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arXiv:0909.0414 · Physical Review A

Enhancing molecular conversion efficiency by a magnetic field pulse sequence

Xiaoqiang Xu, Li-Hua Lü, You‐Quan Li

Published Sep 28, 2009• 5 citations
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Abstract

We propose a strategy to enhance the atom-to-molecule conversion efficiency near a Feshbach resonance. Based on the mean-field approximation, we derive the fixed point solutions of the classical Hamiltonian. Rabi oscillation between the atomic and molecular states around fixed point solutions and its oscillation period are discussed. By designing a sequence of magnetic field pulses in analogy with Ramsey experiments, we show that a much higher atom-to-molecule conversion efficiency can be accessed by tuning the pulse durations appropriately.

DOI
10.1103/physreva.80.033621

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Reply to “Comment on ‘Stimulated Raman adiabatic passage from an atomic to a molecular Bose-Einstein condensate’ ”

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In the preceding Comment, the authors suggest that the molecular conversion efficiency in atom-molecule stimulated Raman adiabatic passage can be improved by lowering the initial atomic density, which in turn requires longer pulse durations to maintain adiabaticity. Apart from the fact that the mean-field approximation becomes questionable at low densities, we point out that a low-density strategy with longer pulses has several problems. It generally requires higher pulse energies and increases radiative losses. We also show that even within the approximations used in the Comment, their example leads to no efficiency improvement compared to our high-density case. In a more careful analysis including radiative losses neglected in the Comment, the proposed strategy gives almost no conversion owing to the longer pulse durations required.

arXiv:physics/0410115•Physical Review A•Jan 20, 2005•18 citations
We propose a strategy to enhance the atom-to-molecule conversion efficiency near a Feshbach resonance. Based on the mean-field approximation, we derive the fixed point solutions of the classical Hamiltonian. Rabi oscillation between the atomic and molecular states around fixed point solutions and its oscillation period are discussed. By designing a sequence of magnetic field pulses in analogy with Ramsey experiments, we show that a much higher atom-to-molecule conversion efficiency can be accessed by tuning the pulse durations appropriately.
A novel atom-molecule conversion technique has been investigated.Ultracold 85 Rb atoms sitting in a DC magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field.There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy.We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the initial phase space density of the sample.This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements.
A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.
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.
Abstract Atom-to-molecule conversion by the technique of optical Feshbach resonance in a magnetic lattice is studied in the mean-field approximation. For the case of a shallow lattice, we give the dependence of the atomto-molecule conversion efficiency on tunnelling strength and atomic interaction by taking a double-well as an example. We find that one can obtain a high atom-to-molecule conversion by tuning the tunnelling and interaction strengths of the system. For the case of a deep lattice, we show that the existence of the lattice can improve the atom-to-molecule conversion for certain initial states.
We present a theoretical model for formation of molecules in an optical lattice well where a resonant coupling of atomic and molecular states is provided by small oscillations of a magnetic field in the vicinity of a Feshbach resonance. As opposed to an adiabatic sweep over the full resonance, this provides a coherent coupling with a frequency that can be tuned to meet resonance conditions in the system. The effective Rabi frequencies for this coupling are calculated and simulations show perfect Rabi oscillations. Robust production of molecules with an adiabatic sweep of the modulation frequency is demonstrated. For very large oscillation amplitudes, the Rabi oscillations are distorted but still effective and fast association is possible.
In the preceding Comment, the authors suggest that the molecular conversion efficiency in atom-molecule stimulated Raman adiabatic passage can be improved by lowering the initial atomic density, which in turn requires longer pulse durations to maintain adiabaticity. Apart from the fact that the mean-field approximation becomes questionable at low densities, we point out that a low-density strategy with longer pulses has several problems. It generally requires higher pulse energies and increases radiative losses. We also show that even within the approximations used in the Comment, their example leads to no efficiency improvement compared to our high-density case. In a more careful analysis including radiative losses neglected in the Comment, the proposed strategy gives almost no conversion owing to the longer pulse durations required.