Correlations and synchronization in a Bose-Fermi mixture

TL;DR

This paper develops a mean-field framework to analyze correlations and synchronization in a Bose-Fermi mixture across different fermionic regimes, deriving reduced equations and studying ground state properties and dynamics.

Contribution

It introduces a variational approximation-based method to derive 1D and 2D coupled equations for Bose-Fermi mixtures, including interaction effects and fermionic regimes.

Findings

Correlations depend strongly on inter-species interaction sign and strength.

Fermionic component significantly influences correlations, especially in the unitarity regime.

VA results agree well with full numerical solutions.

Abstract

We study a Bose-Fermi mixture within the framework of the mean-field theory, including three possible regimes for the fermionic species: fully polarized, BCS, and unitarity. Starting from the 3D description and using the variational approximation (VA), we derive 1D and 2D systems of equations, under the corresponding confining potentials. This method produces a pair of nonlinear Schr\"{o}dinger (NLS) equations coupled to algebraic equations for the transverse widths of the confined state. The equations incorporate interactions between atoms of the same species and between the species, assuming that the latter can be manipulated by means of the Feshbach resonance (FR). As an application, we explore spatial density correlations in the ground state (GS) between the species, concluding that they strongly depend on the sign and strength of the inter-species interaction. Also studied are the dynamics of the mixture in a vicinity of the GS and the corresponding spatiotemporal inter-species correlation. The correlations are strongly affected by the fermionic component, featuring the greatest variation in the unitary regime. Results produced by the VA are verified by comparison with full numerical solutions.