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

TL;DR

This paper investigates the stability and collision behaviors of quantum droplets in PT-symmetric dual-core systems, revealing how gain-loss balance, coupling, and optical lattice influence their dynamics and stability.

Contribution

It introduces a detailed analysis of quantum droplet stability in PT-symmetric dual-core systems, highlighting the roles of gain-loss, coupling strength, and optical lattice potential.

Findings

Stability of symmetric QDs depends on gain-loss, coupling, and optical lattice.

PT-symmetric QDs are unstable against symmetry-breaking at certain norms.

Collisions can lead to merging into breathers or quasi-elastic scattering.

Abstract

We study the effect of the interplay between parity-time ($\mathcal{PT}$) symmetry and optical lattice (OL) potential on dynamics of quantum droplets (QDs) forming in a binary bosonic condensate trapped in a dual-core system. It is found that the stability of symmetric QDs in such non-Hermitian system depends critically on the competition of gain and loss $\gamma$, inter-core coupling $\kappa$, and OL potential. In the absence of OL potential, the $\mathcal{PT}$-symmetric QDs are unstable against symmetry-breaking perturbations with the increase of the total condensate norm $N$, and they retrieve the stability at larger $N$, in the weakly-coupled regime. As expected, the stable region of the $\mathcal{PT}$-symmetric QDs shrinks when $\gamma$ increases, i.e., the $\mathcal{PT}$ symmetry is prone to break the stability of QDs. There is a critical value of $\kappa$ beyond which the $\mathcal{PT}$-symmetric QDs are entirely stable in the unbroken $\mathcal{PT}$-symmetric phase. In the presence of OL potential, the $\mathcal{PT}$-symmetric on-site QDs are still stable for relatively small and large values of $N$. Nevertheless, it is demonstrated that the OL potential can assist stabilization of $\mathcal{PT}$-symmetric on-site QDs for some moderate values of $N$. On the other hand, it is worth noting that the relatively small $\mathcal{PT}$-symmetric off-site QDs are unstable, and only the relatively large ones are stable. Furthermore, collisions between stable $\mathcal{PT}$-symmetric QDs are considered too. It is revealed that the slowly moving $\mathcal{PT}$-symmetric QDs tend to merge into breathers, while the fast-moving ones display quasi-elastic collision and suffer fragmentation for small and large values of $N$, respectively.