Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Abstract

We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bi-stability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in both AA and RR systems, are found too. The impact of a phase mismatch, ∆, between the OLs in the two cores is also studied. It is concluded that ∆ = π/2 only mildly deforms the picture, while ∆ = π changes it drastically, replacing the symmetry-breaking bifurcations by pseudo-bifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the inter-species nonlinear interaction becomes stronger than the intra-species nonlinearity.

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].…”

“…Both the Josephson and self-trapping regimes were implemented in the atomic condensate with contact repulsive interactions [11]. The SSB was also analyzed in one-and two-dimensional (1D and 2D) models of BEC trapped in dual-core configurations [12].…”

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

“…In particular, the symmetry breaking of matter-wave solitons was predicted in various twodimensional (2D) DWP settings [17], including the spontaneous breaking of the skew symmetry of solitons and solitary vortices trapped in double-layer condensates with mutually perpendicular orientations of quasi-one-dimensional optical lattices induced in the two layers [19]. A different variety of the two-dimensional (2D) geometry, which gives rise to a specific mode of the SSB, is based on a symmetric set of four potential wells [20] (a three-well system was considered, too [21]).…”

“…[16] and references therein). As concerns the interpretation of the SSB as the phase transition, it may be categorized as belonging to the first or second kind (known as the sub-or supercritical SSB modes), depending on the form of the nonlinearity, spatial dimension, and the presence or absence of a periodic external potential (an optical lattice) acting along the additional spatial dimension (if any) [17]. In the experiment, the self-trapping of asymmetric states has been demonstrated in the condensate of 87 Rb atoms with repulsive interactions [18].…”

Multiple Fluxon Analogues and Dark Solitons in Linearly Coupled Bose–Einstein Condensates

“…spontaneous symmetry breaking were analyzed in [17] when BECs are loaded in two parallel quasi-one-dimensional traps fitted with optical lattices. Before the experimental birth of BEC, the similar settings have been used in the study of stable defects in nonlinear patterns known as optical domain walls [18].…”