The task of experimentally investigating the inherently dual properties of a supersolid, a simultaneous superfluid and solid, has become more critical following the recent experimental exploration of supersolid regimes in dipolar Bose-Einstein condensates (BECs) of ^{164}Dy. We introduce a supersolid order parameter that uses vortex-vortex trajectory correlations to simultaneously reveal the periodic density of the underlying solid and superfluidity in a single measure. We propose experiments using existing technology to optically create and image trajectories of vortex dipoles in dipolar BECs that is applicable to large system sizes. We numerically test our observable and find that vortex-vortex correlations reveal the supersolid lattice structure while distinguishing it from superfluidity even in the presence of dissipation. Our method sets the stage for experiments to use vortex trajectory correlations to investigate fundamental properties of supersolids arising from their dynamics and phase transitions as experimental system sizes are increased.
The task of experimentally investigating the inherently dual properties of a supersolid, a simultaneous superfluid and solid, has become more critical following the recent experimental exploration of supersolid regimes in dipolar Bose-Einstein condensates (BECs) of ^{164}Dy. We introduce a supersolid order parameter that uses vortex-vortex trajectory correlations to simultaneously reveal the periodic density of the underlying solid and superfluidity in a single measure. We propose experiments using existing technology to optically create and image trajectories of vortex dipoles in dipolar BECs that is applicable to large system sizes. We numerically test our observable and find that vortex-vortex correlations reveal the supersolid lattice structure while distinguishing it from superfluidity even in the presence of dissipation. Our method sets the stage for experiments to use vortex trajectory correlations to investigate fundamental properties of supersolids arising from their dynamics and phase transitions as experimental system sizes are increased.
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 to striped supersolids. By optimizing relevant parameters, we show that transitions between distinct supersolids should be observable in current experiments.
Abstract Supersolid states simultaneously feature properties typically associated with a solid and with a superfluid. Like a solid, they possess crystalline order, manifesting as a periodic modulation of the particle density; but unlike a typical solid, they also have superfluid properties, resulting from coherent particle delocalization across the system. Such states were initially envisioned in the context of bulk solid helium, as a possible answer to the question of whether a solid could have superfluid properties1–5. Although supersolidity has not been observed in solid helium (despite much effort)6, ultracold atomic gases provide an alternative approach, recently enabling the observation and study of supersolids with dipolar atoms7–16. However, unlike the proposed phenomena in helium, these gaseous systems have so far only shown supersolidity along a single direction. Here we demonstrate the extension of supersolid properties into two dimensions by preparing a supersolid quantum gas of dysprosium atoms on both sides of a structural phase transition similar to those occurring in ionic chains17–20, quantum wires21, 22 and theoretically in chains of individual dipolar particles23, 24. This opens the possibility of studying rich excitation properties25–28, including vortex formation29–31, and ground-state phases with varied geometrical structure7, 32 in a highly flexible and controllable system.
Vortices are expected to exist in a supersolid but experimentally their detection can be difficult because the vortex cores are localized at positions where the local density is very low. We address here this problem by performing numerical simulations of a dipolar Bose-Einstein Condensate (BEC) in a pancake confinement at T=0 K and study the effect of quantized vorticity on the phases that can be realized depending upon the ratio between dipolar and short-range interaction. By increasing this ratio the system undergoes a spontaneous density modulation in the form of an ordered arrangement of multi-atom "droplets". This modulated phase can be either a "supersolid" (SS) or a "normal solid" (NS). In the SS state droplets are immersed in a background of low-density superfluid and the system has a finite global superfluid fraction resulting in non-classical rotational inertia. In the NS state no such superfluid background is present and the global superfluid fraction vanishes. We propose here a protocol to create vortices in modulated phases of dipolar BEC by "freezing" into such phases a vortex-hosting superfluid (SF) state. The resulting system, depending upon the interactions strengths, can be either a SS or a NS To discriminate between these two possible outcome of a "freezing" experiment, we show that upon releasing of the radial harmonic confinement, the expanding vortex-hosting SS shows tell-tale quantum interference effects which display the symmetry of the vortex lattice of the originating SF, as opposed to the behavior of the NS which shows instead a ballistic radial expansion of the individual droplets. Such markedly different behavior might be used to prove the supersolid character of rotating dipolar condensates.
We theoretically investigate a supersolid structure taking the form of stacked, disk-shaped superfluid droplets connected via a dilute superfluid, in an antidipolar condensate. A phase diagram is determined for varying the particle number and scattering length, identifying the regions of a regular dipolar superfluid, supersolid stacks, and isolated stacked disk-shaped droplets in an experimentally realizable trapping potential. The collective Bogoliubov excitation spectrum across the superfluid-supersolid phase transition is studied, and the transition point is found to be associated with the breaking of the degeneracy of the two lowest-lying modes. The dynamical generation of the supersolid stacks is also investigated by ramping down the scattering length across the phase transition. Moreover, we have studied the impact of vortex-line penetration on the phase transition. We have found that the presence of a vortex line causes the supersolid region to move towards weaker contact interactions. Our detailed numerical simulations highlight that an antidipolar condensate can create such supersolid stacks within an experimentally reachable parameter regime.
We study the properties of singly quantized linear vortices in the supersolid phase of a dipolar Bose-Einstein condensate at zero-temperature modeling 164Dy atoms. The system is extended in the $x\text{\ensuremath{-}}y$ plane and confined by a harmonic trap in the polarization direction z. Our study is based on a generalized Gross-Pitaevskii equation. We characterize the ground state of the system in terms of spatial order and superfluid fraction and compare the properties of a single vortex and of a vortex dipole in the superfluid phase (SFP) and in the supersolid phase (SSP). At variance with a vortex in the SFP, which is free to move in the superfluid, a vortex in the SSP is localized at the interstitial sites and does not move freely. We have computed the energy barrier for motion from an equilibrium site to another. The fact that the vortex is submitted to a periodic potential has a dramatic effect on the dynamics of a vortex dipole made of two counter-rotating parallel vortices; instead of rigidly translating as in the SFP, the vortex and antivortex approach each other by a series of jumps from one site to another until they annihilate in a very short time and their energy is transferred to bulk excitations.
Supersolids are states of matter that spontaneously break two continuous symmetries: translational invariance due to the appearance of a crystal structure and phase invariance due to phase locking of single-particle wave functions, responsible for superfluid phenomena. While originally predicted to be present in solid helium, ultracold quantum gases provided a first platform to observe supersolids, with particular success coming from dipolar atoms. Phase locking in dipolar supersolids has been probed through e.g. measurements of the phase coherence and gapless Goldstone modes, but quantized vortices, a hydrodynamic fingerprint of superfluidity, have not yet been observed. Here, with the prerequisite pieces at our disposal, namely a method to generate vortices in dipolar gases and supersolids with two-dimensional crystalline order, we report on the theoretical investigation and experimental observation of vortices in the supersolid phase. Our work reveals a fundamental difference in vortex seeding dynamics between unmodulated and modulated quantum fluids. This opens the door to study the hydrodynamic properties of exotic quantum systems with multiple spontaneously broken symmetries, in disparate domains such as quantum crystals and neutron stars.