Self-bound liquid droplets in one-dimensional optical speckle potentials

Abstract

We present a comprehensive description of the equilibrium properties of self-bound liquid droplets in one-dimensional optical speckle potentials at both zero and finite temperatures.
Using the Bogoliubov theory we calculate analytically the equation of state, fluctuations induced by disorder, and the equilibrium density.
In particular, we show that the peculiar competition between the speckle disorder, the interactions and the Lee-Huang-Yang quantum fluctuations 
may strongly affect the stability and the formation of the self-bound droplet.
We address also the static and dynamical properties of such a disorered droplet using the generalized disorder-dependent Gross-Pitaevskii equation.
Notably, impacts of a weak speckle potential are treated numerically for both small droplets of an approximately Gaussian shape and large droplets with a flat-top plateau.