Bosonic quantum mixtures with competing interactions: quantum liquid droplets and supersolids

TL;DR

This paper reviews the emergence of quantum liquid droplets and supersolids in bosonic mixtures and dipolar gases, emphasizing the role of quantum fluctuations, competing interactions, and spin-orbit coupling in stabilizing these exotic phases.

Contribution

It introduces the mechanisms behind quantum liquid droplets and supersolids in bosonic systems, highlighting new stabilization methods like spin-orbit coupling and quantum fluctuation effects.

Findings

Quantum fluctuations stabilize ultradilute quantum liquid droplets.

Dipolar gases can form supersolids with phase coherence.

Spin-orbit coupling induces supersolidity at the mean-field level.

Abstract

These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.