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arXiv:cond-mat/0601140

Relaxation of the molecular state in atomic Fermi gases near a Feshbach resonance

V. S. Babichenko

Published Jan 9, 2006• 0 citations
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Abstract

The relaxation processes in an ultra-cold degenerate atomic Fermi gas near a Feshbach resonance are considered. It is shown that the relaxation rate of the molecules being in a resonance with the atomic Fermi system is of the order of the part of the chemical potential determined by the interaction between resonance molecules. In this connection the lower part of the excitation spectrum in the system of resonance molecules is not well-defined.

DOI
10.48550/arxiv.cond-mat/0601140

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The relaxation processes in an ultra-cold degenerate atomic Fermi gas near a Feshbach resonance are considered. It is shown that the relaxation rate of the molecules being in a resonance with the atomic Fermi system is of the order of the part of the chemical potential determined by the interaction between resonance molecules. In this connection the lower part of the excitation spectrum in the system of resonance molecules is not well-defined.
To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose- Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].
The entropy and kinetic, potential, and interaction energies of an atomic Fermi gas in a trap are studied under the assumption of thermal equilibrium for finite temperature. A Feshbach resonance can cause the fermions to pair into diatomic molecules. The entropy and energies of mixtures of such molecules with unpaired atoms are calculated, in relation to recent experiments on molecular Bose-Einstein condensates produced in this manner. It is shown that, starting with a Fermi gas of temperature T=0.1TF0T=0.1{T}_{F}^{0}T=0.1TF0​, where TF0{T}_{F}^{0}TF0​ is the noninteracting Fermi temperature, an extremely cold degenerate Fermi gas of temperature $T\ensuremath{\lesssim}0.01{T}_{F}^{0}$ may be produced without further evaporative cooling. This requires adiabatic passage of the resonance, subsequent sudden removal of unpaired atoms, and adiabatic return. We also calculate the ratio of the interaction energy to the kinetic energy, a straightforward experimental signal which may be used to determine the temperature of the atoms and indicate condensation of the molecules.
Degenerate Fermi gas interacting with molecules near a Feshbach resonance is unstable with respect to the formation of a mixed state, in which atoms and molecules coexist as a coherent superposition. A theory of this state is developed using a mapping to the Dicke model, treating the molecular field in the single mode approximation. The results are accurate in the strong coupling regime relevant for current experimental efforts. The exact solution of the Dicke model is exploited to study stability, phase diagram, and nonadiabatic dynamics of the molecular field in the mixed state.
The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.
We present a nonequilibrium kinetic theory describing atom-molecule population dynamics in a two-component Fermi gas with a Feshbach resonance. Key collision integrals emerge that govern the relaxation of the atom-molecule mixture to chemical and thermal equilibrium. Our focus is on the pseudogap regime where molecules form above the superfluid transition temperature. In this regime, we formulate a simple model for the atom-molecule population dynamics. The model predicts the saturation of molecule formation that has been observed in recent experiments, and indicates that a dramatic enhancement of the atom-molecule conversion efficiency occurs at low temperatures.