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arXiv:1510.07842 · Physical Review A

Droplet formation in a Bose-Einstein condensate with strong dipole-dipole interaction

Kui-Tian Xi, Hiroki Saito

Published Jan 15, 2016• 79 citations
arXivHTMLPDF

Abstract

Motivated by the recent experiment [H. Kadau et al., arXiv:1508.05007], we study roton instability and droplet formation in a Bose-Einstein condensate of $^{164}\mathrm{Dy}$ atoms with strong magnetic dipole-dipole interaction. We numerically solve the cubic-quintic Gross-Pitaevskii equation with dipole-dipole interaction, and show that the three-body interaction plays a significant role in the formation of droplet patterns. We numerically demonstrate the formation of droplet patterns and crystalline structures, decay of droplets, and hysteresis behavior, which are in good agreement with the experiment. Our numerical simulations provide the first prediction on the values of the three-body interaction in a $^{164}\mathrm{Dy}$ Bose-Einstein condensate. We also predict that the droplets remain stable during the time-of-flight expansion. From our results, further experiments investigating the three-body interaction in dipolar quantum gases are required.

DOI
10.1103/physreva.93.011604

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We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
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.
By numerically solving the Gross–Pitaevskii equation with phenomenological dissipation term, we study the vortex formation properties of a three-dimensional dipolar Bose–Einstein condensate of 164Dy atoms. We studied the influence of the contact interaction between atoms on the formation mechanism of vortices. We also study how the dipole orientation affects the vortex formation properties and the number of vortices. We find that enhancing the interaction of short-range repulsion interaction or dipolar repulsion interaction can shorten the time to form a stable vortex structure and increase the number of vortices.
Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in details. Precisely, we are interested in investigating the possibility of droplet formation in a quasi one dimensional geometry. The recent observation have concluded that the droplets are stabilized by the competition between effective mean-filed and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schr\odinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self bound droplet formations.