The Meissner effect is a hallmark of superconductivity arising from the interplay between charged superfluids and electromagnetic fields. However, superfluidity can also occur in systems of charge-neutral particles with magnetic or electric dipole moments, such as Bose-Einstein condensates of magnons or excitons. Despite this interest, the electromagnetic response of dipole superfluids, including potential analogues or contrasts to the Meissner effect, remains poorly understood. Here we develop a Ginzburg-Landau theory to describe dipole superfluids subjected to a pseudo-magnetic field, which is induced by a spatially modulating electromagnetic field. In magnetic dipole superfluids, the response differs strikingly from the conventional Meissner effect: the external field is enhanced by a positive feedback, forming a vortex lattice separated by singular domain walls with diverging electric charges. In contrast, electric dipole superfluids exhibit screening akin to superconductors, where the pseudo-magnetic field is suppressed except near vortices. The electromagnetic response of dipole superfluids, including potential analogues to the Meissner effect, remains poorly understood. This paper develops a phenomenological theory and shows that magnetic-dipole superfluids form vortex lattices separated by singular domain walls with concentrated electric charge, while electric-dipole superfluids exhibit vortex lattices resembling those in conventional superconductors.
The Meissner effect is a hallmark of superconductivity arising from the interplay between charged superfluids and electromagnetic fields. However, superfluidity can also occur in systems of charge-neutral particles with magnetic or electric dipole moments, such as Bose-Einstein condensates of magnons or excitons. Despite this interest, the electromagnetic response of dipole superfluids, including potential analogues or contrasts to the Meissner effect, remains poorly understood. Here we develop a Ginzburg-Landau theory to describe dipole superfluids subjected to a pseudo-magnetic field, which is induced by a spatially modulating electromagnetic field. In magnetic dipole superfluids, the response differs strikingly from the conventional Meissner effect: the external field is enhanced by a positive feedback, forming a vortex lattice separated by singular domain walls with diverging electric charges. In contrast, electric dipole superfluids exhibit screening akin to superconductors, where the pseudo-magnetic field is suppressed except near vortices. The electromagnetic response of dipole superfluids, including potential analogues to the Meissner effect, remains poorly understood. This paper develops a phenomenological theory and shows that magnetic-dipole superfluids form vortex lattices separated by singular domain walls with concentrated electric charge, while electric-dipole superfluids exhibit vortex lattices resembling those in conventional superconductors.
A theory determining the electric and magnetic properties of vortex states in Bose-Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system, which we derive correct to the first order in the atomic centre-of-mass velocity. For the first time using centre-of-mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov-Casher and the Röntgen interaction terms. The constitutive relations, which link the electromagnetic fields to the matter fields via their electric polarization and magnetization, follow from the Lagrangian as well as the corresponding Hamiltonian. These relations, together with a generalized Gross-Pitaevskii equation, determine the magnetic (electric) monopole charge distributions accompanying an order n vortex state when the constituent atoms are characterized by an electric dipole (magnetic dipole). Field distributions associated with electric dipole active (magnetic dipole active) BECs in a vortex state are evaluated for an infinite- and a finite-length cylindrical BEC. The predicted monopole charge distributions, both electric and magnetic, automatically satisfy the requirement of global charge neutrality and the derivations highlight the exact symmetry between the electric and magnetic properties. Order of magnitude estimates of the effects are given for an atomic gas BEC, superfluid helium and a spin-polarized hydrogen BEC.
A theory determining the electric and magnetic properties of vortex states in Bose–Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system, which we derive correct to the first order in the atomic centre-of-mass velocity. For the first time using centre-of-mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov–Casher and the Röntgen interaction terms. The constitutive relations, which link the electromagnetic fields to the matter fields via their electric polarization and magnetization, follow from the Lagrangian as well as the corresponding Hamiltonian. These relations, together with a generalized Gross–Pitaevskii equation, determine the magnetic (electric) monopole charge distributions accompanying an order n vortex state when the constituent atoms are characterized by an electric dipole (magnetic dipole). Field distributions associated with electric dipole active (magnetic dipole active) BECs in a vortex state are evaluated for an infinite- and a finite-length cylindrical BEC. The predicted monopole charge distributions, both electric and magnetic, automatically satisfy the requirement of global charge neutrality and the derivations highlight the exact symmetry between the electric and magnetic properties. Order of magnitude estimates of the effects are given for an atomic gas BEC, superfluid helium and a spin-polarized hydrogen BEC.
Within a gauge-invariant microscopic kinetic theory, we study the electromagnetic response in the superconducting states. Both superfluid and normal-fluid dynamics are involved. We predict that the normal fluid is present only when the excited superconducting velocity vs is larger than a threshold ${v}_{L}=|\mathrm{\ensuremath{\Delta}}|/{k}_{F}$. Interestingly, with the normal fluid, we find that there exists friction between the normal-fluid and superfluid currents. Due to this friction, part of the superfluid becomes viscous. Therefore a three-fluid model, normal fluid and nonviscous and viscous superfluids, is proposed. For the stationary magnetic response, at vs<vL with only the nonviscous superfluid, the Meissner supercurrent is excited and the gap equation can be reduced to the Ginzburg-Landau equation. At ${v}_{s}\ensuremath{\ge}{v}_{L}$, with the normal fluid and nonviscous and viscous superfluids, in addition to the directly excited Meissner supercurrent in the superfluid, a normal-fluid current is also induced through the friction drag with the viscous superfluid current. Due to the normal-fluid and viscous-superfluid currents, the penetration depth is influenced by the scattering effect. In addition, a modified Ginzburg-Landau equation is proposed. We predict an exotic phase in which both the resistivity and superconducting gap are finite. As for the optical response, the excited vs oscillates with time. When vs<vL, only the nonviscous superfluid is present, whereas at ${v}_{s}\ensuremath{\ge}{v}_{L}$, normal fluid and nonviscous and viscous superfluids are present. We show that the excited normal-fluid current exhibits the Drude-model behavior, while the superfluid current consists of the Meissner supercurrent and Bogoliubov quasiparticle current. Due to the friction between the superfluid and normal-fluid currents, the optical conductivity is captured by the three-fluid model. Finally, we also study the optical excitation of the Higgs mode. By comparing the contributions from the drive and Anderson-pseudospin pump effects, we find that the drive effect is dominant at finite temperature whereas at zero temperature, both effects contribute.
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
It is shown that, in the presence of a magnetic field, a quantized vortex line in a superfluid liquid acquires a linear polarization charge, which is localized near the vortex axis over a length on the order of the coherence length. It is found that the total charge of a rectilinear vortex is nonzero, while the vortex pair and vortex ring have a nonzero dipole moment. The electric fields of rectilinear vortices near the end surface of a cylindrical vessel filled with a superfluid liquid are calculated. The electric polarization of superfluid systems in the presence of thermally activated vortex pairs and vortex rings has been studied. It is shown that such a polarization arises in the presence of relative motion of the normal and superfluid components.
Quantized vortices are the hallmark of superfluidity, and are often sought out as the first observable feature in new superfluid systems. Following the recent experimental observation of vortices in Bose–Einstein condensates comprised of atoms with inherent long-range dipole-dipole interactions [ Nat. Phys. 18 , 1453-1458 (2022)], we thoroughly investigate vortex properties in the three-dimensional dominantly dipolar regime, where beyond-mean-field effects are crucial for stability, and investigate the interplay between trap geometry and magnetic field tilt angle.