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arXiv:1106.2876 · Physical Review A

Dissipative hydrodynamic equation of a ferromagnetic Bose-Einstein condensate: Analogy to magnetization dynamics in conducting ferromagnets

Kazue Kudo, Yuki Kawaguchi

Published Oct 7, 2011• 19 citations
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Abstract

The hydrodynamic equation of a spinor Bose-Einstein condensate (BEC) gives a simple description of spin dynamics in the condensate. We introduce the hydrodynamic equation of a ferromagnetic BEC with dissipation originating from the energy dissipation of the condensate. The dissipative hydrodynamic equation has the same form as an extended Landau-Lifshitz-Gilbert (LLG) equation, which describes the magnetization dynamics of conducting ferromagnets in which localized magnetization interacts with spin-polarized currents. Employing the dissipative hydrodynamic equation, we demonstrate the magnetic domain pattern dynamics of a ferromagnetic BEC in the presence and absence of a current of particles, and discuss the effects of the current on domain pattern formation. We also discuss the characteristic lengths of domain patterns that have domain walls with and without finite magnetization.

DOI
10.1103/physreva.84.043607

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The hydrodynamic equation of a spinor Bose-Einstein condensate (BEC) gives a simple description of spin dynamics in the condensate. We introduce the hydrodynamic equation of a ferromagnetic BEC with dissipation originating from the energy dissipation of the condensate. The dissipative hydrodynamic equation has the same form as an extended Landau-Lifshitz-Gilbert (LLG) equation, which describes the magnetization dynamics of conducting ferromagnets in which localized magnetization interacts with spin-polarized currents. Employing the dissipative hydrodynamic equation, we demonstrate the magnetic domain pattern dynamics of a ferromagnetic BEC in the presence and absence of a current of particles, and discuss the effects of the current on domain pattern formation. We also discuss the characteristic lengths of domain patterns that have domain walls with and without finite magnetization.
Magnetic domain patterns in a ferromagnetic Bose-Einstein condensate (BEC) show different properties depending on the quadratic Zeeman effect and dissipation. Another important factor that affects domain patterns and domain growth is superfluid flow of atoms. Domain growth in a ferromagnetic BEC with negative quadratic Zeeman energy is characterized by the same growth law as a (classical) binary fluid in the inertial hydrodynamic regime. In the absence of the superfluid flow, the domain growth law for negative quadratic Zeeman energy is the same as that of scalar conserved fields, such as binary alloys.
We introduce equations of motion for spin dynamics in a ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction, written using a vector expressing the superfluid velocity and a complex scalar describing the magnetization. This simple hydrodynamical description extracts the dynamics of spin wave and affords a straightforward approach by which to investigate the spin dynamics of the condensate. To demonstrate the advantages of the description, we illustrate dynamical instability and magnetic fluctuation preference, which are expressed in analytical forms.
Abstract We develop a novel model of the magnetized spin-1 Bose–Einstein condensate (BEC) of neutral atoms, using the method of many-particle quantum hydrodynamic (QHD) and propose an original derivation of the system of continual equations. We consider bosons with a spin-spin interaction and a short range interaction in the first order in the interaction radius, on the of basis of the self-consistent field approximation of the QHD equations. We demonstrate that the dynamics of the fluid velocity and magnetization is determined by a nontrivial modification of the Euler and Landau–Lifshitz equation, and show that a nontrivial modification of the spin density evolution equation contains the spin torque effect that arises from the self-interactions between spins of the bosons. The properties of the dispersion spectrum of collective excitations are described. We obtain the new contribution of the self-interaction of spins in the spin wave spectrum together with the influence of an external magnetic field and spin-spin interactions between polarized particles. The anisotropic spin wave instability is predicted.
We obtain the equations of motion for a ferromagnetic Bose condensate of arbitrary spin in the long-wavelength limit. We find that the magnetization of the condensate is described by a nontrivial modification of the Landau-Lifshitz equation, in which the magnetization is advected by the superfluid velocity. This hydrodynamic description, valid when the condensate wave function varies on scales much longer than either the density or spin healing lengths, is physically more transparent than the corresponding time-dependent Gross-Pitaevskii equation. We discuss the conservation laws of the theory and its application to the analysis of the stability of magnetic helices and Larmor precession. Precessional instabilities, in particular, provide a novel physical signature of dipolar forces.
We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is, with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uniaxial ferromagnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction accelerates the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., those produced with the large magnetic-dipole-moment atoms 166Er^{166}\mathrm{Er}166Er. This enables experimental access to the dissipation parameter $\mathrm{\ensuremath{\Gamma}}$ in the Gross-Pitaevskii mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that $\mathrm{\ensuremath{\Gamma}}$ is a single scalar independent of spin indices.
Abstract A dynamical theory is presented for the domain wall in the spinor Bose-Einstein condensate of “effective” one dimension. The formulation is based on the time-dependent Landau-Ginzburg (LG) theory written in terms of the spinor order parameter. The procedure is carried out in such a way that an adiabatic change of the collective coordinates which are given by the kink position as well as the phase function built in the spinor, is adapted to the canonical term (alias geometric phase) in the LG Lagrangian. Two problems are discussed: The first one is to explore the translational motion of the kink center in the presence of the pinning potential, which results in the quantum potential problem. The other one concerns the steering of the domain wall by modulating the externally driven magnetic field assisted with dissipation. The present attempt would shed light on the spinor Bose-Einstein condensates from a novel viewpoint.