Engineering quantum droplet formation by cavity-induced long-range interactions

TL;DR

This paper explores how cavity-induced long-range interactions can lead to the formation of self-bound quantum droplets in a dilute Bose gas, providing analytical insights into their size and density dependence.

Contribution

It introduces a generic Bogoliubov theory for quantum droplets formed by cavity-mediated long-range interactions, applicable to different cavity setups.

Findings

Quantum droplets' size depends on contact interaction strength.

Density of droplets is influenced by the shape of the long-range interaction envelope.

Analytical relations derived for two cavity configurations.

Abstract

We investigate a dilute Bose gas with both a short-range contact and an effective long-range interaction between the atoms. The latter is induced by the strong coupling to a cavity light mode and is spatially characterized by a periodic signature and a tunable envelope rooted in the pumping of the cavity. We formulate a Bogoliubov theory based on a homogeneous mean-field description and quantum fluctuations around it. The competition between the repulsive contact interaction and the long-range interaction allows the formation of self-bound quantum droplets. This generic approach is applied to two cavity setups, one without and one with a momentum-conserving effective long-range interaction between the atoms in the form of a driven dispersive cavity mode and a multimode cavity, respectively. For both cases we show analytically how the size and the central density of the cavity-induced quantum droplets depend on the contact interaction strength and on the shape of the spatial envelope of the long-range interaction.