Two-Dimensional Supersolid Formation in Dipolar Condensates

Abstract

Dipolar condensates have recently been coaxed into supersolid phases supporting both superfluid and crystal excitations. While one-dimensional (1D) supersolids may be prepared via a roton instability, we find that such a procedure in two dimensions (2D) leads to greater heating. We go on to show that 2D roton modes have little in common with the supersolid configuration: instead, unstable centralized rotons trigger a process of nonlinear crystal growth. By evaporatively cooling directly into the supersolid phase-hence bypassing the first-order roton instability-we experimentally produce a 2D supersolid in a near-circular trap. We develop a stochastic Gross-Pitaevskii theory that includes beyond-meanfield effects to further explore the formation process. We calculate the static structure factor for a 2D supersolid, and compare to a 1D array. These results provide insight into the process of supersolid formation in 2D, and define a realistic path to the formation of large two-dimensional supersolid arrays.

Can angular oscillations probe superfluidity in dipolar supersolids?

“…By varying the applied magnetic field in the vicinity of Feshbach resonances near 18-23 G, we can access scattering lengths that correspond to either unmodulated BECs or modulated states. In past works, we have demonstrated that modulated states created at the corresponding field have global phase coherence [23,24]. In this work, we expect the same to be true, but refer to these experimental states simply as modulated, as we do not repeat the characterization for every trap condition used.…”

“…In the present work, we study the angular response of recently demonstrated supersolids with two-dimensional structure [23,24]. With this more favorable geometry, one may expect to observe unambiguous effects of superfluidity on the frequency of oscillations following a sudden angular rotation.…”

“…Experimentally, we use a dipolar quantum gas of 164 Dy atoms (up to approximately 5 × 10 4 condensed atoms), confined within an optical dipole trap (ODT) of tunable geometry, formed at the intersection of three laser beams [23][24][25]. The trap geometry and particle number at the end of the evaporative cooling sequence determine the character of the modulated ground state, which can form linear, zigzag, or triangular lattice configurations [26].…”

Maintaining supersolidity in one and two dimensions

“…While almost all dipolar supersolids have been experimentally realized as one-dimensional (1D) droplet arrays-see, for example, Refs. [10][11][12][13][14][15]-two recent experiments have for the first time created two-dimensional (2D) supersolids [29,30], thus opening an exciting frontier. An early theoretical study in 2D predicted a rich phase diagram determined by competing metastable crystal configurations [31].…”

Dimensional crossover in the superfluid-supersolid quantum phase transition

“…So, it is not clear whether in one-row dipolar supersolids one can observe continuous, discontinuous or both types of quantum phase transitions, nor how these transitions relate to the general theory. For trapped supersolids with 2D lattice structures, numerical simulations predict discontinuous transitions [23,24].…”