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 Helium-four, 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.

20 pages, 7 figures, accepted for publication as a Colloquium in the Review of Modern Physics

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Cited by in corpus (283)

• Observation of the supersolid stripe phase in spin-orbit coupled Bose-Einstein condensates
• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Observation of a dipolar quantum gas with metastable supersolid properties
• Transient supersolid properties in an array of dipolar quantum droplets
• Long-lived and transient supersolid behaviors in dipolar quantum gases
• Dipolar physics: A review of experiments with magnetic quantum gases
• Long-range interacting quantum systems
• Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas
• The low-energy Goldstone mode in a trapped dipolar supersolid
• Observation of Roton Mode Population in a Dipolar Quantum Gas
• Excitation spectrum of a trapped dipolar supersolid and its experimental evidence
• New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids
• Superstripes and the excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate
• Two-dimensional supersolidity in a dipolar quantum gas
• Giant Magnetocaloric Effect in Spin Supersolid Candidate Na${}_2$BaCo(PO${}_4$)${}_2$
• Photon solid phases in driven arrays of nonlinearly coupled cavities
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Defect-induced supersolidity with soft-core bosons
• Probing the roton excitation spectrum of a stable dipolar Bose gas
• Supersolid behaviour of a dipolar Bose-Einstein condensate confined in a tube
• Supersolidity around a critical point in dipolar Bose Einstein condensates
• Stable dilute supersolid of two-dimensional dipolar bosons
• Elementary excitations of ultracold soft-core bosons across the superfluid-supersolid phase transition
• Two-Dimensional Supersolid Formation in Dipolar Condensates
• Spin-Orbit Coupling and Spin Textures in Optical Superlattices
• Pattern Formation in Quantum Ferrofluids: from Supersolids to Superglasses
• Dipolar quantum solids emerging in a Hubbard quantum simulator
• Nonequilibrium Phase Transition of Interacting Bosons in an Intra-Cavity Optical Lattice
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• First principles simulations of dense hydrogen
• Tricriticalities and Quantum Phases in Spin-Orbit-Coupled Spin-$1$ Bose Gases
• Counting Rules of Nambu-Goldstone Modes
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Imaging the evolution of an ultracold strontium Rydberg gas
• Spatial coherence of spin-orbit-coupled Bose gases
• Self-bound dipolar droplets and supersolids in molecular Bose-Einstein condensates
• Supersolidity in an elongated dipolar condensate
• Cluster Luttinger Liquids of Rydberg-dressed Atoms in Optical Lattices
• The Fate of the Higgs Mode in a Trapped Dipolar Supersolid
• Supersolid with nontrivial topological spin textures in spin-orbit-coupled Bose gases
• Supersolidity in Two-Dimensional Trapped Dipolar Droplet Arrays
• Density Fluctuations across the Superfluid-Supersolid Phase Transition in a Dipolar Quantum Gas
• Microscopic molecular superfluid response: theory and simulations
• Dipolar Bose Superstripes
• Two-dimensional dipolar Bose gas with the roton-maxon excitation spectrum
• Supersolid properties of a Bose-Einstein condensate in a ring resonator
• Classical and quantum filaments in the ground state of trapped dipolar Bose gases
• Properties of a dipolar condensate with three-body interactions
• Crystallisation of a dilute atomic dipolar condensate
• Persistent Currents in Toroidal Dipolar Supersolids
• Supersolidity in ultra-cold dipolar gases
• Rydberg-Blockade Effects in Autler-Townes Spectra of Ultracold Strontium
• Driven-Dissipative Supersolid in a Ring Cavity
• Superfluid filaments of dipolar bosons in free space
• Driven-dissipative dynamics of a strongly interacting Rydberg gas
• On Holographic Insulators and Supersolids
• Maintaining supersolidity in one and two dimensions
• Vortex properties in the extended supersolid phase of dipolar Bose-Einstein condensates
• Chiral Supersolid in Spin-Orbit-Coupled Bose Gases with Soft-Core Long-Range Interactions
• Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas
• Experimental realization of a superfluid stripe phase in a spin-orbit-coupled Bose-Einstein condensate enabled by momentum-space hopping
• Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration
• Patterned Supersolids in Dipolar Bose Systems
• Superglass phase of interaction-blockaded gases on a triangular lattice
• Exciting the Goldstone Modes of a Supersolid Spin-Orbit-Coupled Bose Gas
• Searching for Supersolidity in Ultracold Atomic Bose Condensates with Rashba Spin-Orbit Coupling
• Alternating-domain supersolids in binary dipolar condensates
• Combined topological and Landau order from strong correlations in Chern bands
• Supersolidity and crystallization of a dipolar Bose gas in an infinite tube
• Bose-Einstein condensation with spin-orbit coupling
• Can angular oscillations probe superfluidity in dipolar supersolids?
• Catalyzation of supersolidity in binary dipolar condensates
• Spin orders in the supersolid phases in binary Rydberg-dressed Bose-Einstein condensates
• Phase diagram of ${}^4$He on graphene
• Engineering matter interactions using squeezed vacuum
• Self-bound supersolid stripe phase in binary Bose-Einstein condensates
• The Vacua of Dipolar Cavity Quantum Electrodynamics
• Supersolid structure and excitation spectrum of soft-core bosons in 3D
• A supersolid-based gravimeter in a ring cavity
• Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model
• Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations
• A Rydberg-dressed Magneto-Optical Trap
• Ground state of weakly repulsive soft-core bosons on a sphere
• Prediction of a supersolid phase in high-pressure deuterium
• Massive and modified gravity as self-gravitating media
• Coexistence, interfacial energy, and the fate of microemulsions in 2D dipolar bosons
• Supersolid stripe crystal from finite-range interactions on a lattice
• Quantum simulators based on the global collective light-matter interaction
• Dynamics of Stripe Patterns in Supersolid Spin-Orbit-Coupled Bose Gases
• Superfluid-quasicrystal in a Bose-Einstein condensate
• Quantum Plasticity and Supersolid Response in Helium-4
• Supersolid-like square- and honeycomb-lattice crystallization of droplets in a dipolar condensate
• Ground state and excitation properties of soft-core bosons
• Phases of dipolar bosons in a bilayer geometry
• Observation of anisotropic superfluid density in an artificial crystal
• Absence of superfluidity in 2D dipolar Bose striped crystals
• Quantum hydrodynamics for supersolid crystals and quasicrystals
• Angular Stripe Phase in Spin-Orbital-Angular-Momentum Coupled Bose Condensates
• Metallic state in bosonic systems with continuously degenerate minima
• Quantum Phases of Dipolar Bosons in Bilayer Geometry
• Freezing of soft-core bosons at zero temperature: A variational theory
• Collective excitations and supersolid behavior of bosonic atoms inside two crossed optical cavities
• Supersolid phases of bosonic particles in a bubble trap
• Control of ${}^{164}$Dy Bose-Einstein condensate phases and dynamics with dipolar anisotropy
• Supersolidity of cnoidal waves in an ultracold Bose gas
• Superfluidity of strongly correlated bosons in two- and three-dimensional traps
• Competing quantum phases of hard-core boson with tilted dipole-dipole interaction
• Hydrodynamics of a superfluid smectic
• Ground-state stability and excitation spectrum of a one-dimensional dipolar supersolid
• Creation and robustness of quantized vortices in a dipolar supersolid when crossing the superfluid-to-supersolid transition
• Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice
• Moiré super-lattice structures in kicked Bose-Einstein condensates
• Dynamical preparation of stripe states in spin-orbit coupled gases
• Segregated quantum phases of dipolar bosonic mixtures in two-dimensional optical lattices
• Visibility and stability of superstripes in a spin-orbit-coupled Bose-Einstein condensate
• Quasicrystalline Bose glass in the absence of disorder and quasidisorder
• Probing the supersolid order via high-energy scattering: analytical relations among response, density modulation, and superfluid fraction
• Degeneracy and Inversion of Band Structure for Wigner Crystals on a Toroidal Helix
• Supersolid Stacks in Antidipolar Bose-Einstein Condensates
• Optical-lattice-assisted magnetic phase transition in a spin-orbit-coupled Bose-Einstein condensate
• Two-dimensional dipolar bosons with weak disorder
• Spin-orbital-angular-momentum-coupled quantum gases
• Thermodynamics of a two-dimensional dipolar Bose gas with correlated disorder in the roton regime
• Toroidal Dipolar Supersolid with a Rotating Weak Link
• Topological States with Broken Translational and Time-Reversal Symmetries in a Honeycomb-Triangular Lattice
• Bipolarons bound by repulsive phonon-mediated interactions
• Holographic Supersolids
• $2^{1296}$ Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method
• Decoupled sound and amplitude modes in trapped dipolar supersolids
• Symbiotic solitons in a quasi-one- and quasi-two-dimensional spin-1 condensates
• Frustration-induced supersolids in the absence of inter-site interactions
• Excitations of a binary dipolar supersolid
• Autler-Townes doublet in single-photon Rydberg spectra of Cesium atomic vapor with a 319 nm UV laser
• Anharmonicity Induced Supersolidity In Spin-Orbit Coupled Bose-Einstein Condensates
• Exploring quantum quasicrystal patterns: a variational study
• Resonant Pairing of Excitons in Semiconductor Heterostructures
• Phonon and Shifton from a Real Modulated Scalar
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Coexistence of density wave and superfluid order in a dipolar Fermi gas
• Tunable spin-orbit coupling and magnetic superstripe phase in a BEC
• Phase Crystals
• Fine structure of the stripe phase in ring-shaped Bose-Einstein condensates with spin-orbital-angular-momentum coupling
• Classical linear chain behavior from dipolar droplets to supersolids
• Superstripes : superconductivity in complex granular striped matter
• Optical lattices as a tool to study defect-induced superfluidity
• Feedback-stabilized dynamical steady states in the Bose-Hubbard model
• Tuneable defect interactions and supersolidity in dipolar quantum gases on a lattice potential
• Supersolid formation in a dipolar condensate by roton instability
• Autolocalization in a dipolar exciton system
• Supersolidity of polariton condensates in photonic crystal waveguides
• Wannier states and spin supersolid physics in the triangular antiferromagnet K${}_2$Co(SeO${}_3$)${}_2$
• Tuning photon-mediated interactions in a multimode cavity: from supersolid to insulating droplets hosting phononic excitations
• Second layer crystalline phase of helium films on graphite
• Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study
• Dynamical response and competing orders in two-band Hubbard model
• Supersolid-like square- and triangular-lattice crystallization of dipolar droplets in a box trap
• Nonequilibrium scenarios in cluster-forming quantum lattice models
• Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems
• Worm quantum Monte-Carlo study of phase diagram of extended Jaynes-Cummings-Hubbard model
• Trimer superfluid and supersolid on two-dimensional optical lattices
• Many-Body Phases of a Planar Bose-Einstein Condensate with Cavity-Induced Spin-Orbit Coupling
• Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice
• Tuning the quantumness of simple Bose systems: A universal phase diagram
• Stripe-ordered superfluid and supersolid phases in attractive Hofstadter-Hubbard model
• Measuring Berry curvature with quantum Monte Carlo
• Crossing the superfluid-supersolid transition of an elongated dipolar condensate
• Specific heat of thin ${}^4$He films on graphite
• Quantum phases of dipolar bosons in multilayer optical lattice
• Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples
• Pseudo-Goldstone Excitations in a Striped Bose-Einstein Condensate
• Nonuniversal beyond mean field properties of quasi-two-dimensional dipolar Bose gases
• Quantum walks of interacting Mott insulator defects with three-body interactions
• Self-ordered supersolid phase beyond Dicke superradiance in a ring cavity
• Synchronization in rotating supersolids
• Quantum fluctuations in one-dimensional supersolids
• Suppression of infrared instability in trans-sonic flows by condensation of zero-frequency short wave length phonons
• Oscillations of a quasi-one-dimensional dipolar supersolid
• Nonlinear dependence observed in quadrupolar collective excitation of a trapped BEC
• Supersolid Gap Soliton in a Bose-Einstein Condensate and Optical Ring Cavity coupling system
• Broken symmetry and competing orders in Weyl semimetal interfaces
• Supersolidity in Rydberg tweezer arrays
• Easy-axis Heisenberg model on the triangular lattice: from supersolid to gapped solid
• Supersolid behavior in one-dimensional self-trapped Bose-Einstein condensate
• Probing supersolidity through excitations in a spin-orbit-coupled Bose-Einstein condensate
• NMR study of supersolid phases in the triangular-lattice antiferromagnet Na2BaCo(PO4)2
• Disordered Supersolids in the Extended Bose-Hubbard Model
• Strain-induced superfluid transition for atoms on graphene
• Drag force and superfluidity in the supersolid stripe phase of a spin-orbit-coupled Bose-Einstein condensate
• Excitations and stability of weakly interacting Bose gases with multi-body interactions
• Three-body interacting dipolar bosons and the fate of lattice supersolidity
• Supersolid phases of dipolar fermions in a two-dimensional-lattice bilayer array
• Demixing in symmetric supersolid mixtures
• Vortex core order and field-driven phase coexistence in the attractive Hubbard model
• Dipolar bosons in one dimension: the case of longitudinal dipole alignment
• Superfluid transition of the second layer of He-4 on graphite: does substrate corrugation matter?
• Morphology of dipolar Bose droplets
• Ground state phase diagram of Gaussian-Core bosons in two dimensions
• Supersolidity of the $\alpha$ cluster structure in the nucleus ${}^{12}$C
• Induced supersolidity in a Dy-Er mixture
• Incommensurability effects on dipolar bosons in optical lattices
• Magnetic phases in the S=1 Shastry-Sutherland model with uniaxial anisotropy
• Cluster stability driven by quantum fluctuations
• Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas
• Bose-Einstein condensates with Raman-induced spin-orbit coupling : An overview
• Supersolid induced by dislocations with superfluid cores (Review article)
• Quantum crystallography of Rydberg-dressed Bose gases on a square lattice
• Density-wave-type supersolid of two-dimensional tilted dipolar bosons
• Study of long-range orders of hard-core bosons coupled to cooperative normal modes in two-dimensional lattices
• Supersolid-like states in a two-dimensional trapped spin-orbit-coupled spin-1 condensate
• Models of Mixed Matter
• Signature of Supersolidity in a Driven Cubic-Quartic Nonlinear Schrödinger Equation
• Exotic Haldane Superfluid Phase of Soft-Core Bosons in Optical Lattices
• Self-induced Bose glass phase in quantum cluster quasicrystals
• Absence of off-diagonal long-range order in hcp ${}^4$He dislocation cores
• Unveiling Supersolid Order via Vortex Trajectory Correlations
• Muonium hydride: the lowest density crystal
• Rydberg-dressed Fermi liquid: correlations and signatures of droplet crystallization
• Three-body and Coulomb interactions in a quasi two-dimensional dipolar Bose condensed gas
• Larkin-Ovchinikov superfluidity in time-reversal symmetric bilayer Fermi gases
• Thermal and Quantum Fluctuation Effects in Quasiperiodic Systems in External Potentials
• Defects and glassy dynamics in solid He-4: Perspectives and current status
• Impurity induced phase competition and supersolidity
• Josephson vortices and persistent current in a double-ring supersolid system
• Superfluid-like TO Responses in Rotating Solid Helium
• Mini droplet, mega droplet and stripe formation in a dipolar condensate
• Phase-induced vortex pinning in rotating supersolid dipolar systems
• Spatial order in a two-dimensional spin-orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation
• Emergent Spin Supersolids in Frustrated Quantum Materials
• Transverse Quantum Superfluids
• Dipole-mode and scissors-mode oscillations of a dipolar supersolid
• Dimensional crossover in self-organised super-radiant phases of ultra cold atoms inside a cavity
• Frustration-Induced Supersolid Phases of Extended Bose-Hubbard Model in the Hard-Core Limit
• ${\mathbb{Z}}_n$ symmetry broken supersolid in spin-orbit-coupled Bose-Einstein condensates
• Mixed-order transition and tricritical point associated with checkerboard supersolidity in the two-dimensional $t_2-V_1$ model
• Hydrodynamic theory of Rotating Ultracold Bose Einstein Condensates in Supersolid Phase
• Spin-orbit coupled mean-field Bose gas at finite temperature
• Phase diagram and crystal melting of helium-4 in two dimensions
• Dislocation Mobility and Anomalous Shear Modulus Effect in ${}^4$He Crystals
• Formation of paired phases of bosons and their excitations in a square lattice
• Vortex supersolid in the XY model with tunable vortex fugacity
• Reflections on dipolar quantum fluids
• From elastic to inelastic deformation of a dipolar supersolid
• Supersolidity of dipolar Bose-Einstein condensates induced by coupling to fermions
• Hard core repulsion and supersolid cluster crystals
• Supersolidity of $\alpha$ cluster structure in ${}^{40}$Ca
• Supersolid phase in two-dimensional soft-core bosons at finite temperature
• Competing phases and intertwined orders in coupled wires near the self-dual point
• Rotons and their damping in elongated dipolar Bose-Einstein condensates
• Self-Ordered Supersolid in Spinor Condensates with Cavity-Mediated Spin-Momentum-Mixing Interactions
• Spatially-periodic states in a strongly dipolar ${}^{164}$Dy-${}^{162}$Dy mixture
• The solid phase of He-4: A Monte Carlo simulation study
• Unified theory of quantum crystals and optical lattices with Bose-Einstein condensate
• Fractional vorticity, Bogomol'nyi-Prasad-Sommerfield systems and complex structures for the (generalized) spinor Gross-Pitaevskii equations
• Chiral supersolid and dissipative time crystal in Rydberg-dressed Bose-Einstein condensates with Raman-induced spin-orbit coupling
• Superfluid Field response to Edge dislocation motion
• The anisotropic Heisenberg model close to the Ising limit: triangular lattice vs. effective models
• Saga of Superfluid Solids
• Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities
• He-4 monolayer on Graphene: a Quantum Monte Carlo study
• Finite temperature instabilities of 2D dipolar Bose gas at arbitrary tilt angle
• The amazing properties of crystalline color superconductors
• Finite temperature phases and excitations of bosons on a square lattice: A cluster mean field study
• Vortex core ordering in Abrikosov lattices
• Superfluid transition in a correlated defect network
• Dynamic formation of supersolid phase in a mixture of ultracold bosonic and fermionic atoms
• Vorticity-Crystalline Order Coupling in Supersolids: Excitations and Re-entrant Phases
• The attractive Hubbard model as an $SO(3)$ system of competing phases: supersolid order and its thermal melting
• Strongly dipolar molecular Bose-Einstein condensates: From few- to many-body physics
• One-dimensional extended Hubbard model with soft-core potential
• Supersolid phase of a spin-orbit-coupled Bose-Einstein condensate: a perturbation approach
• Quasiparticle spectra of mixtures of dipolar and non-dipolar condensates at zero and finite temperatures
• Dissipation induced elastic-mode instability with topological excitation in holographic non-equilibrium steady cnoidal wave supersolid
• Thermal Casimir effect in the spin-orbit coupled Bose gas
• Generation of wave turbulence in dipolar gases driven across their phase transitions
• Supersolid light in a semiconductor microcavity
• Asymmetry analysis of Autler-Townes doublet in the trap-loss fluorescence spectroscopy of cesium MOT with single step Rydberg excitation
• Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model
• Pauli crystal superradiance
• Coexistence of long-range orders in a Bose-Holstein model
• Orbital Optical Raman Lattice
• A symbiotic nondipolar droplet supersolid in a binary dipolar-nondipolar Dy-Rb mixture
• Bi-Josephson Effect in a Driven-Dissipative Supersolid
• End-point singularity of the $XY$-paramagnetic phase boundary for the $(2+1)$D $S=1$ square-lattice $J_1$-$J_2$ $XY$ model with the single-ion anisotropy