We theoretically propose and numerically realize spin echo in a spinor Bose-Einstein condensate (BEC). We investigate the influence on the spin echo of phase separation of the condensate. The equation of motion of the spin density exhibits two relaxation times. We use two methods to separate the relaxation times and hence demonstrate a technique to reveal magnetic dipole-dipole interactions in spinor BECs.
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-π , 0-running, running-running, 2nπ & running-2π , single nonrigid pendulum, and two rigid pendulums phase modes. These Josephson modes in the three states are expected to be found in real atomic Bose gas systems.
We used the Gross-Pitaevskii equations to investigate ferromagnetic resonance in spin-1 BoseEinstein 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.
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