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arXiv:0812.4474 · Physical Review A

Feshbach molecule production in fermionic atomic gases

Victor Gurarie

Published Aug 31, 2009• 14 citations
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Abstract

This paper examines the problem of molecule production in an atomic fermionic gas close to an $s$-wave Feshbach resonance by means of a magnetic field sweep through the resonance. In the solvable case of a narrow resonance, the density of molecules at the end of the process is derived for a slow sweep. It is shown that the density of the produced molecules is lower than what an application of a naive Landau-Zener formula for level crossing would imply. However, in the limit of a very slow sweep it is still possible to achieve full conversion of fermions into the molecules. It appears that the origin of the failure of the Landau-Zener picture of the molecule production is due to the fact that the sweep goes through a quantum phase transition in the limit of an infinitely narrow resonance, in agreement with general results recently discussed in the literature. However, the precise connection of this problem to other problems with this feature is not established.

DOI
10.1103/physreva.80.023626

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This paper examines the problem of molecule production in an atomic fermionic gas close to an sss-wave Feshbach resonance by means of a magnetic field sweep through the resonance. In the solvable case of a narrow resonance, the density of molecules at the end of the process is derived for a slow sweep. It is shown that the density of the produced molecules is lower than what an application of a naive Landau-Zener formula for level crossing would imply. However, in the limit of a very slow sweep it is still possible to achieve full conversion of fermions into the molecules. It appears that the origin of the failure of the Landau-Zener picture of the molecule production is due to the fact that the sweep goes through a quantum phase transition in the limit of an infinitely narrow resonance, in agreement with general results recently discussed in the literature. However, the precise connection of this problem to other problems with this feature is not established.
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 investigate the production efficiency of ultracold molecules in bosonic 85Rb and fermionic 40K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the 85Rb molecule conversion efficiency follow a Landau-Zener model.
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.
\n 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.\n
We study the mean-field dynamics of ppp-wave Feshbach-molecule production in an ultracold gas of Fermi atoms in the same internal state. We derive a separable potential to describe the low-energy scattering properties of such atoms, and use this potential to solve the mean-field dynamics during a magnetic-field sweep. Initially, on the negative scattering length side of a Feshbach resonance the gas is described by the BCS theory. We adapt the method by Szyma\ifmmode \acute{n}\else \'{n}\fi{}ska et al. [Phys. Rev. Lett. 94, 170402 (2005)] to ppp-wave interacting Fermi gases and model the conversion dynamics of the gas into a Bose-Einstein condensate of molecules on the other side of the resonance under the influence of a linearly varying magnetic field. We have analyzed the dependence of the molecule production efficiency on the density of the gas, temperature, initial value of the magnetic field, and magnetic-field ramp speed. Our results show that in this approximation molecule production by a linear magnetic-field sweep is highly dependent on the initial state.
In this thesis I present a nonequilibrium quantum field theory that describes the\nproduction of molecular dimers from a two-component quantum-degenerate atomic\nFermi gas, via a linear downward sweep of a magnetic field across an s-wave Feshbach\nresonance. This problem raises interest because it is presently unclear as to why\ndeviations from the universal Landau-Zener formula for the transition probability at\ntwo-level crossing are observed in the experimentally measured production efficiencies.\nThe approach is based on evaluating real-time Green functions within the Keldysh-\nSchwinger formalism. The effects of quantum statistics associated with Pauli blocking\nfor fermions and induced emission for bosons, characteristic of particle scattering in\na quantum-degenerate many-body medium, are fully accounted for. I show that the\nmolecular conversion efficiency is represented by a power series in terms of a dimensionless\nparameter which, in the zero-temperature limit, depends solely on the initial\ngas density and the Landau-Zener parameter. This result reveals a hindrance of the\ncanonical Landau-Zener transition probability due to many-body effects, and presents\nan explanation for the experimentally observed deviations.\nA second topic treated in this thesis concerns the study of non-adiabatic transitions\nin N-state Landau-Zener systems. In connection to this, I provide a proof of\nthe conjecture put forth by Brundobler and Elser, regarding the survival probability\non the diabatic levels with maximum/minimum slope.