Symmetry breaking of quantum droplets in a dual-core trap

Abstract

We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigarshaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with cubic self-repulsive terms and quadratic attractive ones,which represent the Lee-Huang-Yang corrections to the mean-field theory in this geometry. The main subject is spontaneous symmetry breaking (SSB) of quantum droplets (QDs), followed by restoration of the symmetry, with respect to the identical parallel-coupled trapping cores, following the increase of the QD's total norm. The SSB transition and inverse symmetry-restoring one form a bifurcation loop, whose shape in concave at small values of the inter-core coupling constant, κ, and convex at larger κ. The loop does not exist above a critical value of κ. At very large values of the norm, QDs do not break their symmetry, featuring a flat-top shape. Some results are obtained in an analytical form, including an exact front solution connecting asymptotically constant zero and finite values of the wave function. Collisions between moving QDs are considered too, demonstrating a trend to merger into breathers.

Modulational Instability, Inter-Component Asymmetry, and Formation of Quantum Droplets in One-Dimensional Binary Bose Gases

“…which is an analytical continuation of expression (15). This dependence also satisfies the VK criterion.…”

“…Eq. (15). At µ 2 ≥ 0, the ψ 2 component undergoes delocalization, with its tails developing a nonzero background at |z| → ∞, as seen in the density profile displayed in Fig.…”

Stability and collisions of quantum droplets in PT-symmetric dual-core couplers

“…The objective of this work is to extend the study of the spontaneous symmetry breaking of quantum droplets (QDs) in the dual-core trap [30], to dynamics of QDs in parity-time (PT )-symmetric dual-core setting. Such PT -symmetric system cannot support stable asymmetric QDs as the balance between the gain and loss is impossible for them.…”

“…The spontaneous symmetry breaking of QDs associating with bifurcation loop is not expected to occur in the PTsymmetric system. Thus, a drastic difference of QDs in the PT -symmetric dual-core system from QDs in its conservative counterpart is that unstable symmetric QDs are not replaced by stable asymmetric QDs beyond the symmetry-breaking boundary [30]. It is well known that the exact analytical solutions can give a deeper understanding than direct numerical simulations [65,66].…”

Semidiscrete Quantum Droplets and Vortices

“…Self-trapped states in this model demonstrate Gaussianlike and flat-top shapes in the case of relatively small or large numbers of atoms, respectively [23]. The next natural step is the consideration of a tunnel-coupled pair of 1D waveguides, in which spontaneous symmetry breaking of QDs was predicted [24] (similar systems, combining the LHY term and linear mixing between two components, were introduced too [25,26]).…”