Physical Review A

Atom-molecule conversion at a Feshbach resonance in the nondegenerate limit

Juha Javanainen

Published Jun 28, 2006• 3 citations

Abstract

We study the efficiency of atom-molecule conversion in a sweep of the magnetic field across a Feshbach resonance in a nondegenerate gas by integrating numerically the time-dependent Schr\"odinger equation. In an approach that works at low conversion efficiencies, we show that in the limit of a slow sweep the atom-molecule conversion efficiency is proportional to the phase-space density.

DOI: 10.1103/physreva.73.061605

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Physical Review A

Atom-molecule conversion at a Feshbach resonance in the nondegenerate limit

Juha Javanainen

Published Jun 28, 2006• 3 citations

Publisher

Abstract

We study the efficiency of atom-molecule conversion in a sweep of the magnetic field across a Feshbach resonance in a nondegenerate gas by integrating numerically the time-dependent Schr"odinger equation. In an approach that works at low conversion efficiencies, we show that in the limit of a slow sweep the atom-molecule conversion efficiency is proportional to the phase-space density.

DOI: 10.1103/physreva.73.061605

Related papers

Feshbach molecule production in fermionic atomic gases

Victor Gurarie

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.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.

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Production Efficiency of Ultracold Feshbach Molecules in Bosonic and Fermionic Systems

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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 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.

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In many experiments involving conversion of quantum-degenerate atomic gases into molecular dimers via a Feshbach resonance, an external magnetic field is linearly swept from above resonance to below resonance. In the adiabatic limit, the fraction of atoms converted into molecules is independent of the functional form of the sweep and is predicted to be 100%. However, for nonadiabatic sweeps through resonance, Landau-Zener theory predicts that a linear sweep will result in a negligible production of molecules. Here we employ a genetic algorithm to determine the functional time dependence of the magnetic field that produces the maximum number of molecules for sweep times that are comparable to the period of resonant atom-molecule oscillations, $2\ensuremath{\pi}{\ensuremath{\Omega}}_{\mathit{\text{Rabi}}}^{\ensuremath{-}1}$. The optimal sweep through resonance indicates that more than 95% of the atoms can be converted into molecules for sweep times as short as $2\ensuremath{\pi}{\ensuremath{\Omega}}_{\mathit{\text{Rabi}}}^{\ensuremath{-}1}$ while the linear sweep results in a conversion of only a few percent. We also find that the qualitative form of the optimal sweep is independent of the strength of the two-body interactions between atoms and molecules and the width of the resonance.In many experiments involving conversion of quantum-degenerate atomic gases into molecular dimers via a Feshbach resonance, an external magnetic field is linearly swept from above resonance to below resonance. In the adiabatic limit, the fraction of atoms converted into molecules is independent of the functional form of the sweep and is predicted to be 100%. However, for nonadiabatic sweeps through resonance, Landau-Zener theory predicts that a linear sweep will result in a negligible production of molecules. Here we employ a genetic algorithm to determine the functional time dependence of the magnetic field that produces the maximum number of molecules for sweep times that are comparable to the period of resonant atom-molecule oscillations, $2\ensuremath{\pi}{\ensuremath{\Omega}}_{\mathit{\text{Rabi}}}^{\ensuremath{-}1}$. The optimal sweep through resonance indicates that more than 95% of the atoms can be converted into molecules for sweep times as short as $2\ensuremath{\pi}{\ensuremath{\Omega}}_{\mathit{\text{Rabi}}}^{\ensuremath{-}1}$ while the linear sweep results in a conversion of only a few percent. We also find that the qualitative form of the optimal sweep is independent of the strength of the two-body interactions between atoms and molecules and the width of the resonance.

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We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of ${}^{40}$ K and ${}^{87}$ Rb atoms, where we can create ${}^{40}$ K ${}^{87}$ Rb 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 investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of ${}^{40}$K and ${}^{87}$Rb atoms, where we can create ${}^{40}$K${}^{87}$Rb 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.

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Zero-Temperature Theory of Collisionless Rapid Adiabatic Passage from a Fermi Degenerate Gas of Atoms to a Bose-Einstein Condensate of Molecules

Matt Mackie, Olavi Dannenberg

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.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.

arXiv:physics/0412048APSDec 8, 20040 citations

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.

We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of

{}^{40}

K and

{}^{87}

Rb atoms, where we can create

{}^{40}

{}^{87}

Rb 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.