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

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, and 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 40 K and 87 Rb. 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 the GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relationship 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.

Localization of a Bose-Fermi mixture in a bichromatic optical lattice

“…In Eqs. (1) and (2), we set the transverse oscillator lengths a ⊥B = a ⊥F ≡ a ⊥ and ω ⊥B = ω ⊥F ≡ ω ⊥ , measuring length, energy, and time in units of a ⊥ ,hω ⊥ , and ω −1 ⊥ , respectively [23]. This implies that 2m F = m B , a condition which is roughly satisfied by the 87 Rb-40 K mixture.…”

“…[21] for a cigar-shaped superfluid Bose-Fermi mixture can then be reduced to an effective 1D form by integrating out the dependence on the radial spatial variables [23]. The dynamics of the 1D mixture is described by the dimensionless coupled time-dependent nonlinear equations [23] i ∂u B ∂t = − 1 2…”

“…The bosons and fermions are assumed to interact by a zero-range potential. Within the framework of the densityfunctional theory, a coupled GP-type equation for the mixture can be obtained [21,23].…”

Switch between the Types of the Symmetry Breaking Bifurcation in Optically Induced Photorefractive Rotational Double-Well Potential

“…Among many kinds of nonlinear systems, double-well potential (DWP) or dual-core system is the most essential model employed to study the phase transition and SSB of the nonlinear states [2][3][4][5][6][7][8][9]. In DWP system, the important process relating to the phase transition and SSB is symmetric breaking bifurcation (SBB), which determines the process of symmetric states transiting to the asymmetric ones [10][11][12][13][14][15][16][17]. There are two kinds of SBB, subcritical and super critical, which are tantamount to the phase transition of the first and second kind respectively.…”

Nonlinear modes and symmetry breaking in rotating double-well potentials

“…[1]. Its significance has been later recognized in various physical settings, including numerous ones originating in nonlinear optics [2]- [5], Bose-Einstein condensates (BECs) [6]- [12], and degenerate fermionic gases [13]. A general analysis of the SSB phenomenology was developed too [14], which is closely related to the theory of bifurcations in nonlinear systems [15].…”