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arXiv:cond-mat/0403503 · Journal of Physics B Atomic Molecular and Optical Physics

Atom–molecule equilibration in a degenerate Fermi gas with resonant interactions

J E Williams, T Nikuni, N Nygaard, C W Clark

Published Oct 27, 2004• 12 citations
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Abstract

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.

DOI
10.1088/0953-4075/37/21/l01

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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.
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.
We model collisionless collective conversion of a degenerate Fermi gas of atoms into bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a classical field and seeding the pairing amplitudes with random phases. A dynamical instability of the Fermi sea against association with molecules drives the conversion. The model qualitatively reproduces several experimental observations [Regal et al., Nature (London), (2003)]. We predict that the initial temperature of the Fermi gas sets the limit for the efficiency of atom-molecule conversion.
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.
We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of 40{}^{40}40K and 87{}^{87}87Rb atoms, where we can create 40{}^{40}40K87{}^{87}87Rb molecules with a conversion efficiency as high as 45%. In the limit of fast magnetic sweeps and small molecule fraction, we find that the time scale of molecule production is accurately predicted by a parameter-free model that uses only the atomic densities, masses, and the known Feshbach resonance parameters. We find that molecule production efficiency saturates for slower magnetic sweeps, at which point the maximum number of Feshbach molecules depends primarily on the atoms' phase-space density. At higher temperatures, our measurements agree with a phenomenological model that successfully describes the formation of bosonic molecules from either Bose or Fermi gases. However, for quantum degenerate atom gas mixtures, we measure significantly fewer molecules than this model predicts.
We theoretically examine a zero-temperature system of Fermi degenerate atoms coupled to bosonic molecules via collisionless rapid adiabatic passage across a Feshbach resonance, focusing on saturation of the molecular conversion efficiency at the slowest magnetic-field sweep rates. Borrowing a novel MANY-FERMION Fock-state theory, we find that a proper model of the magnetic-field sweep can systematically remove saturation. We also debunk the common misconception that many-body effects are responsible for molecules existing above the two-body threshold.