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arXiv:cond-mat/0609725 · Physical Review A

Association of molecules using a resonantly modulated magnetic field

Thomas M. Hanna, Thorsten Köhler, Keith R. Burnett

Published Jan 5, 2007• 41 citations

Abstract

We study the process of associating molecules from atomic gases using a magnetic field modulation that is resonant with the molecular binding energy. We show that maximal conversion is obtained by optimizing the amplitude and frequency of the modulation for the particular temperature and density of the gas. For small modulation amplitudes, resonant coupling of an unbound atom pair to a molecule occurs at a modulation frequency corresponding to the sum of the molecular binding energy and the relative kinetic energy of the atom pair. An atom pair with an off-resonant energy has a probability of association which oscillates with a frequency and time-varying amplitude which are primarily dependent on its detuning. Increasing the amplitude of the modulation tends to result in less energetic atom pairs being resonantly coupled to the molecular state and also alters the dynamics of the transfer from continuum states with off-resonant energies. This leads to maxima and minima in the total conversion from the gas as a function of the modulation amplitude. Increasing the temperature of the gas leads to an increase in the modulation frequency providing the best fit to the thermal distribution, and weakens the resonant frequency dependence of the conversion. Mean-field effects can alter the optimal modulation frequency and lead to the excitation of higher modes. Our simulations predict that resonant association can be effective for binding energies of order $h\ifmmode\times\else\texttimes\fi{}1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$.

DOI: 10.1103/physreva.75.013606

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We study the process of associating molecules from atomic gases using a magnetic field modulation that is resonant with the molecular binding energy. We show that maximal conversion is obtained by optimizing the amplitude and frequency of the modulation for the particular temperature and density of the gas. For small modulation amplitudes, resonant coupling of an unbound atom pair to a molecule occurs at a modulation frequency corresponding to the sum of the molecular binding energy and the relative kinetic energy of the atom pair. An atom pair with an off-resonant energy has a probability of association which oscillates with a frequency and time-varying amplitude which are primarily dependent on its detuning. Increasing the amplitude of the modulation tends to result in less energetic atom pairs being resonantly coupled to the molecular state and also alters the dynamics of the transfer from continuum states with off-resonant energies. This leads to maxima and minima in the total conversion from the gas as a function of the modulation amplitude. Increasing the temperature of the gas leads to an increase in the modulation frequency providing the best fit to the thermal distribution, and weakens the resonant frequency dependence of the conversion. Mean-field effects can alter the optimal modulation frequency and lead to the excitation of higher modes. Our simulations predict that resonant association can be effective for binding energies of order

h\ifmmode\times\else\texttimes\fi{}1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}

.

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.

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.

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.

We report on the creation of heterospecies bosonic molecules, associated from an ultracold Bose-Bose mixture of

^{41}\mathrm{K}

and

^{87}\mathrm{Rb}

, by using a resonantly modulated magnetic field close to two Feshbach resonances. We measure the binding energy of the weakly bound molecular states versus the Feshbach field and compare our results to theoretical predictions. We observe the broadening and asymmetry of the association spectrum due to the thermal distribution of the atoms and a frequency shift occurring when the binding energy depends nonlinearly on the Feshbach field. A simple model is developed to quantitatively describe the association process. This work represents a required step toward Bose-Einstein condensates of dipolar molecules.

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.