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Castaing's instability in a trapped ultracold gas

Jean-Noël Fuchs, Prevote, O., Dimitri M. Gangardt

Published Jan 1, 2003• 4 citations
OpenAlex

Abstract

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to an experiment at JILA. It shows the presence of Castaing's instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.

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We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to an experiment at JILA. It shows the presence of Castaing's instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.
Ultracold trapped atomic systems are ideal model systems to investigate physical phenomena in the quantum regime.In this work we studied instabilities in spin dynamics of a sample of nondegenerate trapped 87 Rb gas.This is the first experimental investigation of the so-called Castaing instability in such systems.The Castaing instability is an instability in the spin dynamics of spin-polarized systems as a result of introducing sharp spin gradients in their spin profile.We used an optical technique via the ac Stark effect to initialize arbitrary spin profiles in a sample of evaporatively cooled nondegenerate 87 Rb gas.The experimental results manifest evidence for the presence of the Castaing instability in both transverse and longitudinal spin channels.The results agree reasonably well with theoretical studies and results of a numerical solution to the spin transport equation.Some imperfection in the longitudinal spin gradient due to the spin-state preparation technique makes the signature of the instability less clear in the transverse channel.We propose another preparation technique to overcome this shortcoming in future experiments.First, I would like to thank my supervisor, Dr. Jeffrey McGuirk.This thesis would not be possible without his help and guidance.I have been fortunate to work in his group and benefit from his incredible knowledge, enthusiasm and patience.He is always supportive and willing to give advice, yet knows when to let you experience research and learn science on your own.I am grateful for having two great physicists
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.
Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes. PACS numbers: 03.75.Mn,05.30Jp,05.60.Gg,51.10.+y,67.20.+k. In recent JILA experiments,1,2 a mixture of two hyperfine states was found to segregate by species. The theoretical explanation3−8 for this behav-ior is based on the two states playing the role of a pseudo-spin-1/2 system,
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 study the stability of two-domain spin structures in an ultracold gas of magnetically trapped 87Rb^{87}\mathrm{Rb}87Rb atoms above quantum degeneracy. Adding a small effective magnetic field gradient stabilizes the domains via coherent collective spin rotation effects, despite negligibly perturbing the potential energy relative to the thermal energy. We demonstrate that domain stabilization is accomplished through decoupling the dynamics of longitudinal magnetization, which remains in time-independent domains, from transverse magnetization, which undergoes a purely transverse spin wave trapped within the domain wall. We explore the effect of temperature and density on the steady-state domains, and compare our results to a hydrodynamic solution to a quantum Boltzmann equation.