We theoretically investigate the merging behavior of two identical supersolids through dipolar Bose-Einstein condensates confined within a double-well potential. By adiabatically tuning the barrier height and the spacing between the two wells for specific trap aspect ratios, the two supersolids move toward each other and lead to the emergence of a variety of ground-state phases, including a supersolid state, a macrodroplet state, a ring state, and a labyrinth state. We construct a phase diagram that characterizes various states seen during the merging transition. Further, we calculate the force required to pull the two portions of the gas apart, finding that the merged supersolids act like a deformable plastic material. Our work paves the way for future studies of layer structure in dipolar supersolids and the interaction between them in experiments.
We theoretically investigate the merging behaviour of two identical supersolids through dipolar Bose-Einstein condensates confined within a double-well potential. By adiabatically tuning the barrier height and the spacing between the two wells for specific trap aspect ratios, the two supersolids move toward each other and lead to the emergence of a variety of ground state phases, including a supersolid state, a macrodroplet state, a ring state, and a labyrinth state. We construct a phase diagram that characterizes various states seen during the merging transition. Further, we calculate the force required to pull the two portions of the gas apart, finding that the merged supersolids act like a deformable plastic material. Our work paves the way for future studies of layer structure in dipolar supersolids and the interaction between them in experiments.
We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas under the confinement of a bubble trapping potential. We do so in terms of the scattering length a and the number of particles. We observe the emergence of a wide variety of dipolar solids, consisting on arrangements of different number of droplets along a ring over the equator of the spherical shell confinement. We also show that the transition between the different phases of the system can be engineered by varying a , the number of particles or the radius of the trap, parameters, which can be experimentally tuned. Finally, we show the importance of working in microgravity conditions as gravity unstabilizes the observed dipolar solids. Published by the American Physical Society 2024
Dipolar Bose-Einstein condensates represent a powerful platform for the exploration of quantum many-body phenomena arising from long-range interactions. A series of recent experiments has demonstrated the formation of supersolid states of matter. Subsequent theoretical works have shown that quantum fluctuations can affect the underlying phase transition and may lead to the emergence of supersolids with various lattice structures in dipolar condensates. In this work, we explore the signatures of such different geometries in confined finite condensates. In addition to previously found triangular lattices, our analysis reveals a rich spectrum of states, from honeycomb patterns to striped supersolids. By optimizing relevant parameters, we show that transitions between distinct supersolids should be observable in current experiments.
We investigate the dynamics of Bose-Einstein condensate droplets composed of
164Dy atoms formed in a double-well potential following removal of the interwell barrier. By solving the dipolar Gross-Pitaevskii equation, we determine phase diagrams of ground-state configurations as functions of the atom number confined in the double-well potential. For an interwell separation
2d=3μm, we consider the relative dipolar-to-contact interaction strengths
εdd=1.4,
1.45, and
1.5. Symmetry-broken lowest-energy configurations are found for
εdd=1.5 and, over a reduced range of atom numbers, for
εdd=1.45, whereas no symmetry-broken states are found for
εdd=1.4 up to
N=5×104. We analyze the subsequent time evolution after removal of the central barrier, revealing both droplet oscillations and merger events leading to the formation of larger droplets. The oscillations are driven by the external potential and by the repulsive tails of the in-plane component of the dipolar interaction. For the two-droplet states at
εdd=1.5 and
2d=3μm, merging is found for
N=8000 and
8800, whereas the droplets remain separated for the investigated cases with
N≥9000. Increasing the initial separation to
2d=5μm shifts the approximate upper atom number for merging to
N≃1.65×104, demonstrating that the crossover is controlled by the competition between the post-quench excess energy and the repulsive inter-droplet barrier.
We study the dynamics of merging two initially independent Bose–Einstein condensates by adiabatically deforming the trap potential from a double well into a single well. The process of slowly decreasing the height of the central barrier of the double well is simulated by a full 3D calculation of the Gross–Pitaevskii equation. We investigate the dynamics by considering some factors relevant to experiments, e.g., the atom number, the initial state in each well, the initial relative phase between the two condensates. For a small number of 4400 atoms in each well and the same initial phase, we find for both condensates in the ground state or the p-wave soliton state that the final state is the ground state or the p-wave soliton state of the final trap potential. For cases in which both condensates are vortex states, we find much richer dynamics with the appearance of an extra vortex. We also discuss the cases for different initial relative phases. For comparison, we present results for 44 000 atoms corresponding to a larger nonlinear term in the Gross–Pitaevskii equation. In support of future experimental observations, we show both probability density and current maps.
Due to its peculiar superfluid-crystal duality feature, the supersolid has received great research interest. Recently, researchers have paid much attention to its elastic response properties; however, the inelastic deformation has barely been explored. In this work, we study the transition from elastic to inelastic deformation of a dipolar supersolid Bose-Einstein condensate trapped in a box potential (i.e., a dipolar supersolid with finite size). We obtain the stationary supersolid states (both ground and excited) of the system and examine the relation between the supersolid size and the number of unit cells it can accommodate, which can essentially help us to understand the dynamical responses of the supersolid during a dilation or compression process. We found that within a certain dilation or compression extent, the supersolid can retain its original crystal structure, that is, it endures an elastic deformation; however, when the extent exceeds a critical threshold, the original crystal structure of the supersolid will be disrupted, which signifies an inelastic deformation. Furthermore, we both analytically and numerically determine the critical point of the transition from elastic to inelastic deformation and map out a phase diagram. These results open up new territory in the research of supersolid mechanical properties and may find applications in quantum material science and quantum-based technologies.