Coexistence of ordinary elasticity and superfluidity in a model of a defect-free supersolid

Sound, Superfluidity, and Layer Compressibility in a Ring Dipolar Supersolid

We propose a protocol to excite the Goldstone modes of a supersolid dipolar Bose-Einstein condensed gas confined in a ring geometry. By abruptly removing an applied periodic modulation proportional to cos(φ), where φ is the azimuthal angle, we explore the resulting oscillations of the gas by solving the extended Gross-Pitaevskii equation. The value of the two longitudinal sound velocities exhibited in the supersolid phase are analyzed using the hydrodynamic theory of supersolids at zero temperature, which explicitly takes into account both the superfluid and the crystal nature of the system. This approach allows for the determination of the layer compressibility modulus as well as of the superfluid fraction, f_{S}, in agreement with the Leggett estimate of the nonclassical moment of inertia.

Evidence of superfluidity in a dipolar supersolid from nonclassical rotational inertia

A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Nonclassical rotational effects have also been considered in the context of the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here, we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. Using a dipolar gas of dysprosium atoms, we studied a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, previously investigated in ordinary superfluids. From the measured moment of inertia, we deduced a superfluid fraction that is different from zero and of order of unity, providing direct evidence of the superfluid nature of the dipolar supersolid.

Saga of Superfluid Solids

The article presents the state of the art and reviews the literature on the long-standing problem of the possibility for a sample to be at the same time solid and superfluid. Theoretical models, numerical simulations, and experimental results are discussed.

Rotating a Supersolid Dipolar Gas

Distinctive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment of inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation, we show that the moment of inertia determines the value of the frequency of the scissors mode, which is significantly affected by the reduction of superfluidity in the supersolid phase. The case of an in-plane isotropic trapping is instead well suited to study the formation of quantized vortices, which are shown to be characterized, in the supersolid phase, by a sizeable deformed core, caused by the presence of the surrounding density peaks.

Integrable model for density-modulated quantum condensates: Solitons passing through a soliton lattice

An integrable model possessing inhomogeneous ground states is proposed as an effective model of nonuniform quantum condensates such as supersolids and Fulde-Ferrell-Larkin-Ovchinnikov superfluids. The model is a higher-order analog of the nonlinear Schrödinger equation. We derive an n-soliton solution via the inverse scattering theory with elliptic-functional background and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons. We also provide the exact bosonic and fermionic quasiparticle eigenstates and show their tunneling phenomena. The solutions are expressed by a determinant of theta functions.

From coherent shocklets to giant collective incoherent shock waves in nonlocal turbulent flows

Understanding turbulent flows arising from random dispersive waves that interact strongly through nonlinearities is a challenging issue in physics. Here we report the observation of a characteristic transition: strengthening the nonlocal character of the nonlinear response drives the system from a fully turbulent regime, featuring a sea of coherent small-scale dispersive shock waves (shocklets) towards the unexpected emergence of a giant collective incoherent shock wave. The front of such global incoherent shock carries most of the stochastic fluctuations and is responsible for a peculiar folding of the local spectrum. Nonlinear optics experiments performed in a solution of graphene nano-flakes clearly highlight this remarkable transition. Our observations shed new light on the role of long-range interactions in strongly nonlinear wave systems operating far from thermodynamic equilibrium, which reveals analogies with, for example, gravitational systems, and establishes a new scenario that can be common to many turbulent flows in photonic quantum fluids, hydrodynamics and Bose–Einstein condensates.

Understanding turbulent flows arising from random dispersive waves that interact through nonlinearities is a challenging issue in physics. Here, the authors model and observe experimentally in a nonlinear optics set-up the transition between a sea of small-scale shocklets and a giant collective shock wave.

Activated nucleation of vortices in a dipole-blockaded supersolid condensate

We investigate theoretically and numerically a model of a supersolid in a dipole-blockaded Bose-Einstein condensate. The dependence of the superfluid fraction with an imposed thermal bath and a uniform boost velocity on the condensate is considered. Specifically, we observe a critical velocity for the nucleation of vortices in our system that is strongly linked to a steplike decrease in the superfluid fraction. We are able to use a scaling argument based on the energy required to activate a vortex, relating the critical temperature to the critical velocity, and find that this relationship is in good agreement with the numerical simulations carried out on the nonlocal Gross-Pitaevskii equation.

Supersolid vortex crystals in Rydberg-dressed Bose-Einstein condensates

We study rotating quasi-two-dimensional Bose-Einstein condensates, in which atoms are dressed to a highly excited Rydberg state. This leads to weak effective interactions that induce a transition to a mesoscopic supersolid state. Considering slow rotation, we determine its superfluidity using quantum Monte Carlo simulations as well as mean field calculations. For rapid rotation, the latter reveal an interesting competition between the supersolid crystal structure and the rotation-induced vortex lattice that gives rise to new phases, including arrays of mesoscopic vortex crystals.

Excitation spectrum of a supersolid

Conclusive experimental evidence of a supersolid phase in any known condensed matter system is presently lacking. On the other hand, a supersolid phase has been recently predicted for a system of spinless bosons in continuous space, interacting via a broad class of soft-core, repulsive potentials. Such an interaction can be engineered in assemblies of ultracold atoms, providing a well-defined pathway to the unambiguous observation of this fascinating phase of matter. In this Letter, we study by first principles computer simulations the elementary excitation spectrum of the supersolid, and show that it features two distinct modes, namely, a solidlike phonon and a softer collective excitation, related to broken translation and gauge symmetry, respectively.

Impurity crystal in a bose-einstein condensate

We investigate the behavior of impurity fields immersed in a larger condensate field in various dimensions. We discuss the localization of a single impurity field within a condensate and note the effects of surface energy. We derive the functional form of the attractive condensate-mediated interaction between two impurities. Generalizing the analysis to N impurity fields, we show that within various parameter regimes a crystal of impurity fields can form spontaneously in the condensate. Finally, the system of condensate and crystallized impurity structure is shown to have nonclassical rotational inertia, which is characteristic of superfluidity; i.e., the system can be seen to exhibit supersolid behavior.

Hydrodynamics of superfluids confined in blocked rings and wedges

Motivated by many recent experimental studies of nonclassical rotational inertia (NCRI) in superfluid and supersolid samples, we present a study of the hydrodynamics of a superfluid confined in the two-dimensional region (equivalent to a long cylinder) between two concentric arcs of radii b and a (b<a) subtending an angle beta , with 0< or =beta< or =2pi . The case beta=2pi corresponds to a blocked ring. We discuss the methodology to compute the NCRI effects and calculate these effects both for small angular velocities, when no vortices are present, and in the presence of a vortex. We find that, for a blocked ring, the NCRI effect is small and that therefore there will be a large discontinuity in the moment of inertia associated with blocking or unblocking circular paths. For blocked wedges (b=0) with beta>pi , we find an unexpected divergence of the velocity at the origin, which implies the presence of either a region of normal fluid or a vortex for any nonzero value of the angular velocity. Implications of our results for experiments on "supersolid" behavior in solid 4He are discussed. A number of mathematical issues are pointed out and resolved.

Are neutron stars with crystalline color-superconducting cores relevant for the LIGO experiment?

We estimate the maximal deformation that can be sustained by a rotating neutron star with a crystalline color-superconducting quark core. Our results suggest that current gravitational-wave data from the Laser Interferometer Gravitational-Wave Observatory have already reached the level where a detection would have been possible over a wide range of the poorly constrained QCD parameters. This leads to the nontrivial conclusion that compact objects do not contain maximally strained color crystalline cores drawn from this range of parameter space. We discuss the uncertainties associated with our simple model and how it can be improved in the future.

Nonclassical rotational inertia of a supersolid

As proposed by Leggett [Phys. Rev. Lett. 25, 1543 (1970)10.1103/PhysRevLett.25.1543], the supersolidity of a crystal is characterized by the nonclassicalical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau, and Rica [Phys. Rev. Lett. 72, 2426 (1994)10.1103/PhysRevLett.72.2426], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the moment of inertia. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity.

Fermionic stabilization and density-wave ground state of a polar condensate

We examine the stability of a trapped dipolar condensate mixed with a single-component fermion gas at T=0. Whereas pure dipolar condensates with a small s-wave interaction are unstable even at small dipole-dipole interaction strength, we find that the admixture of fermions can significantly stabilize them, depending on the strength of the boson-fermion interaction. Within the stable regime we find a region where a ground state is characterized by a density wave along the soft trap direction.