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arXiv:1010.1075 · Physical Review A

Ferromagnetic resonance in spinor dipolar Bose-Einstein condensates

Masashi Yasunaga, Makoto Tsubota

Published Jan 24, 2011• 4 citations
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Abstract

We used the Gross-Pitaevskii equations to investigate ferromagnetic resonance in spin-1 Bose-Einstein condensates with a magnetic dipole-dipole interaction. By introducing the dipole interaction, we obtained equations similar to the Kittel equations used to represent ferromagnetic resonance in condensed-matter physics. These equations indicated that the ferromagnetic resonance originated from dipolar interaction, and that the resonance frequency depended upon the shape of the condensate. Furthermore, spin currents driven by spin diffusions are characteristic of this system.

DOI
10.1103/physreva.83.013618

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We used the Gross-Pitaevskii equations to investigate ferromagnetic resonance in spin-1 Bose-Einstein condensates with a magnetic dipole-dipole interaction. By introducing the dipole interaction, we obtained equations similar to the Kittel equations used to represent ferromagnetic resonance in condensed-matter physics. These equations indicated that the ferromagnetic resonance originated from dipolar interaction, and that the resonance frequency depended upon the shape of the condensate. Furthermore, spin currents driven by spin diffusions are characteristic of this system.
Bose-Einstein condensates which are dominated by magnetic dipole-dipole interaction are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from the large spin limit to obtain an effective minimal Hamiltonian. This is a version extended from a nonlinear sigma model. By solving the Gross-Pitaevskii equation, we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.
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.
We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the nonlocal Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 87Rb condensate by changing the number of atoms or the trap frequency.
We theoretically study the internal Josephson effect, which is driven by spin-exchange interactions and magnetic dipole-dipole interactions, in a three-level system for spin-1 Bose--Einstein condensates, obtaining novel spin dynamics. We introduce single spatial mode approximations into the Gross--Pitaevskii equations and derive the Josephson-type equations, which are analogous to tunneling currents through three junctions between three superconductors. From an analogy with two interacting nonrigid pendulums, we identify unique varied oscillational modes, called the $0--\ensuremath{\pi}$, 0−−running0--\mathit{running}0−−running, running−−running\mathit{running}--\mathit{running}running−−running, $2n\ensuremath{\pi} & \mathit{running}--2\ensuremath{\pi}$, singlenonrigidpendulum\mathit{single nonrigid pendulum}singlenonrigidpendulum, and tworigidpendulums\mathit{two rigid pendulums}tworigidpendulums phase modes. These Josephson modes in the three states are expected to be found in real atomic Bose gas systems.
We study the spin dynamics of a spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction (MDDI) based on the Gross-Pitaevskii and Bogoliubov theories. We find that various magnetic structures such as checkerboards and stripes emerge in the course of the dynamics due to the combined effects of spin-exchange interaction, MDDI, quadratic Zeeman and finite-size effects, and nonstationary initial conditions. However, the short-range magnetic order observed by the Berkeley group [Phys. Rev. Lett. 100, 170403 (2008)] is not fully reproduced in our calculations; the periodicity of the order differs by a factor of 3 and the checkerboard pattern eventually dissolves in the course of time. Possible reasons for the discrepancy are discussed.
We propose an experiment which proves the possibility of spinning gaseous media via dipolar interactions in the spirit of the famous Einstein-de Haas effect for ferromagnets. The main idea is to utilize resonances that we find in spinor condensates of alkali atoms while these systems are placed in an oscillating magnetic field. A significant transfer of angular momentum from spin to motional degrees of freedom observed on resonance is a spectacular manifestation of dipolar effects in spinor condensates.