We analyze the spontaneous symmetry breaking (SSB) induced by one specific component of a linearly coupled binary Bose-Einstein condensate (BEC). The model is based on linearly coupled Schrödinger equations with cubic nonlinearity and with a double-well (DW) potential acting on only one of the atomic components. By numerical simulations, symmetric and asymmetric ground-states were obtained, and an induced asymmetry in the partner field was observed. In this sense, we properly demonstrated that the linear coupling mixing the two-field component (Rabi coupling) promotes the (in)balance between atomic species, as well as the appearance of the Josephson and SSB phases.
We analyze the spontaneous symmetry breaking (SSB) induced by one specific component of a linearly coupled binary Bose-Einstein condensate (BEC). The model is based on linearly coupled Schrödinger equations with cubic nonlinearity and with a double-well (DW) potential acting on only one of the atomic components. By numerical simulations, symmetric and asymmetric ground-states were obtained, and an induced asymmetry in the partner field was observed. In this sense, we properly demonstrated that the linear coupling mixing the two-field component (Rabi coupling) promotes the (in)balance between atomic species, as well as the appearance of the Josephson and SSB phases.
We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta functions, a fully analytical solution is obtained for symmetric, antisymmetric, and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.
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 40K and 87Rb. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture, NF and NB, and by phase diagrams in the (NF,NB) 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 NF and NB, 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.
We investigate an attractive atomic Bose-Einstein condensate (BEC) trapped by a double-well potential in the axial direction and by a harmonic potential in the transverse directions. We obtain numerically a quantum phase diagram which includes all the three relevant phases of the system: Josephson, spontaneous symmetry breaking (SSB), and collapse. We consider also the coherent dynamics of the BEC and calculate the frequency of population-imbalance mode in the Josephson phase and in the SSB phase up to the collapse. We show that these phases can be observed by using ultracold vapors of 7Li atoms in a magneto-optical trap.
Models of two-dimensional (2D) traps, with double-well structure in the third direction, for Bose-Einstein condensates are introduced with attractive or repulsive interactions between atoms. The models are based on systems of linearly coupled 2D Gross-Pitaevskii equations, where the coupling accounts for tunneling between the wells. Each well carries an optical lattice (OL) (stable 2D solitons cannot exist without OLs). The linear coupling splits each finite band gap in the spectrum of the single-component model into two subgaps. The main subject of the work is spontaneous symmetry breaking (SSB) in two-component 2D solitons and localized vortices (SSB was not considered before in 2D settings). Using variational approximation (VA) and numerical methods, we demonstrate that, in a system with attraction or repulsion, SSB occurs in families of symmetric or antisymmetric solitons (or vortices), respectively. The corresponding bifurcation destabilizes the original solution branch and gives rise to a stable branch of asymmetric solitons or vortices. The VA provides for an accurate description of the emerging branch of asymmetric solitons. In the model with attraction, all stable branches eventually terminate due to the onset of collapse. Stable asymmetric solitons in higher finite band gaps and vortices with a multiple topological charge are found too. The models also give rise to first examples of embedded solitons and embedded vortices (the states located inside Bloch bands) in two dimensions. In the linearly coupled system with opposite signs of the nonlinearity in the two cores, two distinct types of stable solitons and vortices are found, dominated by either the self-attractive component or the self-repulsive one. In the system with a mismatch between the two OLs, a pseudobifurcation is found: when the mismatch attains its largest value $(\ensuremath{\pi})$, the bifurcation does not happen, as branches of different solutions asymptotically approach each other, but fail to merge.
In this paper we investigate the existence of Anderson localization induced by one specific component of a binary Bose-Einstein condensate (BEC). We use a mean-field approach, in which each type of particle of the BEC is considered as a specific field, and we consider that only one kind of particle is subject to a quasiperiodic potential, which induces a localization in the partner field. We assume the system is under a Rabi coupling, i.e., a linear coupling mixing the two-field component, and we investigate the conditions associated with the parameter values of the system for observing the localization. Numerical simulations are performed, confirming the existence of Anderson localization in the partner field.
We report results of an analysis of the spontaneous symmetry breaking (SSB) in a basic (actually, simplest) model that is capable of producing the SSB phenomenology in a one-dimensional setting. It is based on the Gross-Pitaevskii-nonlinear Schrödinger equation with the cubic self-attractive term and a double-well potential built as an infinitely deep potential box split by a narrow (δ functional) barrier. The barrier's strength ɛ is the single free parameter of the scaled form of the model. It may be implemented in atomic Bose-Einstein condensates and nonlinear optics. The SSB bifurcation of the symmetric ground state (g.s.) is predicted analytically in two limit cases, viz., for deep or weak splitting of the potential box by the barrier (ɛ≫1 or ɛ≪1, respectively). For the generic case, a variational approximation (VA) is elaborated. The analytical findings are presented along with systematic numerical results. The stability of stationary states is studied through the calculation of eigenvalues for small perturbations and by means of direct simulations. The g.s. always undergoes the SSB bifurcation of the supercritical type, as predicted by the VA at moderate values of ɛ, although the VA fails at small ɛ, due to inapplicability of the underlying ansatz in that case. However, the latter case is correctly treated by the approximation based on a soliton ansatz. On top of the g.s., the first and second excited states are studied too. The antisymmetric mode (the first excited state) is destabilized at a critical value of its norm. The second excited state undergoes SSB bifurcation, like the g.s., but, unlike it, the bifurcation produces an unstable asymmetric mode. All unstable modes tend to spontaneously reshape into the asymmetric g.s.