Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices

Abstract

Models of two-dimensional (2D) traps, with the double-well structure in the third direction, for Bose-Einstein condensate (BEC) are introduced, with attractive or repulsive interactions between atoms. The models are based on systems of linearly coupled 2D Gross-Pitaevskii equations (GPEs), 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 bandgap 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 the 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 bandgaps, 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 pseudo-bifurcation is found: when the mismatch attains its largest value (π), the bifurcation does not happen, as branches of different solutions asymptotically approach each other but fail to merge.

Stability of solitons in time-modulated two-dimensional lattices

“…For the parameters in both Eqs. (15) and (28), which might be more relevant for the comparison with the full numerical results (see below), this particular high-frequency stability peak attains height ε max ≈ 1, significantly lower than the one seen in the optimized stability diagram. Figure 9: The stability diagram predicted by the variational equations (11) for the attractive nonlinearity and phase shift δ = π/2 between the modulations applied to the x-and ysublattices, in the plane of (ω, ε).…”

“…The initial conditions are given by Eqs. (27), (28), (14) and (15), for panels (a), (b), (c) and (d), respectively.…”

“…In the experiment, effectively 1D GSs, composed of a few hundreds of atoms, were created in 87 Rb condensate, loaded into the OL potential [21].Besides the fundamental solitons and GSs, other types of multidimensional modes were also studied. In particular, many works dealt with vortex solitons i.e., multi-peak ring-shaped structures with embedded global vorticity imprinted onto the ring complex, in the semi-infinite gap, under the attractive nonlinearity [22,9,25,26,27,28,29,30,31], as well as gap vortex solitons under the repulsive nonlinearity [23,24,28,29,30,31,32]. The vortex solitons with the most basic structure are composed of four density peaks and may be classified into two categories: square-shaped, alias off-site-centered vortices, which are built as dense patterns with the central point positioned at a local maximum of the OL potential [9,25,26,27,23,30,31,32], and rhombic configurations, alias "diamonds" or on-site-centered vortices, which feature a vacant lattice site at the center [26,27,28,29,30,31,32].Another effective means for controlling the dynamics of the BEC may be provided by subjecting various parameters, which affect properties of the condensate, to periodic time-modulation (these tools belong to the general class of management techniques [33]).…”

Competition between the symmetry breaking and onset of collapse in weakly coupled atomic condensates

“…The model developed for this setting is based on a pair of linearly coupled 2D GPEs, which give rise to the SSB of 2D solitons and solitary vortices, for either sign of the nonlinearity, provided that the model includes an in-plane OL potential (otherwise, all 2D solitons are unstable) [14].…”

“…(In Refs. [14], the possibility of the collapse of asymmetric solitons in the 2D dual-core model with the attractive cubic nonlinearity and OL potential was mentioned, but not investigated, as the SSB happened there at much lower density values than those necessary for the onset of the collapse.) Below we derive the NPSE system and then produce a diagram in its parameter space, which reveals regions of stable symmetric and asymmetric solitons and a collapse area.…”