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arXiv:1212.5568 · Physical Review A

Symmetry breaking in dipolar matter-wave solitons in dual-core couplers

Yongyao Li, Jingfeng Liu, Wei Pang, Boris A. Malomed

Published Jan 7, 2013• 28 citations
arXivHTMLPDF

Abstract

We study the effects of spontaneous symmetry breaking (SSB) in solitons composed of a dipolar Bose-Einstein condensate trapped in a dual-core system with dipole-dipole interactions (DDIs) and hopping between the cores. Two realizations of such a matter-wave coupler are introduced: weakly and strongly coupled. The former is based on two parallel pipe-shaped traps, whereas the latter is represented by a single pipe sliced by an external field into parallel layers. The dipoles are oriented along the axes of the pipes. In these systems, the dual-core solitons feature SSB of the supercritical and subcritical types, respectively. Stability regions are identified for symmetric and asymmetric solitons and nonbifurcating antisymmetric solitons, as well as for symmetric flat states, which may also be stable in the strongly coupled system due to competition between the attractive and repulsive intracore and intercore DDIs. The effects of the contact interactions are considered too. Collisions between moving asymmetric solitons in the weakly symmetric system feature an elastic rebound, a merger into a single breather, and passage accompanied by excitation of intrinsic vibrations of the solitons for small, intermediate, and large collision velocities, respectively. A $\mathcal{PT}$-symmetric version of the weakly coupled system is considered briefly, which may be relevant for matter-wave lasers. Stability boundaries for $\mathcal{PT}$-symmetric and -antisymmetric solitons are identified.

DOI
10.1103/physreva.87.013604

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We study the effects of spontaneous symmetry breaking (SSB) in solitons composed of a dipolar Bose-Einstein condensate trapped in a dual-core system with dipole-dipole interactions (DDIs) and hopping between the cores. Two realizations of such a matter-wave coupler are introduced: weakly and strongly coupled. The former is based on two parallel pipe-shaped traps, whereas the latter is represented by a single pipe sliced by an external field into parallel layers. The dipoles are oriented along the axes of the pipes. In these systems, the dual-core solitons feature SSB of the supercritical and subcritical types, respectively. Stability regions are identified for symmetric and asymmetric solitons and nonbifurcating antisymmetric solitons, as well as for symmetric flat states, which may also be stable in the strongly coupled system due to competition between the attractive and repulsive intracore and intercore DDIs. The effects of the contact interactions are considered too. Collisions between moving asymmetric solitons in the weakly symmetric system feature an elastic rebound, a merger into a single breather, and passage accompanied by excitation of intrinsic vibrations of the solitons for small, intermediate, and large collision velocities, respectively. A PT\mathcal{PT}PT-symmetric version of the weakly coupled system is considered briefly, which may be relevant for matter-wave lasers. Stability boundaries for PT\mathcal{PT}PT-symmetric and -antisymmetric solitons are identified.
We study the spontaneous symmetry breaking of dipolar Bose–Einstein condensates trapped in stacks of two-well systems, which may be effectively built as one-dimensional trapping lattices sliced by a repelling laser sheet. If the potential wells are sufficiently deep, the system is modeled by coupled discrete Gross–Pitaevskii equations with nonlocal self- and cross-interaction terms representing dipole–dipole interactions. When the dipoles are not polarized perpendicular or parallel to the lattice, the crossinteraction is asymmetric, replacing the familiar symmetric two-component solitons with a new species of cross-symmetric or -asymmetric ones. The orientation of the dipole moments and the interwell hopping rate strongly affect the shapes of the discrete two-component solitons as well as the characteristics of the cross-symmetry breaking and the associated phase transition. The sub- and super-critical types of cross-symmetry breaking can be controlled by either the hopping rate between the components or the total norm of the solitons. The effect of the interplay between the contact nonlinearity and the dipole angle on the cross-symmetry breaking is also discussed.
We consider a dipolar Bose-Einstein condensate trapped in an array of two-well systems with an arbitrary orientation of the dipoles relative to the system's axis. The system can be built as a chain of local traps sliced into two parallel lattices by a repelling laser sheet. It is modeled by a pair of coupled discrete Gross-Pitaevskii equations, with dipole-dipole self-interactions and cross interactions. When the dipoles are not polarized perpendicular or parallel to the lattice, the cross interaction is asymmetric, replacing the familiar symmetric two-component discrete solitons by two new species of cross-symmetric ones, viz., on-site- and off-site-centered solitons, which are strongly affected by the orientation of the dipoles and separation between the parallel lattices. A very narrow region of intermediate asymmetric discrete solitons is found at the boundary between the on- and off-site families. Two different types of solitons in the PT-symmetric version of the system are constructed too, and stability areas are identified for them.
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 band gaps 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, bistability 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, $\ensuremath{\Delta}$, between the OLs in the two cores is also studied. It is concluded that $\ensuremath{\Delta}=\ensuremath{\pi}∕2$ only mildly deforms the picture, while $\ensuremath{\Delta}=\ensuremath{\pi}$ changes it drastically, replacing the symmetry-breaking bifurcations by pseudobifurcations, 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 interspecies nonlinear interaction becomes stronger than the intraspecies nonlinearity.
We study stationary states of a two-dimensional (2D) Bose-Einstein condensate with both attractive and repulsive nonlinearities in a combination of a double-square-well potential in one direction and a perpendicular optical lattice. We look for dual-core solitons in this configuration, focusing on their symmetry-breaking bifurcations. For attractive interactions, without the lattice, a similar analysis was performed [M. Matuszewski et al., Phys. Rev. A 75, 063621 (2007)], where subcritical bifurcation transforming antisymmetric gap solitons into asymmetric ones was found. Here we focus on the effect of an optical lattice and the so created gap solitons. We discover that a phase transition occurs when the lattice depth increases and the additional dimension becomes strongly suppressed. The bifurcation type changes from subcritical (typical for a 2D system, with hysteresis) to supercritical (typical for a one-dimensional system). An additional advantage of the lattice is that gap solitons exist even for repulsive interactions. In this case we also discover bifurcation of a supercritical type. The analysis is based on a variational approximation, which is surprisingly well verified by numerical results.
We investigate an attractive Bose-Einstein condensate in two coupled one dimensional channels. In this system a stable double channel soliton can be formed. It is symmetric for small interaction parameters and asymmetric for large ones. We study this symmetry breaking phenomenon in detail. Next, we investigate the dynamics of symmetric double channel soliton collisions. For sufficiently strong interactions we observe spontaneous symmetry breaking during the collision. Approximate considerations based on two different methods, Bogoliubov and variational, are used to describe this effect. The results are compatible.
We analyze the symmetry breaking of matter-wave solitons in a pair of cigar-shaped traps coupled by tunneling of atoms. The model is based on a system of linearly coupled nonpolynomial Schr\"odinger equations. Unlike the well-known spontaneous-symmetry-breaking (SSB) bifurcation in coupled cubic equations, in the present model the SSB competes with the onset of collapse in this system. Stability regions of symmetric and asymmetric solitons, as well as the collapse region, are identified in the system's parameter space.