Signature of Supersolidity in a Driven Cubic-Quartic Nonlinear Schr\"odinger Equation

TL;DR

This paper analytically investigates a driven cubic-quartic nonlinear Schrödinger equation in optical lattices, revealing density wave creation, stripe phases, and potential supersolid behavior in condensates.

Contribution

It provides an analytical solution for the driven cubic-quartic nonlinear Schrödinger equation and explores supersolid signatures in nonlinear quantum systems.

Findings

Analytical periodic solutions indicating density wave formation.

Identification of stripe phases with phase coherence.

Possible emergence of supersolid phase in condensates.

Abstract

We present analytical solution, which is periodic in nature, for a driven cubic-quartic nonlinear Schr\"odinger equation (DCQNLSE) placed in a bi-chromatic optical lattice. The solution indicates the creation of density wave. Since, beyond mean-field contribution in quasi one dimensional and one-dimensional geometry differs on the even exponents of the nonlinearity thus we extend our analysis towards quadratic-cubic-quartic and quadratic-cubic nonlinearities as well. Later, we study the dynamics of DCQNLSE. Our study indicates the existence of stripe phase along with considerable phase coherence. These findings allow us to comment on the possible emergence of supersolid phase in a condensate.