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arXiv:0704.3867 · New Journal of Physics

Role of particle interactions in the Feshbach conversion of fermionic atoms to bosonic molecules

Jie Liu, Libin Fu, Bin Liu, Biao Wu

Published Dec 16, 2008• 21 citations
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Abstract

We investigate the Feshbach conversion of fermionic atom pairs to condensed bosonic molecules with a microscopic model that accounts for the repulsive interactions among all the particles involved. We find that the conversion efficiency is enhanced by the interaction between bosonic molecules, while it is suppressed by the interactions between fermionic atoms and between atoms and molecules. In the adiabatic limit, the combined effect of these interactions can lead to a ceiling of less than 100% on the conversion efficiency for a narrow Feshbach resonance. Our theory agrees with the recent Rice experiment on 6 Li.

DOI
10.1088/1367-2630/10/12/123018

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We investigate the Feshbach conversion of fermionic atom pairs to condensed bosonic molecules with a microscopic model that accounts for the repulsive interactions among all the particles involved. We find that the conversion efficiency is enhanced by the interaction between bosonic molecules, while it is suppressed by the interactions between fermionic atoms and between atoms and molecules. In the adiabatic limit, the combined effect of these interactions can lead to a ceiling of less than 100% on the conversion efficiency for a narrow Feshbach resonance. Our theory agrees with the recent Rice experiment on 6 Li.
We investigate a generalized many-body model of Feshbach molecule formation that includes the atom-atom, atom-molecule, and molecule-molecule interactions. We show that the picture of two-body molecule production depicted by the Landau-Zener model is significantly altered by the particle interactions. In the adiabatic limit, we work out a formula for the ceiling of conversion efficiency when the interaction strength is larger than a critical value. In the sudden limit, we derive a closed equation for the conversion efficiency using stationary phase approximation. Our theory predicts a significant role of the particle interactions in atom-molecule conversion when the atom density is high and the Feshbach resonance width is narrow.
In some recent experiments an ultracold gas of 40^{40}40K2_22​ (or 6^{6}6Li2_22​) molecules has been produced from a degenerate two-component Fermi gas of 40^{40}40K (or 6^{6}6Li) atoms by adiabatic passage through a Feshbach resonance. The maximum atom-molecule transfer efficiency is reported to be about 50%. We propose a simple microscopic model to characterize the ground state of the gas in the vicinity of the resonance, and show that the term describing the atom-molecule coupling is responsible for the observed efficiency 50%. Our result also suggests that the experiments have produced a molecular condensate.
We investigate the production efficiency of ultracold molecules in bosonic 85 Rb and fermionic 40 K when the magnetic field is swept across a Feshbach resonance.For adiabatic sweeps of the magnetic field, the conversion efficiency of each species is solely determined by the phase space density of the atomic cloud, in contrast to a number of theoretical predictions.Our novel model for the adiabatic pairing process, developed from general physical principles, accurately predicts the conversion efficiency for both ultracold gases of bosons and of fermions.In the non-adiabatic regime our measurements of the 85 Rb molecule conversion efficiency follow a Landau Zener model, with a conversion efficiency that is characterized by the density divided by the time derivative of the magnetic field.
We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of 40K and 6Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau-Zener transition but faster than "the collision rate" in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter, thereby increasing the conversion efficiency; "the collision rate" is the pair decorrelation rate.
The efficiency of converting two-species fermionic atoms into bosonic molecules is investigated in terms of mean-field Lagrangian density. We find that the stimulated Raman adiabatic passage technique aided by Feshbach resonance is more effective than the bare Feshbach resonance for 6Li^{6}\text{L}\text{i}6Li atoms rather than 40K^{40}\text{K}40K atoms. We also generally consider the symmetry and its relevant conservation law, which enables us to introduce a natural definition of adiabatic fidelity for a coherent population trapping state. The calculated values of the fidelity are presented and then we provide an explanation of why the conversion efficiencies for 40K^{40}\text{K}40K and 6Li^{6}\text{L}\text{i}6Li are distinctly different.
Trapped cold atoms at very low temperatures, now readily accessible experimentally, can be controlled and serve as a testing ground for many theoretical physical properties which are paralleled in condensed matter systems. Ultracold trapped atom experiments show promise to recreate analogous condensed matter systems in a controlled environment and to create novel many-body quantum states of matter. The tunability of trapping laser intensities and magnetically controlled Feshbach interactions are the main tools for varying lattice hopping strengths and inter-particle interactions. In this thesis, we search for the phase of a many-body system of cold fermion atoms that can convert to boson molecules and vice versa. We then look at the microscopic details of two atoms that interact to form a quasibound molecule. Our two-atom model explains the mechanism behind the magnetically tunable interparticle interaction known as the Feshbach resonance. We find a dependence of the bound pair formation on the two-particle energy. Our results show that if a magnetic field can be fine tuned to sufficient precision, of order 10 mG, a narrow resonance can be achieved where longer lived bound states can be created. This narrow resonance reconciliates the two-body physics with the effective Hamiltonian that describes the many-body system.