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arXiv:2409.04865

Vortex dynamics in two-dimensional supersolids

Chi-Deuk Yoo, Alan T. Dorsey

Published Sep 7, 2024• 0 citations
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Abstract

We investigate the dynamics of quantized vortices in a model two-dimensional supersolid. Starting from an effective action that captures the dynamics of the superfluid condensate and its coupling to the lattice displacements, we integrate out the low-energy Goldstone modes-the phonons of the solid and the superfluid condensate-to arrive at an effective action for the vortices in the condensate. In the low-velocity limit we calculate the effective inertial mass for the vortices, and we find that the mass has a logarithmic frequency dependence, similar to the inertial mass found in superfluid vortices. The vortex dynamics also includes a Magnus force term in the equation of motion that arises from the Berry phase in the effective action.

DOI
10.48550/arxiv.2409.04865

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We derive an effective action for the vortex-position degree of freedom in a superfluid by integrating out condensate phase- and density-fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius RRR, or the typical distance between vortices, is very much larger than the coherence length $\ensuremath{\xi}$. We go beyond the adiabatic approximation numerically, accounting for the quantum dynamics of environmental modes and capturing their dissipative coupling to condensate dynamics. For the case of an optical-lattice superfluid, we demonstrate that vortex motion damping can be adjusted by tuning the ratio between the tunneling energy JJJ and the on-site interaction energy UUU. We comment on the possibility of realizing vortex-Landau-level physics.
We derive an effective action for the vortex-position degree of freedom in a superfluid by integrating out condensate phase- and density-fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius R ,o r the typical distance between vortices, is very much larger than the coherence length ξ. We go beyond the adiabatic approximation numerically, accounting for the quantum dynamics of environmental modes and capturing their dissipative coupling to condensate dynamics. For the case of an optical-lattice superfluid, we demonstrate that vortex motion damping can be adjusted by tuning the ratio between the tunneling energy J and the on-site interaction energy U. We comment on the possibility of realizing vortex-Landau-level physics.
Rotation is a natural tool in ultracold gases to break time-reversal symmetry, yet its impact on the collective excitations of supersolids remains largely unexplored. We show theoretically that tuning the rotation frequency, rather than the interparticle interactions, can trigger the superfluid-to-supersolid transition in Bose-Einstein condensates. Computing excitation spectra in the presence of vortices and persistent currents, we uncover a vortex-driven desoftening mechanism whereby quantized vorticity elevates the gapless Goldstone mode to a finite-energy roton, restoring superfluidity. This effect results in reentrant supersolid phases as a function of rotation frequency, revealing a fundamental coupling between topological defects and crystalline order.
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system.
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.
Motion of vortices in two-dimensional superfluids in the classical limit is studied by solving the Gross-Pitaevskii equation numerically on a uniform lattice. We find that, in the presence of a superflow directed along one of the main lattice periods, vortices move with the superflow on fine lattices but perpendicular to it on coarse ones. We interpret this result as a transition from the full Magnus force in a Galilean-invariant limit to vanishing effective Magnus force in a discrete system, in agreement with the existing experiments on vortex motion in Josephson junction arrays.