We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for nearest-neighbor and long-range dipolar interactions, relevant for two-dimensional arrays of ultra-cold polar molecules, here we address directly the nature of the superfluid-to-supersolid transition. Based on symmetry arguments and quantum Monte Carlo simulations, we conclude that this quantum phase transition is driven first-order beyond the line of particle-hole symmetry. Along this line, the transition is continuous and its scaling behavior consistent with the three-dimensional (3D) XY universality class. We relate this finding to a 3D Z6 clock model description of the enlarged symmetry of the solid order parameter field. In the generic case however, the symmetry reduces to that of a 3D Z3 clock model, which reflects the first-order nature of the generic superfluid-to-supersolid quantum phase transition on the triangular lattice.
Breakthrough experiments have newly explored the fascinating physics of dipolar quantum droplets and supersolids. The recent realization of dipolar mixtures opens further intriguing possibilities. We show that under rather general conditions, the presence of a second component catalyzes droplet nucleation and supersolidity in an otherwise unmodulated condensate. Droplet catalyzation in miscible mixtures, which may occur even for a surprisingly small impurity doping, results from a local roton instability triggered by the doping-dependent modification of the effective dipolar strength. The cata…
We present a theory for the emergence of a supersolid state in a cigar-shaped dipolar quantum Bose gas. Our approach is based on a reduced three-dimensional (3D) theory, where the condensate wavefunction is decomposed into an axial field and a transverse part described variationally. This provides an accurate fully 3D description that is specific to the regime of current experiments and efficient to compute. We apply this theory to understand the phase diagram for a gas in an infinite tube potential. We find that the supersolid transition has continuous and discontinuous regions as the average…
We calculate the ground states of a dipolar Bose gas confined in an infinite tube potential. We use the extended Gross-Pitaevskii equation theory and present a novel numerical method to efficiently obtain solutions. A key feature of this method is an analytic result for a truncated dipole-dipole interaction potential that enables the long-ranged interactions to be accurately evaluated within a unit cell. Our focus is on the transition of the ground state to a crystal driven by dipole-dipole interactions as the short ranged interaction strength is varied. We find that the transition is continuo…
Experiments on dipolar Bose-Einstein condensates have recently reported the observation of supersolidity. Although quantized vortices constitute a key probe of superfluidity, their observability in dipolar supersolids is largely prevented by the strong density depletion caused by the formation of droplets. We present a novel approach to the nucleation of vortices and their observation, based on the quenching of the s-wave scattering length across the superfluid-supersolid transition. Starting from a slowly rotating, vortex-free, configuration in the superfluid phase, we predict vortex nucleati…
Atom-light crystallization of BECs in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration
We investigate the dynamics of a Bose-Einstein condensate interacting with two non-interfering and counterpropagating modes of a ring resonator. Superfluid, supersolid and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid …
Collective Excitations and Stability of Nonequilibrium Polariton Supersolids
Abrikosov Center for Theoretical Physics, Moscow Center for Advanced Studies（莫斯科高级研究中心阿布里科索夫理论物理中心）；National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)（莫斯科工程物理国立研究核大学）；Russian Quantum Center, Skolkovo IC（俄罗斯量子中心斯科尔科沃创新中心）
The existence of a paradoxical supersolid phase of matter, possessing the apparently incompatible properties of crystalline order and superfluidity, was predicted 50 years ago. Solid helium was the natural candidate, but there supersolidity has not been observed yet, despite numerous attempts. Ultracold quantum gases have recently shown the appearance of the periodic order typical of a crystal, due to various types of controllable interactions. A crucial feature of a D-dimensional supersolid is the occurrence of up to D+1 gapless excitations reflecting the Goldstone modes associated with the s…
