Collective excitations of a trapped boson-fermion mixture across demixing

TL;DR

This paper investigates how collective excitations in a trapped boson-fermion mixture change as the system approaches demixing, revealing a softening and sharp upturn in mode frequencies that signal a quantum phase transition.

Contribution

It provides a detailed analysis of collective mode behavior across the demixing transition in a confined boson-fermion mixture, including an analytical expression for the transition point.

Findings

Collective mode frequencies soften near demixing transition

A sharp upturn in frequencies indicates the quantum phase transition

Proposed a simple analytical expression for the transition point

Abstract

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.