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arXiv:1908.10633 · Physical Review Research

Interplay of spin and mass superfluidity in antiferromagnetic spin-1 Bose-Einstein condensates and bicirculation vortices

E. B. Sonin

Published Nov 14, 2019• 2 citations
arXivHTMLPDF

Abstract

This paper presents a hydrodynamic approach to the interplay of spin and mass superfluidity in the antiferromagnetic spin-1 Bose Einstein condensate. The author uses a Gross--Pitaevskii formalism and explores the similarities with the Landau--Lifshitz--Gilbert theory of bipartite solids
DOI
10.1103/physrevresearch.1.033103

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The paper investigates the coexistence and interplay of spin and mass superfluidity in a ferromagnetic spin-1 Bose-Einstein condensate. Superfluidity is possible only in the presence of uniaxial anisotropy (linear and quadratic Zeeman effect). This follows from the topology of the order-parameter space (vacuum manifold). According to the Landau criterion, the critical phase gradients, both for mass and spin supercurrents, vanish at the phase transition from the easy-plane to the easy-axis anisotropy. However, mass superfluidity is still possible at the phase transition. This is because the Landau criterion signals instability only with respect to nonsingular vortices with special ratio between circulations of mass and spin currents. Phase slips produced by these vortices are not sufficient for complete decay of supercurrents. Full decay of supercurrents requires phase slips with vortices of another topological class and larger energy. These phase slips are suppressed by energetic barriers up to the upper critical velocity (gradient) exceeding the Landau critical velocity. The upper critical velocity does not vanish nor has any anomaly in the critical point at the phase transition from the easy-plane to the easy-axis anisotropy.
We establish a complete set of hydrodynamic equations for a spin-1 Bose-Einstein condensate, which are equivalent to the multicomponent Gross-Pitaevskii equations and expressed in terms of only observable physical quantities: the spin and the nematic (or quadrupolar) tensor in addition to the density of particles and the mass current that appear in the hydrodynamic description of a scalar condensate. The obtained hydrodynamic equations involve a generalized Mermin-Ho relation that is valid regardless of the spatiotemporal dependence of the spin polarization. Low-lying collective modes for phonons and magnons are reproduced by linearizing the hydrodynamic equations. We also apply the single-mode approximation to the hydrodynamic equations and find a complete set of analytic solutions.
This work rectifies the hydrodynamic equations commonly used to describe the superfluid velocity field in such a way that vortex dynamics are also taken into account. In the field of quantum turbulence, it is of fundamental importance to know the correct form of the equations which play similar roles to the Navier-Stokes equation in classical turbulence. Here, such equations are obtained by carefully taking into account the frequently overlooked multivalued nature of the U(1)U(1)U(1) phase field. Such an approach provides exact analytical explanations to some numerically observed features involving the dynamics of quantum vortices in Bose-Einstein condensates, such as the universal t1/2{t}^{1/2}t1/2 behavior of reconnecting vortex lines. It also expands these results beyond the Gross-Pitaevskii theory so that some features can be generalized to other systems such as superfluid 4He^{4}\mathrm{He}4He, dipolar condensates, and mixtures of different superfluid systems.
Superfluidity and Bose-Einstein condensation (BEC) in ultracold atomic gases represent macroscopic quantum phenomena arising from collective particle behavior at near-zero temperatures. Experimental realizations of BEC in alkali gases have enabled the observation of quantized vortices, matter-wave interference, and nonclassical excitations. This article reviews theoretical frameworks including Gross-Pitaevskii and Bogoliubov models, experimental techniques such as evaporative cooling and optical trapping, and computational approaches for simulating condensate dynamics. Two graphical analyses illustrate the condensate density profile and vortex lattice formation. Understanding these phenomena has implications for quantum simulation, atom interferometry, and exploration of quantum hydrodynamics.
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.
Hydrodynamic theory of the spinor BEC condensate with Rashba spin-orbit coupling is presented. A close mathematical analogy of the Rashba-Bose-Einstein condensate model to the recently developed theory of chiral magnetism is found. Hydrodynamic equations for mass density, superfluid velocity, and the local magnetization are derived. The mass current is shown to contain an extra term proportional to the magnetization direction, as a result of the Rashba coupling. Elementary excitations around the two known ground states of the Rashba-Bose-Einstein condensate Hamiltonian, the plane-wave, and the stripe states, are worked out in the hydrodynamic framework, highlighting the cross coupling of spin and superflow velocity excitations due to the Rashba term.