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Modern Physics Letters B

A NOTE ON SPIN-GAUGE EFFECT OF THE BOSE–EINSTEIN CONDENSATES IN ATOMIC GASES

Jun-Ping Wang

Published Dec 30, 2006• 0 citations
Publisher

Abstract

The Bose–Einstein condensates of the alkali atomic gases trapped in magnetic traps are spinor fields with local "spin-gauge" symmetry.5 Here we show that there is fundamental difference in the manifestation of spin-gauge effects between two low-field-seeking states: |F=2,mF=2〉 and |1,-1〉.
DOI
10.1142/s0217984906012468

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The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge'' symmetry. This symmetry is manifested by a superfluid velocity us{\mathbf{u}}_{s}us​ (or gauge field) generated by the Berry phase of the spin field. In ``static'' traps, us{\mathbf{u}}_{s}us​ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\mathbf{\ensuremath{\Omega}}}_{c1}$, and can lead to vortex ground states.
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.
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.
In a spinor Bose-Einstein gas, the non-zero hyperfine spin of the gas becomes an accessible degree of freedom. At low temperature, such a gas shows both magnetic and superfluid order, and undergoes both density and spin dynamics. These lecture notes present a general overview of the properties of spinor Bose-Einstein gases. The notes are divided in five sections. In the first, we summarize basic properties of multi-component quantum fluids, focusing on the specific case of spinor Bose-Einstein gases and the role of rotational symmetry in defining their properties. Second, we consider the magnetic state of a spinor Bose-Einstein gas, highlighting effects of thermodynamics and Bose-Einstein statistics and also of spin-dependent interactions between atoms. In the third section, we discuss methods for measuring the properties of magnetically ordered quantum gases and present newly developed schemes for spin-dependent imaging. We then discuss the dynamics of spin mixing in which the spin composition of the gas evolves through the spin-dependent interactions within the gas. We discuss spin mixing first from a microscopic perspective, and then advance to discussing collective and beyond-mean-field dynamics. The fifth section reviews recent studies of the magnetic excitations of quantum-degenerate spinor Bose gases. We conclude with some perspectives on future directions for research.
In this thesis we investigate the static, dynamic, and thermodynamic properties\nof atomic spin-1 Bose gases in external magnetic fields. At low magnetic fields\nthe properties of single-component, or scalar condensates, are essentially\nunaffected but can become significantly altered for spinor Bose condensates as\nshown by our studies.\n\nWe first study the Bose-Einstein condensation of trapped spin-1 Bose gases by\nemploying the Hartree-Fock approximation and the two-fluid model within a mean\nfield approximation. Our detailed investigation reveals that the\nferromagnetically interacting spin-1 condensates exhibit triple condensations\nwhile the antiferromagnetically interacting ones show double condensations.\n\nThe ground state structure of homogeneous and trapped spin-1 Bose condensates\nwith ferromagnetic and antiferromagnetic interactions at zero temperature in\nmagnetic fields are then investigated systematically. We further illuminate the\nimportant effect of quadratic Zeeman shift which causes a preferred occupation\nof the $|m_F=0\nangle$ state through spin exchange collisions, $2|m_F=0\nangle\nleftrightarrow |m_F=1\nangle + |m_F=-1\nangle$.\n\nWe also present detailed studies of the off-equilibrium coherent dynamics of\nspin-1 Bose condensates in magnetic fields within the single spatial mode\napproximation. Dynamical instabilities of the off-equilibrium oscillations are\nshown to be responsible for the formation of multiple domains as recently\nobserved in several 87^{87}87Rb experiments.\n\nFinally, we discuss briefly excited condensate states, or soliton-like states,\nin cigar-shaped spin-1 Bose condensates with an effective quasi-1D description,\nusing the developed nonpolynomial Schr"odinger equation.
Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently been predicted to develop spin textures. However, observation of the spin textures requires us to decrease the magnetic field down to approximately 10 microG for spin-1 alkali BECs, so that they are not washed out by the Zeeman effect. We present a scheme to observe the magnetic dipole-dipole interaction in alkali BECs under a realistic magnetic field of approximately 100 mG. Our scheme enables us to extract genuine dipolar effects and should apply also to (52)Cr BECs.