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arXiv:0905.2890 · Physical Review A

Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field

Bin Liu, Libin Fu, Jie Liu

Published Jan 4, 2010• 12 citations
arXivHTMLPDF

Abstract

We study the process of the production of ultracold molecules from ultracold atoms using a sinusoidally oscillating magnetic-field modulation. Our study is based on a two-mode mean-field treatment of the problem. When the magnetic field is resonant roughly with the molecular binding energy, Shapiro-like resonances are observed. Their resonance profiles are well fitted by the Lorentzian functions. The linewidths depend on both the amplitude and the duration of the applied modulations and are found to be dramatically broadened by the thermal dephasing effect. The resonance centers shift due to both the many-body effect and the finite temperature effect. Our theory is consistent with a recent experiment [S. T. Thompson, E. Hodby, and C. E. Wieman, Phys. Rev. Lett. 95, 190404 (2005)]. Our model predicts a $1/3$ ceiling for the molecular production yield in uncondensed ultracold atomic clouds for a long coupling time, while for condensed atoms the optimal conversion yield could be beyond the limit.

DOI
10.1103/physreva.81.013602

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We study the process of the production of ultracold molecules from ultracold atoms using a sinusoidally oscillating magnetic-field modulation. Our study is based on a two-mode mean-field treatment of the problem. When the magnetic field is resonant roughly with the molecular binding energy, Shapiro-like resonances are observed. Their resonance profiles are well fitted by the Lorentzian functions. The linewidths depend on both the amplitude and the duration of the applied modulations and are found to be dramatically broadened by the thermal dephasing effect. The resonance centers shift due to both the many-body effect and the finite temperature effect. Our theory is consistent with a recent experiment [S. T. Thompson, E. Hodby, and C. E. Wieman, Phys. Rev. Lett. 95, 190404 (2005)]. Our model predicts a 1/31/31/3 ceiling for the molecular production yield in uncondensed ultracold atomic clouds for a long coupling time, while for condensed atoms the optimal conversion yield could be beyond the limit.
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.
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.
Abstract The conversion of ultracold atoms to molecules via a magnetic Feshbach resonance with a sinusoidal modulation of the field is studied. Different practical realizations of this method in Bose atomic gases are analyzed. Our model incorporates many-body effects through an effective reduction of the complete microscopic dynamics. Moreover, we simulate the experimental conditions corresponding to the preparation of the system as a thermal gas and as a condensate. Some of the experimental findings are clarified. The origin of the observed dependence of the production efficiency on the frequency, amplitude, and application time of the magnetic modulation is elucidated. Our results uncover also the role of the atomic density in the dynamics, specifically, in the observed saturation of the atom–molecule conversion process.
The variation of a magnetic field in the vicinity of a zero-energy resonance allows highly vibrationally excited molecules (‘Feshbach molecules’) to be produced from an ultracold atomic gas. In this thesis, we study the dynamics of this process. We begin by studying the dissociation of Feshbach molecules, showing that in the limit of a sudden jump the shape of the spectrum of dissociated atoms can act as a probe of the zero-energy resonance. For some resonances, such jumps are within reach of current experiments. We also study the intermediate region between sudden jumps and asymptotically wide, linear ramps. It is shown from a precise derivation how the latter limit leads to a universal spectrum with a shape independent of the implementation of the two-body physics, provided that the near-resonant scattering properties are correctly modelled. We then turn to the dynamics of Feshbach molecule production from thermal and condensed gases. Our microscopic quantum dynamics approach includes the exact twobody evolution as an input to the many-body calculations. We show that in the long-time limit, and the Markov limit for the interactions, the non-Markovian Boltzmann equation (NMBE) we derive for the one-body density matrix reduces to the normal Boltzmann equation. In the limit of short times and small depletion of the atomic gas, the molecule production efficiency can be calculated by thermally averaging the two-body transition probability density. This thermal averaging technique is applied to studies of the formation of Feshbach molecules using a magnetic field modulation that is near-resonant with the molecular bound state energy. The continuum is shown to have a significant effect on both the dynamics and efficiency of this process. We examine the dependence of the molecule production efficiency on the duration, amplitude and frequency of the modulation, as well as the temperature and density of the gas. This method of producing molecules is effective for a wide range of bound state energies, but requires sufficient variation of the two-body energy levels with magnetic field. Lastly, we implement the NMBE for the case of a fast linear ramp across a Feshbach resonance. The solution of this equation is made feasible by including a large part of the required computation in the kernel, which is calculated in advance. The NMBE allows predictions of the molecule production efficiency which go beyond the thermal averaging technique by accounting for the depletion and rethermalisation of the continuum. In the limit of small depletions, the two approaches give the same results. As the depletion increases, the two approaches differ due to many-body effects limiting the maximum possible molecule production efficiency. We have observed this in our simulations by considering higher-density gases. We have therefore shown the suitability and practicability of this beyond mean-field approach for application to further problems in the production of Feshbach molecules from ultracold gases.
Motivated by recent experiments [Zhang et al., Nat. Phys. 19, 1466 (2023)], we study the interconversion between ultracold atomic and molecular condensates, quantifying the resulting oscillations and their slow decay. We find that near equilibrium the dominant damping source is the decay of condensed molecules into noncondensed pairs, with a pair kinetic energy that is resonant with the frequency of the oscillating atom-molecule interconversions. The decay, however, is nonexponential, as strong population of the resonant pairs leads to Bose enhancement. Introducing an oscillating magnetic field, which periodically modulates the molecular binding energy, enhances the oscillations at short times. However, the resulting enhancement of the pair-production process results in an accelerated decay, which rapidly cuts off the initial oscillation growth.
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.