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arXiv:1712.08610 · Physical Review Letters

Droplet Crystal Ground States of a Dipolar Bose Gas

D. Baillie, P. B. Blakie

Published Nov 9, 2018• 119 citations
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Abstract

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.

DOI
10.1103/physrevlett.121.195301

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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 introduce a rigorous method to quantify the superfluidity of these states by analysing their nonclassical translational inertia, which allows us to identify favourable parameter regimes for observing supersolid ground states. The resulting superfluid fraction is a rank-2 tensor which is isotropic for the triangular and honeycomb states but anisotropic for the stripe case. 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.
We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.