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arXiv:cond-mat/0506630 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of dipolar spinor condensates

Rong Cheng, J-Q Liang, Yunbo Zhang

Published Jul 6, 2005• 13 citations
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Abstract

We study the semiclassical dynamics of a spinor condensate with the magnetic dipole–dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depend greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin-exchange and dipole–dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and macroscopic quantum self-trapping. A simple estimate demonstrates that these effects are accessible and controllable by modifying the geometry of the trapping potential.

DOI
10.1088/0953-4075/38/14/019

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We study the semiclassical dynamics of a spinor condensate with the magnetic dipole–dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depend greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin-exchange and dipole–dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and macroscopic quantum self-trapping. A simple estimate demonstrates that these effects are accessible and controllable by modifying the geometry of the trapping potential.
We consider a spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms in the F=1F=1F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in the mF=0{m}_{F}=0mF​=0 component, we find that the system evolves toward a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin-mixing contact potential. Our results show that because of a dynamical separation of magnetic components, the spin-mixing dynamics in the 87Rb^{87}\mathrm{Rb}87Rb condensate is governed by the dipolar interaction which plays no role in a single-component rubidium system in a magnetic trap.
Selected topics on spinor-dipolar aspects of Bose-Einstein condensation are overviewed. Spinor aspects include spin correlations, fragmentation, dynamical symmetries, and quantum mass acquisition. Dipolar aspects include magnetostriction, d-wave collapse, roton-maxon spectrum, supersolidity, and ferrofluidity. Finally, spinor-dipolar aspects concern the Einstein–de Haas effect and spontaneous mass and spin currents in the ground state. Introduction Bose-Einstein condensation is a phenomenon in which a macroscopic number of particles occupy the same single-particle state as a consequence of symmetrization of a many-body wave function and thereby quantum effects are amplified to the macroscopic level. The amplified single-particle state serves as a complex order parameter whose phase behaves as an emergent thermodynamic quantity, with its temporal and spatial variations giving the chemical potential and the superfluid velocity, respectively. If the interparticle interaction is repulsive, a Bose-Einstein condensate (BEC) acquires stability against excitations out of the condensate because they would cost the Fock exchange energy. This rigidity of the order parameter or the condensate wave function endows a BEC with several remarkable transport properties which are collectively known as superfluidity. In particular, the superfluid fraction can be 100% at zero temperature even though the condensate fraction is depleted due to interparticle interactions. Interparticle interactions also make excited particles phase-locked to the condensate, leading to Bogoliubov quasiparticles, which are the manifestation of phase-coherent particle– hole excitations. When constituent particles have spin degrees of freedom, a BEC features magnetism and spin nematicity which conspire with superfluidity to produce a rich phase diagram. In the absence of an external magnetic field, the mean-field groundstate phase diagram includes two [1, 2], five [3, 4, 5], and eleven phases [6, 7] for spin-1, 2, and 3 BECs, respectively. BECs with spin degrees of freedom are called spinor condensates. Moreover, the magnetic dipole–dipole interaction (MDDI) between atoms lends distinct twists to spinor condensates because it is long-ranged and anisotropic in sharp contrast with other interactions, which are short-ranged and isotropic. In this chapter, we will present a brief overview on the spinordipolar aspects of BEC. An early experimental work of spinor BECs is reviewed in Ref. [8]. Later developments with an emphasis on theoretical aspects are described in Ref. [9]. Many-body physics of polarized dipolar gases is reviewed in Ref. [10].
We study the static and dynamic responses of an F=1F=1F=1 dipolar spinor condensate with magnetic dipole moment under external magnetic fields, focusing on the effects induced by the magnetic dipolar interactions between atoms. A rich set of phenomena are investigated such as the ground state quantum phases, the magnetization steps, spin squeezing, and macroscopic entanglement generation.