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arXiv:2606.07266 · Physical Review A

Vortex dynamics in rotating dipolar supersolids across Josephson and self-trapping regimes

Aitor Alaña, Michele Modugno, P. Capuzzi

Published Jun 22, 2026• 0 citations
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Abstract

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.

DOI
10.1103/djd1-y93x

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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.
We analyze the pinning of vortices for a stationary rotating dipolar supersolid along the low-density paths between droplets as a function of the rotation frequency. We restrict ourselves to the stationary configurations of vortices with the same symmetry as that of the array of droplets. In particular, such an analysis clearly reveals that vortices are not only pinned at local density minima, but instead their coordinates are smooth functions of the rotation frequency. Our approach to explaining such a behavior exploits the fact that the wave function of each rotating droplet acquires a linear phase on the coordinates. Hence, the relative phases between the nearest neighboring droplets allow us to predict the position of the vortices in the intermediate low-density region. Here, we show that, for a droplet distribution forming a triangular lattice, the phases of three neighboring droplets are needed for the correct description of the vortex location. In particular, for our confined system, we demonstrate that the estimate accurately reproduces the extended Gross-Pitaevskii results in the spatial regions where the neighboring droplets are well defined.
A dipolar condensate confined in a toroidal trap constitutes a self-induced Josephson junction when the dipoles are oriented perpendicularly to the trap symmetry axis and the sss-wave scattering length is small enough. The ring-shaped double-well potential coming from the anisotropic character of the mean-field dipolar interaction is robust enough to sustain self-trapping dynamics, which takes place when the initial population imbalance between the two wells is large. We show that, in this system, the self-trapping regime is directly related to a vortex-induced phase-slip dynamics. A vortex and antivortex are spontaneously nucleated in the low-density regions before a minimum of the population imbalance is reached and then cross the toroidal section in opposite directions through the junctions. This vortex dynamics yields a phase slip between the two weakly linked condensates causing an inversion of the particle flux.
We study the nucleation and dynamics of vortices in rotating lattice potentials where weakly linked condensates are formed with each condensate exhibiting an almost axial symmetry. Due to such a symmetry, the on-site phases acquire a linear dependence on the coordinates as a result of the rotation, which allows us to predict the position of vortices along the low-density paths that separate the sites. We first show that, for a system of atoms loaded in a four-site square lattice potential, subject to a constant rotation frequency, the analytical expression that we obtain for the positions of vortices of the stationary arrays accurately reproduces the full three-dimensional Gross-Pitaevskii results. We then study the time-dependent vortex nucleation process when a linear ramp of the rotation frequency is applied to a lattice with 16 sites. We develop a formula for the number of nucleated vortices which turns out to have a linear dependence on the rotation frequency with a smaller slope than that of the standard estimate which is valid in the absence of the lattice. From time-dependent Gross-Pitaevskii simulations we further find that the on-site populations remain almost constant during the time evolution instead of spreading outwards, as expected from the action of the centrifugal force. Therefore, the time-dependent phase difference between neighboring sites acquires a running behavior typical of a self-trapping regime. We finally show that, in accordance with our predictions, this fast phase-difference evolution provokes a rapid vortex motion inside the lattice. Our analytical expressions may be useful for describing other vortex processes in systems with the same on-site axial symmetry.
We study the properties of singly quantized linear vortices in the supersolid phase of a dipolar Bose-Einstein condensate at zero-temperature modeling 164Dy^{164}\mathrm{Dy}164Dy atoms. The system is extended in the $x\text{\ensuremath{-}}y$ plane and confined by a harmonic trap in the polarization direction zzz. Our study is based on a generalized Gross-Pitaevskii equation. We characterize the ground state of the system in terms of spatial order and superfluid fraction and compare the properties of a single vortex and of a vortex dipole in the superfluid phase (SFP) and in the supersolid phase (SSP). At variance with a vortex in the SFP, which is free to move in the superfluid, a vortex in the SSP is localized at the interstitial sites and does not move freely. We have computed the energy barrier for motion from an equilibrium site to another. The fact that the vortex is submitted to a periodic potential has a dramatic effect on the dynamics of a vortex dipole made of two counter-rotating parallel vortices; instead of rigidly translating as in the SFP, the vortex and antivortex approach each other by a series of jumps from one site to another until they annihilate in a very short time and their energy is transferred to bulk excitations.
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 study the relation between Josephson dynamics and topological excitations in a dilute Bose-Einstein condensate confined in a double-well trap. We show that the phase slips responsible for the self-trapping regime are created by vortex rings entering and annihilating inside the weak-link region or created at the center of the barrier and expanding outside the system. Large amplitude oscillations just before the onset of self-trapping are also strictly connected with the dynamics of vortex rings at the edges of the inter-well barrier. Our results extend and analyze the dynamics of the vortex-induced phase slippages suggested a few decades ago in relation to the "ac" Josephson effect of superconducting and superfluid helium systems.