Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

TL;DR

This paper investigates the spontaneous symmetry breaking in Bose-Fermi mixtures within double-well potentials, revealing conditions under which symmetry breaking occurs and providing analytical and numerical insights into the ground states and dynamics.

Contribution

It demonstrates the possibility of symmetry breaking in Bose-Fermi mixtures with attractive interactions, using a coupled GPE and density functional model, including analytical approximations.

Findings

Symmetry breaking occurs in mixtures with attractive boson-fermion interactions.

Phase diagrams show regions of symmetric and asymmetric ground states.

Analytical approximation via Thomas-Fermi reduces the model to a single effective equation.

Abstract

We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi (BF) mixture in a double-well potential (DWP). The mixture is described by the Gross-Pitaevskii equation (GPE) for the bosons, coupled to an equation for the order parameter of the Fermi superfluid, which is derived from the respective density functional in the unitarity limit (a similar model applies to the BCS regime too). Straightforward SSB in the degenerate Fermi gas loaded into a DWP is impossible, as it requires an attractive self-interaction, while the intrinsic nonlinearity in the Fermi gas is repulsive. Nonetheless, we demonstrate that the symmetry breaking is possible in the mixture with attraction between fermions and bosons, like 40K and 87Rb. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture, N_F and N_B, and by phase diagrams in the (N_F,N_B) plane, which displays regions of symmetric and asymmetric ground states. The dynamical picture of the SSB, induced by a gradual transformation of the single-well potential into the DWP, is reported too. An analytical approximation is proposed for the case when GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relation between N_F and N_B, the TF approximation allows us to reduce the model to a single equation for the fermionic function, which includes competing repulsive and attractive nonlinear terms. The latter one directly displays the mechanism of the generation of the effective attraction in the Fermi superfluid, mediated by the bosonic component of the mixture.