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arXiv:cond-mat/9803160 · Journal of the Physical Society of Japan

Bose-Einstein Condensation with Internal Degrees of Freedom in Alkali Atom Gases

Tetsuo Ohmi, Kazushige Machida

Published Jun 15, 1998• 1,095 citations
arXivHTMLPDF

Abstract

The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in $^{23}$Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian constructed from general gauge and spin rotation symmetry principles fundamental equations for condensate are derived. The ground state where time reversal symmetry is broken in some case and low-lying collective modes, e.g. spin and density wave modes, are discussed. Novel vortex as a topological defect can be created experimentally.

DOI
10.1143/jpsj.67.1822

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The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in 23^{23}23Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian constructed from general gauge and spin rotation symmetry principles fundamental equations for condensate are derived. The ground state where time reversal symmetry is broken in some case and low-lying collective modes, e.g. spin and density wave modes, are discussed. Novel vortex as a topological defect can be created experimentally.
Since the discovery of Bose-Einstein condensation in dilute atomic vapours in 1995, there has been a monumental increase in the research effort in the field of atomic physics due to the unforeseen opportunities and challenges that the degenerate quantum gases present. In particular, quantum gases can emulate complicated models that arise in solid state and high energy physics, allowing realisations of exotic phenomena that have proven to be elusive in their original context. An outstanding example is the existence of various topological defects in degenerate quantum gases with internal degrees of freedom. Topological excitations such as skyrmions and several types of monopoles can be shown to take place in Bose gases with a hyperfine spin degree of freedom as a result of a coupling to an external field or due to thermal fluctuations. A central question in the context of dilute Bose gases is the relation between superfluidity and Bose-Einstein condensation. The dimensionality of the underlying space as well as the internal degrees of freedom have a direct impact on the existence and the nature of the Bose-Einstein condensate. For example, any uniform Bose gas in two spatial dimensions or an antiferromagnetic spinor Bose gas can give rise to a superfluid state which does not involve a conventional Bose-Einstein condensate corresponding to a single macroscopically occupied quantum state. In this Thesis, properties of different topological defects and their relation to superfluidity in dilute Bose gases are investigated. Stability and creation of coreless vortices are first studied and a method to cyclically increase the angular momentum of the condensate is introduced. Subsequently, the properties and creation of different types of monopoles are investigated and an experimentally feasible method to create a Dirac monopole is presented. Finally, finite temperature phase transitions in quasi-two-dimensional Bose gases with a spin degree of freedom are analysed and, as a related subject, the stability of vortex clusters formed by vortices and antivortices is studied.
Superfluidity and Bose-Einstein condensation (BEC) in ultracold atomic gases represent macroscopic quantum phenomena arising from collective particle behavior at near-zero temperatures. Experimental realizations of BEC in alkali gases have enabled the observation of quantized vortices, matter-wave interference, and nonclassical excitations. This article reviews theoretical frameworks including Gross-Pitaevskii and Bogoliubov models, experimental techniques such as evaporative cooling and optical trapping, and computational approaches for simulating condensate dynamics. Two graphical analyses illustrate the condensate density profile and vortex lattice formation. Understanding these phenomena has implications for quantum simulation, atom interferometry, and exploration of quantum hydrodynamics.
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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.