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arXiv:1005.2403 · Physical Review Letters

Supersolid Droplet Crystal in a Dipole-Blockaded Gas

Fabio Cinti, Piyush Jain, Massimo Boninsegni, Andrea Micheli, P. Zoller, Guido Pupillo

Published Sep 21, 2010• 256 citations
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Abstract

A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential softened at short distances. Using exact numerical techniques, we study the low-temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighboring droplets.

DOI
10.1103/physrevlett.105.135301

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A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential softened at short distances. Using exact numerical techniques, we study the low-temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighboring droplets.
We discuss the realization of mesoscopic phases of dipolar gases relevant to current experiments with cold polar molecules and Rydberg atoms confined to two dimensions. We predict the existence of superfluid clusters, mesoscopic supersolids, and crystals for a small number of trapped particles, with no counterpart in the homogeneous situation. For certain strengths of the dipole-dipole interactions, the stabilization of purely {\it non-classical crystals} by quantum fluctuations is possible. We propose a magnification scheme to detect the spatial structure of these crystalline phases.
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.
We show that the ground state of a dipolar Bose gas in a cylindrically symmetric harmonic trap has a rich phase diagram, including droplet crystal states in which a set of droplets arrange into a lattice pattern that breaks the rotational symmetry. An analytic model for small droplet crystals is developed and used to obtain a zero temperature phase diagram that is numerically validated. We show that in certain regimes a coherent low-density halo surrounds the droplet crystal, giving rise to a novel phase with localized and extended features.
We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate.The theory reveals a ground state phase diagram with three distinct regimes-a regular Bose-Einstein condensate and incoherent and coherent arrays of quantum droplets.The coherent droplets are connected by a background condensate, which leads-in addition to the periodic density modulation-to a robust phase coherence throughout the whole system.We further theoretically demonstrate that we are able to dynamically approach the ground state in our experiment and that its lifetime is limited only by three-body losses.Experimentally we probe and confirm the signatures of the phase diagram by observing the in situ density modulation as well as the phase coherence using matter wave interference.
A mesoscopic system of dipolar bosons trapped by a harmonic potential is considered. The system has a number of physical realizations including dipole excitons, atoms with large dipolar moment, polar molecules, and Rydberg atoms in inhomogeneous electric field. We carry out a diffusion Monte Carlo simulation to define the quantum properties of a two-dimensional system of trapped dipoles at zero temperature. In dimensionless units the system is described by two control parameters, namely, the number of particles and the strength of the interparticle interaction. We have shown that when the interparticle interaction is strong enough a mesoscopic crystal is formed. As the strength of interactions is decreased a multistage melting takes place. Off-diagonal order in the system is tested using natural-orbitals analysis. We have found that the system might be Bose condensed even in the case of strong interparticle interactions. There is a set of parameters for which a spatially ordered structure is formed while simultaneously the fraction of Bose-condensed particles is nonzero. This might be considered as a realization of a mesoscopic supersolid.
The competition of dipole-dipole and contact interactions leads to exciting new physics in dipolar gases, well illustrated by the recent observation of quantum droplets and rotons in dipolar condensates. We show that the combination of the roton instability and quantum stabilization leads under proper conditions to a novel regime that presents supersolid properties due to the coexistence of stripe modulation and phase coherence. In a combined experimental and theoretical analysis, we determine the parameter regime for the formation of coherent stripes, whose lifetime of a few tens of milliseconds is limited by the eventual destruction of the stripe pattern due to three-body losses. Our results open intriguing prospects for the development of long-lived dipolar supersolids.