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arXiv:2202.13264 · Physical Review A

Supersolid-like square- and honeycomb-lattice crystallization of droplets in a dipolar condensate

Luis E. Young-S., Sadhan K. Adhikari

Published Mar 21, 2022• 28 citations
arXivHTMLPDF

Abstract

We demonstrate a supersolid-like spatially periodic square- and honeycomb-lattice crystallization of droplets in addition to the commonly studied triangular-lattice crystallization in a cylindrically symmetric quasi-two-dimensional trapped dipolar condensate, using a beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-type interaction. These three types of crystallization of droplets may appear for the same atomic interaction and the same trap frequencies. The energies $E$ of all three crystallizations as a function of the number $N$ of atoms satisfy the universal scaling relation $E\ensuremath{\sim}{N}^{0.4}$, indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed $N$, constitute two quasidegenerate ground states, while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.

DOI
10.1103/physreva.105.033311

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We study dipole-mode and scissors-mode oscillations of a harmonically trapped dipolar supersolid, composed of dipolar droplets arranged on a one-dimensional (1D) or a 2D lattice, to establish the robustness of its crystalline structure under translation and rotation, using a beyond-mean-field model including a Lee-Huang-Yang interaction. The dipolar atoms are polarized in the zzz direction with the supersolid crystalline structure lying in the $x\text{\ensuremath{-}}y$ plane. A stable dipole-mode oscillation is possible in the case of both quasi-1D and quasi-2D dipolar supersolids, whereas a sustained angular scissors-mode oscillation is possible only in the case of a quasi-1D dipolar supersolid between a maximum and a minimum of trap anisotropy in the $x\text{\ensuremath{-}}y$ plane. In both cases there is no visible deformation of the crystalline structure of the dipolar supersolid during the oscillation. The theoretical estimate of the scissors-mode-oscillation frequency is in good agreement with the present results and the agreement improves with an increase in the number of droplets in the supersolid and also with an increase in the confining trap frequencies. The results of this study can be tested experimentally with present knowhow.
We study the ground states of rotating atomic Bose-Einstein condensates with dipolar interactions. We present the results of numerical studies on a periodic geometry which show vortex lattice ground states of various symmetries: triangular and square vortex lattices, ``stripe crystal,'' and ``bubble crystal.'' We present the phase diagram (for systems with a large number of vortices) as a function of the ratio of dipolar to contact interactions and of the chemical potential. We discuss the experimental requirements for observing transitions between vortex lattice ground states via dipolar interactions. We finally investigate the stability of mean-field supersolid phases of a quasi-two-dimensional nonrotating Bose gas with dipolar interactions.
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We demonstrate the formation of a novel eigenstate in a strongly dipolar binary $^{164}\mathrm{Dy}\text{\ensuremath{-}}^{162}\mathrm{Dy}$ mixture, where the inter- and intraspecies dipolar lengths are larger than the corresponding scattering lengths. When this mixture is confined by a quasi-two-dimensional harmonic trap, the total density exhibits the formation of droplets on a spatially symmetric triangular or square lattice, where each droplet is formed of a single species of atoms; two types of atoms never exist on the same lattice site. The density of any of the species shows a partially filled incomplete lattice; only the total density exhibits a completely full lattice structure. In this theoretical investigation we employ the numerical solution of an improved mean-field model including a Lee-Huang-Yang-type interaction in the intraspecies components alone, meant to stop a collapse of the atoms at high atom density.
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.