Colloquium: Supersolids: What and where are they?

Abstract

The ongoing experimental and theoretical effort aimed at understanding non-classical rotational inertia in solid helium, has sparked renewed interest in the supersolid phase of matter, its microscopic origin and character, and its experimental detection. The purpose of this colloquium is a) to provide a general theoretical framework for the phenomenon of supersolidity and b) to review some of the experimental evidence for solid 4 He, and discuss its possible interpretation in terms of physical effects underlain by extended defects (such as dislocations). We provide quantitative support to our theoretical scenarios by means of first principle numerical simulations. We also discuss alternate avenues for the observation of the supersolid phase, not involving helium but rather assemblies of ultracold atoms.

A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates

“…Our work establishes a system with * These authors contributed equally to this work. § junruli@mit.edu † Although the original observation of supersolidity 3 turned out to be caused by unusual elastic properties, experiments revealed quantum plasticity and mass supertransport, probably created by superfluid flow through the cores of interconnected dislocations 1,4 …”

“…This spontaneous phase breaks continuous translational symmetry. The two broken U (1) symmetries are reflected in two Goldstone modes, one for density (or charge), the other one for spin transport 19 . Adding a longitudinal Zeeman term 0 σz to (1) leads to a rich phase diagram as a function of 0 and   .…”

On the ‘Supersolid’ Response of the Second Layer of $$^4 \hbox {He}$$ 4 He on Graphite

“…The possible experimental realisation of a supersolid state of matter in bulk solid 4 He has been the subject of intense recent interest [1,2]. In a perfect crystal, supersolidity would rely on the incommensurability of that crystal (spontaneous zero-point vacancies free to tunnel through the crystal) [3].…”

Excitations and stability of weakly interacting Bose gases with multibody interactions

“…These potentials were recently created in optical lattices with Rb atoms excited to Rydberg states [39,40]. The interest for such interactions is general and involves the simulation of novel kinds of spin Hamiltonians [41,42] for the creation of exotic phases, like the supersolid [43][44][45][46], and for metrological applications [47][48][49][50]. Motivated by these experimental results and theoretical investigations, we focus on the study of the stability diagram of a 2-body isotropic step-potential:…”

“…withρ =ρ(r) =Ψ † (r)Ψ(r) and F a function of the density operator, with the normal ordering to be taken in the second term of the right-hand side of (43). Details are given in Appendix A.…”