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arXiv:cond-mat/0512693

Ferromagnetic phase transition in spinor Bose gases

Qiang Gu

Published Dec 29, 2005• 0 citations
arXivHTMLPDF

Abstract

The achievement in cooling alkali atomic gases, such as $^{87}$Rb, $^{23}$Na and $^{7}$Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic transition occurs always above Bose-Einstein condensation and the Bose condensate is fully polarized. The low-lying collective excitations of the spinor condensate, including spin and density modes, are discussed. The spectrum of the density mode is of the Bogliubov form and the spin wave spectrum has a $k^2$-formed dispersion relation at long wavelengths. The spin-wave stiffness coefficient contains contribut

DOI
10.48550/arxiv.cond-mat/0512693

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The achievement in cooling alkali atomic gases, such as 87^{87}87Rb, 23^{23}23Na and 7^{7}7Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic transition occurs always above Bose-Einstein condensation and the Bose condensate is fully polarized. The low-lying collective excitations of the spinor condensate, including spin and density modes, are discussed. The spectrum of the density mode is of the Bogliubov form and the spin wave spectrum has a k2k^2k2-formed dispersion relation at long wavelengths. The spin-wave stiffness coefficient contains contribut
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.
It is shown that the ferromagnetic transition takes place always above Bose-Einstein condensation in ferromagnetically coupled spinor Bose gases. We describe the Bose ferromagnet within Ginzburg-Landau theory by a ``two-fluid'' model below Bose-Einstein condensation. Both the Bose condensate and the normal component are spontaneously magnetized. As a main result we show that spin waves in the two fluids are coupled together so as to produce only one mixed spin-wave mode in the coexisting state. The spin-wave stiffness coefficient of the mixed mode, cs{c}_{s}cs​, includes contributions from both the two phases, implying the ``two-fluid'' feature of the system. cs{c}_{s}cs​ can show a sharp bend at the Bose-Einstein condensation temperature.
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.
We report the observation of strongly ferromagnetic F = 1 spinor Bose-Einstein condensates of 7 Li atoms.The condensates are generated in an optical dipole trap without using magnetic Feshbach resonances, so that the condensates have internal spin degrees of freedom.Studying the nonequilibrium spin dynamics, we have measured the ferromagnetic spin interaction energy and determined the s-wave scattering length difference among total spin f channels to be a f =2a f =0 = -18(3) Bohr radius.This strong collision-channel dependence leads to a large variation in the condensate size with different spin composition.We were able to excite a radial monopole mode after a spin-flip transition between the |m F = 0 and |m F = 1 spin states.From the experiments, we estimated the scattering length ratio a f =2 /a f =0 = 0.27(6), and determined a f =2 = 7(2) and a f =0 = 25(5) Bohr radii, respectively.The results indicate the spin-dependent interaction energy of our system is as large as 46% of the condensate chemical potential.
It is investigated theoretically that magnetized Bose-Einstein condensation (BEC) with the internal (spin) degrees of freedom exhibits a rich variety of phase transitions, depending on the sign of the interaction in the spin channel. In the antiferromagnetic interaction case there exist always double BEC transitions from single component BEC to multiple component BEC. In the ferromagnetic case BEC becomes always unstable at a lower temperature, leading to a phase separation. The detailed phase diagram for the temperature vs the polarization, the spatial spin structure, the distribution of non-condensates and the excitation spectrum are examined for the harmonically trapped systems.
Spinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical progress in understanding the static and dynamic properties of these fluids. The connection between system properties and the rotational symmetry properties of the atomic states and their interactions are investigated. Following a review of the experimental techniques used for characterizing spinor gases, their mean-field and many-body ground states, both in isolation and under the application of symmetry-breaking external fields, are discussed. These states serve as the starting point for understanding low-energy dynamics, spin textures, and topological defects, effects of magnetic-dipole interactions, and various nonequilibrium collective spin-mixing phenomena. The paper aims to form connections and establish coherence among the vast range of works on spinor Bose gases, so as to point to open questions and future research opportunities.