Supersolid State Research Articles

Exploring Quantum Phases of Dipolar Gases through Quasicrystalline Confinement.

The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a superquasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials.

Supercurrent-carrying supersolid in spin-orbit-coupled Bose-Einstein condensates

One of brilliant achievements in spin-orbit-coupled Bose-Einstein condensates is the discovery and observation of the supersolid stripe states. So far, all studied supersolid stripe states do not carry supercurrent. In this paper, we reveal the existence of supercurrent-carrying supersolids in spin-orbit-coupled Bose-Einstein condensates. The supersolid family has a parabolic-like dispersion and carries supercurrent, which is proportional to the quasimomentum. Energetic and dynamical instabilities can break supercurrent-carrying ability of this supersolid family. An insightful interpretation of the dynamical instability of supercurrent-carrying supersolids from the pure plane-wave phase is provided. Published by the American Physical Society 2024

Off-diagonal long-range order in arrays of dipolar droplets

We report quantum Monte Carlo results of harmonically confined quantum Bose dipoles within a range of interactions covering the evolution from a gas phase to the formation of an array of droplets. Scaling the experimental setup to a computationally accessible domain we characterize that evolution in qualitative agreement with experiments. Our microscopic approach generates ground-state results free from approximations, albeit with some controlled statistical noise. The simultaneous estimation of the static structure factor and the one-body density matrix allows for a better knowledge of the quantum coherence between droplets. Our results show a narrow window of interaction strengths where diagonal and off-diagonal long-range order can coexist. This domain, which is the key signal of a supersolid state, is reduced with respect to the one predicted by the extended Gross–Pitaevskii equation. Differences are probably due to an increase of attraction in our model, observed previously in the calculation of critical atom numbers for single dipolar drops.

Two-dimensional miscible-immiscible supersolid and droplet crystal state in a homonuclear dipolar bosonic mixture

The recent realization of a binary dipolar Bose-Einstein condensate [A. Trautmann et al., Phys. Rev. Lett. 121, 213601 (2018)] presents new exciting aspects for studying quantum droplets and supersolids in a binary mixture. Motivated by this experiment, we study the ground-state phases and dynamics of a Dy-Dy mixture. The dipolar bosonic mixture exhibits qualitatively novel and rich physics. Relying on the three-dimensional numerical simulations in the extended Gross-Pitaevskii framework, we unravel the ground-state phase diagrams and characterize their different possible phases. The emergent phases include single-droplet (SD), multiple-droplets (MD), doubly supersolid (SS), and superfluid (SF) states in both miscible and immiscible phases. Intriguing mixed ground states are observed for an imbalanced binary mixture, including a combination of SS-SF, SS-MD, and SS-SS phases. We also explore the dynamics across the phase boundaries by linear quenches of interspecies and intraspecies scattering lengths. During these dynamical processes, we observe an abrupt change in phase which initially results in some instability in the system and forms some metastable states in the intermediate timescale. However, the state produced in long-time evolution is similar to our predicted ground state. Although we demonstrate the possible results for a Dy-Dy mixture and for a specific parameter range of intraspecies and interspecies scattering lengths, our results are in general valid for other dipolar mixtures and may become an important benchmark for future experimental scenarios.

Fractonic Luttinger liquids and supersolids in a constrained Bose-Hubbard model

Dynamical constraints have drastic consequences for the properties of many-particle quantum systems. Here, the authors study the quantum ground state phases in a fracton system of interacting bosons with dipole conservation. Through a combination of low-energy field theory and tensor network simulations, they identify a novel dipole Luttinger liquid phase as well as a fracton analogue of a supersolid state.

Realization of a supersolid phase in a two-channel model

We construct a two-channel model based on the one-dimensional extended Bose–Hubbard model, by including a second channel of free bosons. We use the mean-field theory to map the system to a reduced single-channel one and solve this system by means of the density matrix renormalization group method. We find the region where the superfluid and density-wave orders coexist which signals a supersolid state. Our theory can be realized experimentally with state-dependent optical lattices.

Heating a dipolar quantum fluid into a solid

Raising the temperature of a material enhances the thermal motion of particles. Such an increase in thermal energy commonly leads to the melting of a solid into a fluid and eventually vaporises the liquid into a gaseous phase of matter. Here, we study the finite-temperature physics of dipolar quantum fluids and find surprising deviations from this general phenomenology. In particular, we describe how heating a dipolar superfluid from near-zero temperatures can induce a phase transition to a supersolid state with a broken translational symmetry. We discuss the observation of this effect in experiments on ultracold dysprosium atoms, which opens the door for exploring the unusual thermodynamics of dipolar quantum fluids.

Chester Supersolid of Spatially Indirect Excitons in Double-Layer Semiconductor Heterostructures.

A supersolid, a counterintuitive quantum state in which a rigid lattice of particles flows without resistance, has to date not been unambiguously realized. Here we reveal a supersolid ground state of excitons in a double-layer semiconductor heterostructure over a wide range of layer separations outside the focus of recent experiments. This supersolid conforms to the original Chester supersolid with one exciton per supersolid site, as distinct from the alternative version reported in cold-atom systems of a periodic density modulation or clustering of the superfluid. We provide the phase diagram augmented by the supersolid. This new phase appears at layer separations much smaller than the predicted exciton normal solid, and it persists up to a solid-solid transition where the quantum phase coherence collapses. The ranges of layer separations and exciton densities in our phase diagram are well within reach of the current experimental capabilities.

Alternating-domain supersolids in binary dipolar condensates

Two-component dipolar condensates are now experimentally producible, and we theoretically investigate the nature of supersolidity in this system. We predict the existence of a binary supersolid state in which the two components form a series of alternating domains, producing an immiscible double supersolid. Remarkably, we find that a dipolar component can even induce supersolidity in a nondipolar component. In stark contrast to single-component dipolar supersolids, alternating-domain supersolids do not require quantum stabilization, and the number of crystal sites is not strictly limited by the condensate populations, with the density hence being substantially lower. Our results are applicable to a wide range of dipole moment combinations, marking an important step towards long-lived bulk-supersolidity.

Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2

Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na2BaCo(PO4)2 (NBCP) is a rare, nearly ideal material realization of the S = 1/2 triangular-lattice antiferromagnet with significant easy-axis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network simulations, we establish a microscopic model description of this material with realistic model parameters, which can not only fit well the experimental thermodynamic data but also reproduce the measured magnetization curves without further adjustment of parameters. According to the established model, the NBCP hosts a spin supersolid state that breaks both the lattice translation symmetry and the spin rotational symmetry. Such a state is a spin analog of the long-sought supersolid state, thought to exist in solid Helium and optical lattice systems, and share similar traits. The NBCP therefore represents an ideal material-based platform to explore the physics of supersolidity as well as its quantum and thermal melting.

Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss

Spin-orbital coupling (SOC) and parity-time symmetry both have attracted paramount research interest in condensed matter physics, cold atom physics, optics and acoustics to develop spintronics, quantum computation, precise sensors and novel functionalities. Natural SOC is an intrinsic relativistic effect. However, there is an increasing interest in synthesized SOC nowadays. Here, we show that in a -symmetric pseudo spin-1/2 system (in other words, two-state system), the momentum-dependent balanced gain and loss can synthesize a new type of SOC, which we call imaginary SOC. The imaginary SOC can substantially change the energy spectrum of the system. Firstly, we show that it can generate a pure real energy spectrum with a double-valleys structure. Therefore, it has the ability to generate supersolid stripe states. Especially, the imaginary SOC stripe state can have a high contrast of one. Moreover, the imaginary SOC can also generate a spectrum with tunable complex energy band, in which the waves are either amplifying or decaying. Thus, the imaginary SOC would also find applications in the engineering of -symmetry-based coherent wave amplifiers/absorbers. Potential experimental realizations of imaginary SOC are proposed in cold atomic gases and systems of coupled waveguides constituted of nonlocal gain and loss.

Supersolid induced by dislocations with superfluid cores (Review Article)

The dislocation model of the supersolid state of 4He was proposed in 1987 by one of the authors of the review. The model obtained strong support by numerous experimental and theoretical investigations from 2007 to date. In these investigations, the validity of the idea put forward in 1987 was confirmed, and new conceptions of the superclimb of dislocations and of the giant isochoric compressibility or the syringe effect were proposed. In this paper, we review the main achievements of theoretical and experimental studies of a dislocation-induced supersolid and present current understanding of this phenomenon.

Self-bound dipolar droplets and supersolids in molecular Bose-Einstein condensates

We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquid-like density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.

Superfluidity of vacancies in solid 4He

Under the adiabatic approximation, we present a superfluid state of vacancy motion in solid 4He. The vacancies in solid 4He can sense an attractive effective interaction by exchange of virtual longitudinal acoustic phonons. Such an interaction leads to a Bardeen-Cooper-Schrieffer (BCS) condensation state, in which the vacancies with opposite wave vectors are bound into pairs and single, unpaired bare vacancies are transformed into a new kind of quasiparticle, the dressed vacancy. A dressed vacancy is a vacancy clothed with a cloud of virtual longitudinal-acoustic phonons. The vacancy system undergoes a first-order phase transition from the normal state to the BCS condensation state. The critical temperature may be the transition temperature of the supersolid state. We derive the low-temperature expressions of vacancy heat capacity and vacancy number density in the BCS condensation state. The BCS condensation state of vacancies is the superfluid state of vacancies, which possesses potentially important and novel effects in condensed matter physics.

Bragg scattering of an ultracold dipolar gas across the phase transition from Bose-Einstein condensate to supersolid in the free-particle regime

We present an experimental and theoretical study of the high-energy excitation spectra of a dipolar supersolid. Using Bragg spectroscopy, we study the scattering response of the system to a high-energy probe, enabling measurements of the dynamic structure factor. We experimentally observe a continuous reduction of the response when tuning the contact interaction from an ordinary Bose-Einstein condensate to a supersolid state. Yet the observed reduction is faster than the one theoretically predicted by the Bogoliubov-de-Gennes theory. Based on an intuitive semi-analytic model and real-time simulations, we primarily attribute such a discrepancy to the out-of-equilibrium phase dynamics, which although not affecting the system global coherence, reduces its response.

Oscillations of a quasi-one-dimensional dipolar supersolid

The properties of a supersolid state (SS) in quasi-one-dimensional dipolar Bose–Einstein condensate is studied, considering two possible mechanisms of realization—due to repulsive three-body atomic interactions and quantum fluctuations in the framework of the Lee–Huang–Yang theory. The role of both mechanisms in the formation of SS properties has been emphasized. The proposed theoretical model, based on minimization of the energy functional, allows evaluating the amplitude of the SS for an arbitrary set of parameters in the extended Gross–Pitaevskii equation (eGPE). To explore the dynamics of the SS first we numerically construct its ground state in different settings, including periodic boundary conditions, box-like trap and parabolic potential, then impose a perturbation. In oscillations of the perturbed supersolid we observe the key manifestation of SS, namely the free flow of the superfluid fraction through the crystalline component of the system. Two distinct oscillation frequencies of the supersolid associated with the superfluid fraction and crystalline components of the wave function are identified from numerical simulations of the eGPE.

Phases of supersolids in confined dipolar Bose-Einstein condensates

Dipolar Bose-Einstein condensates represent a powerful platform for the exploration of quantum many-body phenomena arising from long-range interactions. A series of recent experiments has demonstrated the formation of supersolid states of matter. Subsequent theoretical works have shown that quantum fluctuations can affect the underlying phase transition and may lead to the emergence of supersolids with various lattice structures in dipolar condensates. In this work we explore the signatures of such different geometries in confined finite condensates. In addition to previously found triangular lattices, our analysis reveals a rich spectrum of states, from honeycomb patterns and ring structures to striped supersolids. By optimizing relevant parameters we show that transitions between distinct supersolids should be observable in current experiments.

Birth, Life, and Death of a Dipolar Supersolid.

In the short time since the first observation of supersolid states of ultracold dipolar atoms, substantial progress has been made in understanding the zero-temperature phase diagram and low-energy excitations of these systems. Less is known, however, about their finite-temperature properties, particularly relevant for supersolids formed by cooling through direct evaporation. Here, we explore this realm by characterizing the evaporative formation and subsequent decay of a dipolar supersolid by combining high-resolution in-trap imaging with time-of-flight observables. As our atomic system cools toward quantum degeneracy, it first undergoes a transition from thermal gas to a crystalline state with the appearance of periodic density modulation. This is followed by a transition to a supersolid state with the emergence of long-range phase coherence. Further, we explore the role of temperature in the development of the modulated state.

Stationary waves in a superfluid gas of electron-hole pairs in bilayers

Stationary waves in the condensate of electron-hole pairs in the $n-p$ bilayer system are studied. The system demonstrates the transition from a uniform (superfluid) to a nonuniform (supersolid) state. The precursor of this transition is the appearance of the roton-type minimum in the collective mode spectrum. Stationary waves occur in the flow of the condensate past an obstacle. It is shown that the roton-type minimum manifests itself in a rather complicated stationary wave pattern with several families of crests which cross one another. It is found that the stationary wave pattern is essentially modified under variation in the density of the condensate and under variation in the flow velocity. It is shown that the pattern is formed in the main part by shortwave modes in the case of a point obstacle. The contribution of longwave modes is clearly visible in the case of a weak extended obstacle, where the stationary wave pattern resembles the ship wave pattern.

Hydrodynamics of a superfluid smectic

We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose–Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin–orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.