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arXiv:2305.02972 · Physical Review A

Toroidal dipolar supersolid with a rotating weak link

M. Nilsson Tengstrand, Philipp Stürmer, Johan Ribbing, S. M. Reimann

Published Jun 29, 2023• 16 citations
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Abstract

Ring-shaped superfluids with weak links provide a perfect environment for studying persistent currents and dynamic stirring protocols. Here, we investigate the effects of a weak-link system on dipolar supersolids. By calculating the ground-state energy at fixed angular momenta, we find that metastable persistent currents may exist in the supersolid phase near the superfluid transition point. When stirring the weak link rapidly enough, we show that vortices can enter the supersolid. These vortex entries cause phase slips, emitting solitonic excitations that interfere with the crystalline structure of the supersolid, leading to a continuous melting and recrystallization of the droplets. Finally, we examine the release of vortex-carrying supersolids from the trap, observing that the released density exhibits a discrete structure associated with the density modulation and a central hole resulting from the vortex core.

DOI
10.1103/physreva.107.063316

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Ring-shaped superfluids with weak links provide a perfect environment for studying persistent currents and dynamic stirring protocols. Here, we investigate the effects of a weak-link system on dipolar supersolids. By calculating the ground-state energy at fixed angular momenta, we find that metastable persistent currents may exist in the supersolid phase near the superfluid transition point. When stirring the weak link rapidly enough, we show that vortices can enter the supersolid. These vortex entries cause phase slips, emitting solitonic excitations that interfere with the crystalline structure of the supersolid, leading to a continuous melting and recrystallization of the droplets. Finally, we examine the release of vortex-carrying supersolids from the trap, observing that the released density exhibits a discrete structure associated with the density modulation and a central hole resulting from the vortex core.
We investigate the rotational properties of a dipolar Bose-Einstein condensate trapped in a toroidal geometry. Studying the ground states in the rotating frame and at fixed angular momenta, we observe that the condensate acts in distinctly different ways depending on whether it is in the superfluid or in the supersolid phase. We find that intriguingly, the toroidal dipolar condensate can support a supersolid persistent current which occurs at a local minimum in the ground state energy as a function of angular momentum, where the state has a vortex solution in the superfluid component of the condensate. The decay of this state is prevented by a barrier that in part consists of states where a fraction of the condensate mimics solid-body rotation in a direction opposite to that of the vortex. Furthermore, we find that superfluid condensates may enter the supersolid phase when forced to take angular momentum. Last, the rotating toroidal supersolid shows hysteretic behavior that is qualitatively different depending on the superfluid fraction of the condensate.
We theoretically investigate the properties of ultracold dipolar atoms in radially coupled, concentric annular traps created by a potential barrier. The nonrotating ground-state phases are investigated across the superfluid-supersolid phase transition, revealing a particle imbalance between the two rings and a preferential density modulation in the outer ring in the absence of rotation. Near the phase transition on the superfluid side, applying rotation can induce density modulations in either ring, depending on the angular momentum and barrier strength. For low angular momentum, such rotation-induced density modulation forms in the outer ring, while for high angular momentum and weak barriers, it emerges in the inner ring. Rotation can lead to persistent currents and the nucleation of a vortex residing either at the center (central vortex) or at the ring junction (Josephson vortex). Josephson vortices can also form at the junctions of the localized density sites induced by rotation in the inner ring, a behavior that is unique to our system. By switching off the trap and allowing the system to expand, distinct interference patterns emerge, which can be analyzed to identify and distinguish between various vortex configurations, and thus can be observed in current state-of-the-art experiments.
Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase slips are induced by vortex excitations created by a rotating weak link. We analyze the influence of a localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate. We simulate in a three-dimensional dissipative mean-field model the dynamics of the condensate using parameters similar to the experimental conditions. Moreover, we consider the dynamics of the stirred condensate far beyond the experimentally explored region and reveal surprising manifestations of complex vortex dynamics.
We investigate vortex nucleation and transport in a rotating dipolar supersolid arranged in a triangular droplet lattice, exploiting its description as an array of weakly linked condensates. By considering both Josephson and macroscopic self-trapping dynamics, we show that local phase differences between droplets provide a compact and highly predictive framework to explore a wide range of vortex behaviors. In particular, Josephson oscillations can be devised to induce vortex nucleation and motion near the vertices of the low-density hexagonal lattice (between droplets), while self-trapping dynamics induce running phases that enable directed vortex transport, which may be accompanied by vortex-antivortex pair creation and annihilation over finite time scales. Comparison with simulations based on the extended Gross-Pitaevskii equation demonstrates that a three-droplet description is essential to capture vortex motion near hexagon vertices. Together, Josephson and self-trapping dynamics provide a tunable protocol to trigger and track vortex nucleation, transport, and vortex-antivortex pair annihilation, revealing the microscopic topological mechanisms underlying phase slips in rotating dipolar supersolids.
A repulsively interacting Bose-Einstein condensate on a ring is well known to show persistent currents. For attractive interactions, however, a bound state may form that renders the rotation classical. Here we show that in a multiply connected confinement, the strong in-plane attraction of an condensate can form stacks of ring-shaped density lumps which may coherently overlap to form a supersolid along the azimuthal symmetry axis of the system. Intriguingly, the functional behavior of the energy–angular-momentum dispersion of the antidipolar ring condensate differs from that of a usual repulsive superfluid. The periodic maxima between persistent flow and the nonrotating ground state flatten significantly and the typical pronounced cusps in the energy dispersion also occur in the rotationally symmetric supersolid state. A weak link results in the reduction of this minimum, shifting it to smaller angular momenta. With an asymmetric link potential one can selectively induce superfluid and rigid-body rotation in different layers within the same system. This intriguing setup offers new perspectives for atomtronics applications.
We have observed well-defined phase slips between quantized persistent current states around a toroidal atomic (23Na) Bose-Einstein condensate. These phase slips are induced by a weak link (a localized region of reduced superfluid density) rotated slowly around the ring. This is analogous to the behavior of a superconducting loop with a weak link in the presence of an external magnetic field. When the weak link is rotated more rapidly, well-defined phase slips no longer occur, and vortices enter into the bulk of the condensate. A noteworthy feature of this system is the ability to dynamically vary the current-phase relation of the weak link, a feature which is difficult to implement in superconducting or superfluid helium circuits.