Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

TL;DR

This paper models anomalous internal state segregation in ultra-cold rubidium using quantum kinetic theory, revealing that coherent atomic motion causes the effect, with implications for low-temperature spin-wave experiments.

Contribution

It introduces a quantum kinetic model that explains the segregation as due to coherent motion, incorporating collision effects and degeneracy considerations.

Findings

Segregation depends on transport terms in equations of motion.

Ramsey frequency is unaffected by superposition decoherence.

Interactions mainly modify momentum distributions, not internal states.

Abstract

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. 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 of Lewandowski et al. 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 in the experimental report