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Bulletin of the American Physical Society

Spin waves in a spin-1 normal Bose gas

Stefan S. Natu, Erich J. Mueller

Published Mar 15, 2010• 0 citations
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Abstract

We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of {sup 87}Rb is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.

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We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of {sup 87}Rb is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.
We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of 87Rb^{87}\mathrm{Rb}87Rb is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.
We present a theory of spin waves in a non-condensed gas of spin-1 bosons: providing both analytic calculations of the linear theory, and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low energy long wavelength spin waves. In particular, we find that the polar state of Rb-87 is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further we show that for strong enough anti-ferromagnetic interactions, the polar gas is unstable. Finally we explore coherent population dynamics in a collisionless transversely polarized gas.
We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 23Na atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose-Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of 2 change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field.
We study the transverse spin dynamics of trapped polarized Fermi gases in the high-temperature limit. In the non-interacting collisionless regime, a magnetic-field gradient induces collective spin wave oscillations. In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two limits have been extensively studied both experimentally and theoretically, but the crossover between them has received less attention. In this paper, we use a quantum Boltzmann equation to study transverse spin dynamics and show how the excitations evolve from dispersive to diffusive in the high-temperature limit. We provide analytical solutions in the two limiting regimes, which agree well with our numerical results.
We present an analytic Bogoliubov description of a Bose-Einstein condensate of polar molecules trapped in a quasi-two-dimensional geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and static structure factors. This method can be applied to any homogeneous, two-component system with linear coupling and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. The nature of these instabilities is clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave responses in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $\mathrm{\ensuremath{\Lambda}}$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$\mathrm{\ensuremath{\Sigma}}$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field.
We study the transverse spin dynamics of trapped polarized Fermi gases in the high temperature limit. In the non-interacting collisionless regime, a magnetic field gradient induces collective spin wave oscillations. In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two limits have been extensively studied both experimentally and theoretically, but the crossover between them has received less attention. In this paper, we use a quantum Boltzmann equation to study transverse spin dynamics and show how the excitations evolve from dispersive to diffusive in the high temperature limit. We provide analytical solutions in the two limiting regimes, which agree well with our numerical results.