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arXiv:2311.04266

Reentrant supersolidity

Leo Radzihovsky

Published Nov 7, 2023• 0 citations
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Abstract

A "supersolid" -- a crystal that exhibits an off-diagonal long-range order and a superflow -- has been a subject of much research since its first proposal [Andreev and Lifshitz 1969], but has not been realized as a ground state of short-range interacting bosons in a continuum. In this note I point out a simple and generic mechanism for a thermally-driven reentrant supersolidity, and discuss challenges of experimental realization of this idea. In the limit of bosons in a periodic potential, this mechanism reduces to a {\em reentrant} low-temperature normal-superfluid transition, that should be accessible to simulations and in current experiments on bosonic atoms in an optical periodic potential.

DOI
10.48550/arxiv.2311.04266

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A "supersolid" -- a crystal that exhibits an off-diagonal long-range order and a superflow -- has been a subject of much research since its first proposal [Andreev and Lifshitz 1969], but has not been realized as a ground state of short-range interacting bosons in a continuum. In this note I point out a simple and generic mechanism for a thermally-driven reentrant supersolidity, and discuss challenges of experimental realization of this idea. In the limit of bosons in a periodic potential, this mechanism reduces to a {\em reentrant} low-temperature normal-superfluid transition, that should be accessible to simulations and in current experiments on bosonic atoms in an optical periodic potential.
In condensed-matter physics, long-range correlations introduce quantum states of matter that challenge intuition. For example, supersolids combine density order that manifests as symmetry-breaking spatial arrangement, and frictionless superfluid flow. However, supersolids have proven to only exist under very stringent conditions, with evidence limited to a few spontaneously fragmented superfluids observed in the weakly-interacting regime. Here, we demonstrate a framework to realize crystalline supersolids in the strong interaction regime, by confining dipolar bosons in a lattice with long-range hopping. We show that dipolar excitons realize this lattice model. At fractional lattice fillings of one quarter, one third and one half we observe mesoscopic quantum crystals across around 100 sites that spontaneously break the lattice translational symmetry. At the same time, coherent long-range hopping induces off-diagonal long-range order such that the exciton solids are superfluids. Our numerical methods quantitatively confirm that supersolidity builds up in the ground-state of the lattice Hamiltonian.
More than 40 years ago, Andreev, Lifshitz and Chester suggested the possible existence of a peculiar solid phase of matter, the microscopic constituents of which can flow superfluidly without resistance due to the formation of zero-point defects in the ground state of self-assembled crystals. Yet, a physical system where this mechanism is unambiguously established remains to be found, both experimentally and theoretically. Here we investigate the zero-temperature phase diagram of two-dimensional bosons with finite-range soft-core interactions. For low particle densities, the system is shown to feature a solid phase in which zero-point vacancies emerge spontaneously and give rise to superfluid flow of particles through the crystal. This provides the first example of defect-induced, continuous-space supersolidity consistent with the Andreev–Lifshitz–Chester scenario. The peculiar supersolid phase of matter was predicted several decades ago, yet a physical system where it exists remains to be found. Cinti et al.investigate the zero-temperature phase diagram of bosons interacting by soft-core potentials and find that defects in it can give rise to a supersolid phase.
Strong, long-range interactions present a unique challenge for the theoretical investigation of quantum many-body lattice models, due to the generation of large numbers of competing states at low energy. Here, we investigate a class of extended bosonic Hubbard models with off-site terms interpolating between short and infinite range, thus allowing for an exact numerical solution for all interaction strengths. We predict a novel type of stripe crystal at strong coupling. Most interestingly, for intermediate interaction strengths we demonstrate that the stripes can turn superfluid, thus leading to a self-assembled array of quasi-one-dimensional superfluids. These bosonic superstripes turn into an isotropic supersolid with decreasing the interaction strength. The mechanism for stripe formation is based on cluster self-assembling in the corresponding classical ground state, reminiscent of classical soft-matter models of polymers, different from recently proposed mechanisms for cold gases of alkali or dipolar magnetic atoms.
A high-finesse optical cavity allows the establishment of long-range interactions between bosons in an optical lattice when most cold-atom experiments are restricted to short-range interactions. Supersolid phases have recently been experimentally observed in such systems. Using both exact quantum Monte Carlo simulations and the Gutzwiller approximation, we study the ground-state phase diagrams of a two-dimensional Bose-Hubbard model with infinite-range interactions which describes such experiments. In addition to superfluid and insulating Mott phases, the infinite-range checkerboard interactions introduce charge-density waves and supersolid phases. We study here the system at various particle densities, elucidate the nature of the phases and quantum phase transitions, and discuss the stability of the phases with respect to phase separation. In particular we confirm the existence and stability of a supersolid phase detected experimentally.
Abstract Within the mean field Gross–Pitaevskii framework, ultracold atomic condensates with long-range interaction are predicted to have a supersolid-like ground state beyond a critical interaction strength. Such a mean field supersolid-like ground state has periodically modulated superfluid density which implies the coexistence of superfluid and crystalline order. An ultracold atomic system in such a mean field ground state can be subjected to an artificial gauge field created either through rotation or by introducing space dependent coupling among hyperfine states of the atoms using Raman lasers. Starting from this Gross–Pitaevskii energy functional that describes such systems at zero temperature, we construct a hydrodynamic theory to describe the low-energy long-wavelength excitations of a rotating supersolid of weakly interacting ultracold atoms in two spatial dimensions for a generic type of long-range interaction. We treat the supersolidity in such a system within the framework of the well known two-fluid approximation. Considering such a system in the fast rotation limit where a vortex lattice in superfluid coexists with the supersolid lattice, we analytically obtain the dispersion relations of collective excitations around this equilibrium state. The dispersion relation gives the modes of the rotating supersolid which can be experimentally measured within the current technology. We point out that this can clearly identify an ultracold atomic supersolid phase in an unambiguous way.
The coupling of cold atoms to the radiation field within a high-finesse optical resonator, an optical cavity, induces long-range interactions which can compete with an underlying optical lattice. The interplay between short- and long-range interactions gives rise to new phases of matter including supersolidity (SS) and density waves (DW), and interesting quantum dynamics. Here it is shown that for hard-core bosons in one dimension the ground state phase diagram and the quantum relaxation after sudden quenches can be calculated exactly in the thermodynamic limit. Remanent DW order is observed for quenches from a DW ground state into the superfluid (SF) phase below a dynamical transition line. After sufficiently strong SF to DW quenches beyond a static metastability line DW order emerges on top of remanent SF order, giving rise to a dynamically generated SS state. Our method to handle infinite- and short-range interactions in the infinite system size limit opens a way to solve exactly other Hamiltonians with infinite- and short-range interactions as well.