Modulational instability and discrete quantum droplets in a deep quasi-one-dimensional optical lattice

TL;DR

This paper investigates modulational instability and quantum droplet solutions in a quasi-one-dimensional optical lattice, combining analytical and numerical methods to understand their existence and stability.

Contribution

It introduces a comprehensive analysis of quantum droplet solutions and modulational instability conditions in a discrete Gross-Pitaevskii model with Lee-Huang-Yang corrections.

Findings

Identified conditions for modulational instability regions.

Derived existence criteria for various quantum droplet modes.

Validated analytical predictions with numerical simulations.

Abstract

We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions of nonlinear plane waves are determined in parameter space. We analytically investigate the existence of different quantum droplet solutions, including intersite, onsite, front-like, flat-top and dark localized modes, using the Page method and variational approach. Their stability is checked using linear stability analyses and numerical simulations. The analytical predictions corroborated with the numerical simulations.