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arXiv:cond-mat/0212114 · Physical Review A

Phenomenological theory of spinor Bose-Einstein condensates

Qiang Gu

Published Aug 13, 2003• 15 citations
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Abstract

It was reported that Bose-Einstein condensation induces a spontaneous magnetization in spinor bosons. This phenomenon is called Bose-Einstein ferromagnetism (BEF). We propose a phenomenological model consistent with the prediction of BEF and show that BEF might be attributed to the intrinsic magnetic moment of particles. Taking BEF into account, the phase diagram of an optically trapped spinor condensate is reexamined.

DOI
10.1103/physreva.68.025601

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Cambridge University Press eBooks•Oct 4, 2018•0 citations
It was reported that Bose-Einstein condensation induces a spontaneous magnetization in spinor bosons. This phenomenon is called Bose-Einstein ferromagnetism (BEF). We propose a phenomenological model consistent with the prediction of BEF and show that BEF might be attributed to the intrinsic magnetic moment of particles. Taking BEF into account, the phase diagram of an optically trapped spinor condensate is reexamined.
We show that in the two-component Bose gas with Rashba spin-orbit coupling an arbitrarily small attractive interaction between bosons with opposite spin induces spontaneous ferromagnetism below a finite critical temperature Tc{T}_{c}Tc​. In the ferromagnetic phase the single-particle spectrum exhibits a unique minimum in momentum space in the direction of the magnetization. For sufficiently small temperatures below Tc{T}_{c}Tc​ the bosons eventually condense into the unique state at the bottom of the spectrum, forming a ferromagnetic Bose-Einstein condensate.
We calculate the Bose-Einstein condensation (BEC) temperature of spin-1 atomic bosons in external magnetic field, taking into account the influence of the quadratic Zeeman effect. In case that the quadratic Zeeman coefficient is positive, the BEC temperature exhibits a nontrivial dependence on the magnetic field and a magnetic-field-induced reentrant phenomenon of BEC is observed. This phenomenon could be well understood by the competition between the linear and quadratic Zeeman effects. Reentrance of BEC in a trapped spinor Bose gas is also discussed.
The magnetism of Fermi gases and local magnetic moments has long been a key research topic in condensed matter physics,while that of Bose gases has historically been less studied. The reason for this may be due to the fact that He-4,the prototypical Bose system studied in earlier years,is a system of scalar particles and does not display magnetism at all. The realization of Bose-Einstein condensation in alkali atoms opens up a way to study magnetism in spinor bosons,because these constituent atoms usually have a hyperfine spin degree of freedom. This paper will review our current understanding of magnetism in Bose gases,especially focusing on new results obtained regarding ferromagnetic transitions in spinor bosons and the spin dynamics of spinor condensates.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
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].