Theory of Ramsey spectroscopy and anomalous segregation in ultracoldrubidium

Abstract

The recent anomalous segregation experiment (Lewandowski H J, Harber DM, Whitaker D L and Cornell E A 2002 Phys. Rev. Lett. 88 070403)shows dramatic, rapid internal state segregation for two hyperfine levels of 87Rb. We simulate an effective one-dimensional model of the system forexperimental parameters and find reasonable agreement with the data. TheRamsey frequency is found to be insensitive to the decoherence of thesuperposition, and is only equivalent to the interaction energy shift for a puresuperposition. A quantum Boltzmann equation describing collisions is derivedusing quantum kinetic theory, taking into account the different scattering lengthsof the internal states. As spin-wave experiments are likely to be attempted atlower temperatures we examine the effect of degeneracy on decoherence byconsidering the recent experiment, where degeneracy is around 10%. We also findthat the segregation effect is only possible when transport terms are included inthe equations of motion, and that the interactions only directly alter themomentum distributions of the states. The segregation or spin-wave effect is thusentirely due to coherent atomic motion as foreseen by Lewandowski et al.