calculate the effects of interaction, dimensionality and thermal fluctuations on the collective modes of a dilute Bose gas in the hydrodynamic limit. The underlying equation of state is provided by non-perturbative Functional Renormalization Group or by Lee--Yang theory. The spectrum of oscillation frequencies could be measured by response techniques. Our findings are generalized to bosonic or fermionic quantum gases with an arbitrary equation of state in the two-fluid hydrodynamic regime. For any given equation of state P(\mu,T) and normal fluid density n_n(\mu,T) the collective oscillation frequencies in a $d$-dimensional isotropic potential are found to be the eigenvalues of an ordinary differential operator. We suggest a method of numerical solution and discuss the zero-temperature limit. Exact results are provided for harmonic traps and certain special forms of the equation of state. We also present a phenomenological treatment of dissipation effects and discuss the possibility to excite the different eigenmodes individually.