Dynamical Properties of Quasi-One-Dimensional Boson-Fermion Mixtures of Atoms in a Toroidal Potential

TL;DR

This paper investigates the quantum dynamics of quasi-one-dimensional boson-fermion mixtures in a toroidal trap, highlighting the effects of quantum statistics and correlations beyond mean-field approximations, revealing distinct oscillatory behaviors.

Contribution

It introduces a numerical exact diagonalization approach to study beyond mean-field effects in boson-fermion mixtures in a toroidal potential, emphasizing the role of many-body correlations.

Findings

Bosons show low-frequency oscillations due to many-body correlations.

Fermion oscillations are influenced by boson dynamics through interactions.

Quantum statistics cause distinct dynamical behaviors between bosons and fermions.

Abstract

We theoretically investigate quantum-mechanical dynamics of quasi-one-dimensional boson-fermion mixtures of atomic gases trapped in a toroidal potential, where effective inter-atomic interactions are tunable and affect the dynamics. We especially focus on effects of quantum statistics and many-body correlations beyond the Hartree-Fock (HF) mean-field approximation on the dynamics. In order to predict the dynamics, we utilize the numerical exact diagonalization method and also reproduce the calculation in the HF approximation for comparison. The toroidal gases originally have a rotational symmetry in the toroidal direction. We firstly prepare a deformed ground state as an initial state by adding a weak potential deformed in the toroidal direction, and then remove the potential to start the dynamics. In the dynamics, number densities of the deformed gases exhibit oscillations as demonstrated in the present paper. As a result, we find out that the bosons and fermions show quite different behaviors owing to quantum statistics. In particular, the bosons exhibit a low-frequency oscillation in the strong boson-boson attraction regime owing to the many-body correlations, and it can not be reproduced in the HF approximation. The oscillation of the fermions is strongly influenced by that of the bosons through the boson-fermion interaction as a forced oscillator. In addition, we also discuss a relationship between the low-frequency oscillation and restoration of the broken symmetry.