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arXiv:2108.02682 · Physical Review A

Maintaining supersolidity in one and two dimensions

Elena Poli, Thomas Bland, Claudia Politi, Lauritz Klaus, Matthew A. Norcia, Francesca Ferlaino, R. N. Bisset, Luis Santos

Published Dec 9, 2021• 54 citations
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Abstract

We theoretically investigate supersolidity in three-dimensional dipolar Bose-Einstein condensates. We focus on the role of trap geometry in determining the dimensionality of the resulting droplet arrays, which range from one-dimensional to zigzag, through to two-dimensional supersolids in circular traps. Supersolidity is well established in one-dimensional arrays, and may be just as favorable in two-dimensional arrays provided that one appropriately scales the atom number to the trap volume. We develop a tractable variational model---which we benchmark against full numerical simulations---and use it to study droplet crystals and their excitations. We also outline how exotic ring and stripe states may be created with experimentally feasible parameters. Our work paves the way for future studies of two-dimensional dipolar supersolids in realistic settings.

DOI
10.1103/physreva.104.063307

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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 liquidlike 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.
Abstract Supersolid is an exotic state of matter, showing crystalline order with a superfluid background, observed recently in dipolar Bose–Einstein condensate in a trap. Here, we present exact Bloch wave function of the self-trapped supersolid phase, in the presence of mean-field and beyond mean-field interaction. Our general solutions of the amended nonlinear Schrödinger equation are obtained through Möbius transform, connecting a wide class of supersolid solutions to the ubiquitous cnoidal waves. The solutions yield the supersolid phase in the self-trapped quantum matter, where an array of quantum droplets exist, accompanied by a constant condensate. For the supersolid phase, the chemical potential for one class of solutions is the same as that of self-trapped quantum droplets, and is lower for the general non-perturbative solution. Due to the destabilizing effects of fluctuations on long range order in one dimension, the realization of the supersolid phase may be possible in a finite system.
Dipolar condensates have recently been coaxed to form the long-sought supersolid phase. While one-dimensional supersolids may be prepared by triggering a roton instability, we find that such a procedure in two dimensions (2D) leads to a loss of both global phase coherence and crystalline order. Unlike in 1D, the 2D roton modes have little in common with the supersolid configuration. We develop a finite-temperature stochastic Gross-Pitaevskii theory that includes beyond-mean-field effects to explore the formation process in 2D and find that evaporative cooling directly into the supersolid phase-hence bypassing the first-order roton instability-can produce a robust supersolid in a circular trap. Importantly, the resulting supersolid is stable at the final nonzero temperature. We then experimentally produce a 2D supersolid in a near-circular trap through such an evaporative procedure. Our work provides insight into the process of supersolid formation in 2D and defines a realistic path to the formation of large two-dimensional supersolid arrays.
We investigate the crystalline stationary states of a dipolar Bose-Einstein condensate in a planar trapping geometry. Our focus is on the ground-state phase diagram in the thermodynamic limit, where triangular, honeycomb, and stripe phases occur. We quantify the superfluid fraction by calculating the nonclassical translational inertia, which allows us to identify favorable parameter regimes for observing supersolid ground states. We develop two simplified theories to approximately describe the ground states and consider the relationship to roton softening in the uniform ground state. This also allows us to extend the phase diagram to the low density regime. While the triangular and honeycomb states have an isotropic superfluid response tensor, the stripe state exhibits anisotropic superfluidity.