Dipole Oscillations in Fermionic Mixtures

TL;DR

This paper analyzes dipole oscillations in fermionic mixtures using the Boltzmann equation, classifies solutions via eigenvalues, and applies the method to multi-component systems with realistic experimental parameters.

Contribution

It introduces a classification method for dipole oscillations based on eigenvalue analysis and applies it to multi-component fermionic mixtures with explicit calculations.

Findings

Eigenvalue-based classification of oscillation modes

Application to two- and three-component mixtures

Explicit results for realistic experimental setups

Abstract

We study dipole oscillations in a general fermionic mixture: starting from the Boltzmann equation, we classify the different solutions in the parameter space through the number of real eigenvalues of the small oscillations matrix. We discuss how this number can be computed using the Sturm algorithm and its relation with the properties of the Laplace transform of the experimental quantities. After considering two components in harmonic potentials having different trapping frequencies, we study dipole oscillations in three-component mixtures. Explicit computations are done for realistic experimental setups using the classical Boltzmann equation without intra-species interactions. A brief discussion of the application of this classification to general collective oscillations is also presented.