Theory of Ramsey spectroscopy and anomalous segregation in ultracold rubidium

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