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arXiv:cond-mat/0604216 · Physical Review A

Optimal conversion of Bose-Einstein-condensed atoms into molecules via a Feshbach resonance

Jae‐Yoon Jeong, Christopher P. Search, Ivana Djuric

Published Aug 23, 2006• 0 citations

Abstract

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.

DOI: 10.1103/physreva.74.023619

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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.

We consider in detail the situation of applying a time-dependent external magnetic field to a 87 Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Köhler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87 Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.

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.

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 the dynamics of converting cold bosonic atoms to molecules when an external magnetic field is swept across a Feshbach resonance. Our analysis relies on a quantum microscopic model that accounts for many-body effects in the association process. We show that the picture of two-body molecular production depicted by the Landau-Zener model is significantly altered due to many-body effects. In the nonadiabatic regime, we derive an analytic expression for molecular conversion efficiency that explains the discrepancy between the prediction of the Landau-Zener formula and the experimental data [E. Hodby et al., Phys. Rev. Lett. 94, 120402 (2005)]. Our theory is further extended to the formation of heteronuclear diatomic molecules and gives some interesting predictions.

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.