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Physical Review Letters

General Structure of Bose-Einstein Condensates with Arbitrary Spin

Tin-Lun Ho, Lan Yin

Published Mar 13, 2000• 36 citations
Publisher

Abstract

Motivated by the recent discoveries of spin-1 and pseudo-spin-1/2 Bose gas, we have studied the general structure of the Bose gases with arbitrary spin. A general method is developed to uncover the elementary building blocks of the angular momentum eigenstates, as well as the relations (or interactions) between them. Applications of this method to Bose gas with integer spins $(f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,2,3)$ and half integer spins $(f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2,3/2)$ reveal many surprising structures.

DOI
10.1103/physrevlett.84.2302

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Motivated by the recent discoveries of spin-1 and pseudo-spin-1/2 Bose gas, we have studied the general structure of the Bose gases with arbitrary spin. A general method is developed to uncover the elementary building blocks of the angular momentum eigenstates, as well as the relations (or interactions) between them. Applications of this method to Bose gas with integer spins (f=1,2,3)(f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,2,3)(f=1,2,3) and half integer spins (f=1/2,3/2)(f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2,3/2)(f=1/2,3/2) reveal many surprising structures.
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.
Properties of the ground state and the spectrum of elementary excitations are investigated for the low density ultracold spinor 3D Bose gas of particles with arbitrary nonzero spin. Gross-Pitaevskii equations are derived. Within the framework of the considering interaction Hamiltonian it is shown that the ground state spin structure and spin part of the chemical potential is determined by the renormalized interaction, being defined by the contribution of the virtual large momenta. The ferromagnetic structure of the ground state, and the equation of the phase, density, and spin dynamics are obtained from Gross-Pitaevskii equations.