Motivated by the recent experiment [H. Kadau et al., arXiv:1508.05007 (2015], we study roton instability and droplet formation in a Bose-Einstein condensate of 164 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 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. Dipolar Bose-Einstein condensates (BECs) of atoms with large magnetic dipole moments, such as chromium [1], dysprosium [2], and erbium [3], are systems in which the longrange and anisotropic dipole-dipole interaction strongly affects their static and dynamic properties. The researches on such a dipolar system both in theories and in experiments are driven by the search for new novel phases in condensed matter physics. Structured ground states and roton excitation spectrum in a pancake-shaped trap have been studied [4][5][6][7][8][9][10]. Anisotropic expansion [11] and collapsing instability [12][13][14] have been observed in a chromium BEC. Increasing attention has also been focusing on bright solitons [15,16], anisotropic superfluidity [17,18], Faraday patterns [19], and multicomponent BECs [20][21][22][23]. A binary BEC with a strong dipole-dipole interaction exhibits instability and forms patterns similar to those in magnetic liquids, such as hexagonal, soliton-like, and labyrinthine patterns [20]. Droplet formation has also been investigated in dipolar atomic systems [24,25].In the recent experiment reported in Ref.[26], interactioninduced periodic patterns spontaneously formed in a BEC of dysprosium atoms. By using Feshbach resonance to control the ratio between the s-wave and dipole-dipole interactions, they observed discrete droplet patterns arranged in a long-lived triangular lattice. This result indicates possibility that the system possesses a stable periodic state with matterwave coherence, which is therefore a candidate of supersolidity [27][28][29]. Before exploring this possiblity, a theoretical understanding of the experimental results in Ref.[26] is required.In this Rapid Communication, we propose a theoretical model to explain the experimental results in Ref. [26]. One finds that the standard mean-field Gross-Pitaevskii model with dipole-dipole interaction cannot reproduce the experimental results; the strong Roton instability is always followed by the d-wave dipolar collapse, which hinders the droplet formation. To circumvent this problem, we propose to include the th...

We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimensional approximation are performed, and the characteristic lengths of the domains are estimated analytically. Patterns resembling those in magnetic classical fluids are modulated when the number ratio of atoms, the trap ratio of the external potential, or tilted polarization with respect to the z direction is varied.

We consider a two-component Bose-Einstein condensate, which contains atoms with magnetic dipole moments aligned along the z direction (labeled as component 1) and nonmagnetic atoms (labeled as component 2). The problem is studied by means of exact numerical simulations. The effects of dipole-dipole interaction on phase separations are investigated. It is shown that, in the quasi-one-dimensional regime, the atoms in component 2 are squeezed out when the dimensionless dipolar strength parameter is small, whereas the atoms in component 1 are pushed out instead when the parameter is large. This is in contrast to the phenomena in the quasi-two-dimensional regime. These two components are each kicked out by the other in the quasi-one-dimensional regime and this phenomenon is discussed as well.