# Symmetry breaking of quantum droplets in a dual-core trap

## TL;DR

This paper investigates the spontaneous symmetry breaking and restoration of quantum droplets in a dual-core trap, revealing bifurcation loops, critical coupling thresholds, and collision dynamics through analytical and numerical methods.

## Contribution

It introduces a model for quantum droplets in a dual-core trap with Lee-Huang-Yang corrections, analyzing symmetry-breaking bifurcations and collision behaviors.

## Key findings

- Symmetry-breaking bifurcation loops depend on inter-core coupling.
- A critical coupling constant exists beyond which the loop disappears.
- Moving QDs tend to merge into breather states upon collision.

## Abstract

We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigar-shaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with the 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 symmetric 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, $\kappa$, and convex at larger $\kappa $. The loop does not exist above a critical value of $\kappa $. 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 constant zero and finite values of the wave function. Collisions between moving QDs are considered too, demonstrating a trend to merger into breathers.