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Physical Review A

Effect of coupling strength on atomic-to-molecular condensate conversion in Raman photoassociation

Moumita Gupta, Krishna Rai Dastidar

Published Mar 17, 2010• 9 citations
Publisher

Abstract

We study two-photon Raman photoassociation for creating a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. By exploring the dynamics of the coupled system, we show that the atom-to-molecule conversion efficiency can be controlled by changing the atom-molecule coupling strength and the effective two-photon Raman detuning. Atom-molecule coupling strength and the effective two-photon Raman detuning can be controlled by changing the laser intensity. We analyze the dynamics of the coupled atom-molecular condensate system by changing the laser intensity over a broad range, keeping the effective two-photon Raman detuning fixed. The effective two-photon Raman detuning depends on the two-photon detuning, Rabi frequencies, and the light shifting (AC Stark shift) of the levels. To keep the effective two-photon Raman detuning fixed, the two-photon detuning is varied to compensate for the light shifting of levels with laser intensity. The corresponding changes in the effective decay rates and the scattering length due to the change in the Rabi frequencies have been taken into account. Dependence of the conversion efficiency on the effective two-photon Raman detuning has also been studied by varying the laser intensity over a narrow range, keeping the two-photon detuning unchanged. The dynamics of the coupled system has been studied in Gross-Pitaevskii and modified Gross-Pitaevskii approaches to demonstrate the effect of the higher order nonlinearity (Lee-Huang-Yang term) with the increase in the laser intensity.

DOI
10.1103/physreva.81.033610

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Physical Review A•Oct 21, 2009•6 citations
We study two-photon Raman photoassociation for creating a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. By exploring the dynamics of the coupled system, we show that the atom-to-molecule conversion efficiency can be controlled by changing the atom-molecule coupling strength and the effective two-photon Raman detuning. Atom-molecule coupling strength and the effective two-photon Raman detuning can be controlled by changing the laser intensity. We analyze the dynamics of the coupled atom-molecular condensate system by changing the laser intensity over a broad range, keeping the effective two-photon Raman detuning fixed. The effective two-photon Raman detuning depends on the two-photon detuning, Rabi frequencies, and the light shifting (AC Stark shift) of the levels. To keep the effective two-photon Raman detuning fixed, the two-photon detuning is varied to compensate for the light shifting of levels with laser intensity. The corresponding changes in the effective decay rates and the scattering length due to the change in the Rabi frequencies have been taken into account. Dependence of the conversion efficiency on the effective two-photon Raman detuning has also been studied by varying the laser intensity over a narrow range, keeping the two-photon detuning unchanged. The dynamics of the coupled system has been studied in Gross-Pitaevskii and modified Gross-Pitaevskii approaches to demonstrate the effect of the higher order nonlinearity (Lee-Huang-Yang term) with the increase in the laser intensity.
We study the dynamics of the atomic and molecular Bose-Einstein condensates (BECs) of 87Rb^{87}\text{R}\text{b}87Rb in a spherically symmetric trap coupled by stimulated Raman photoassociation process. Considering the higher order nonlinearity in the atom-atom interaction we analyze the dynamics of the system using coupled modified Gross-Pitaevskii (MGP) equations and compare it with mean-field coupled Gross-Pitaevskii (GP) dynamics. Considerable differences in the dynamics are obtained in these two approaches at large scattering length, i.e., for large values of peak-gas parameter ${x}_{pk}\ensuremath{\ge}{10}^{\ensuremath{-}3}$. We show how the dynamics of the coupled system is affected when the atom-molecule and molecule-molecule interactions are considered together with the atom-atom interaction and also when the strengths of these three interactions are increased. The effect of detuning on the efficiency of conversion of atomic fractions into molecules is demonstrated and the feasibility of maximum molecular BEC formation by varying the Raman detuning parameter at different values of time is explored. Thus by varying the Raman detuning and the scattering length for atom-atom interaction one can control the dynamics of the coupled atomic-molecular BEC system. We have also solved coupled Gross-Pitaevskii equations for atomic to molecular condensate formation through magnetic Feshbach resonance in a BEC of 85Rb^{85}\text{R}\text{b}85Rb. We found similar features for oscillations between atomic and molecular condensates noted in previous theoretical study and obtained fairly good agreement with the evolution of total atomic condensate observed experimentally.
We investigate the low-energy excitations of the spherically and axially trapped atomic Bose-Einstein condensate coupled to a molecular Bose gas by coherent Raman transitions. We apply the sum-rule approach of many-body response theory to derive the low-lying collective excitation frequencies of the hybrid atom-molecular system. The atomic and molecular ground-state densities obtained in Gross-Pitaevskii and modified Gross-Pitaevskii (including the higher order Lee-Huang-Yang term in interatomic interaction) approaches are used to find out the individual energy components and hence the excitation frequencies. We obtain different excitation energies for different angular momenta and study their characteristic dependence on the effective Raman detuning, the scattering length for atom-atom interaction, and the intensities of the coupling lasers. We show that the inclusion of the higher-order nonlinear interatomic interaction in modified Gross-Pitaevskii approach introduces significant corrections to the ground-state properties and the excitation frequencies both for axially and spherically trapped coupled 87Rb^{87}\mathrm{Rb}87Rb condensate system with the increase in the sss-wave scattering length (for peak gas-parameter $\ensuremath{\geqslant}{10}^{\ensuremath{-}3}$). It has been shown that the excitation frequencies decrease with the increase in the effective Raman detuning as well as the sss-wave scattering length, whereas excitation frequencies increase with the increase in the atom-molecular coupling strength. The frequencies in modified Gross-Pitaevskii approximation exhibit an upward trend after a certain value of scattering length and also largely deviate from the Gross-Pitaevskii results with the increase in sss-wave scattering length. The strong dependence of excitation frequencies on the laser intensities used for Raman transitions manifests the role of atom-molecular coupling strength on the control of collective excitations. The collective excitation frequencies for the hybrid atom-molecular BEC differ significantly from the excitation frequencies of a pure atomic BEC system when the atom-to-molecule conversion efficiency increases due to the decrease in the effective Raman detuning and increase in the atom-molecule coupling strength.
We theoretically examine Raman photoassociation of a Bose-Einstein condensate, revisiting stimulated Raman adiabatic passage (STIRAP). Due to collisional mean-field shifts, efficient molecular conversion requires strong coupling and low density, either of which can bring about rogue photodissociation to noncondensate modes. We demonstrate explicitly that rogue transitions are negligible for low excited-state fractions and photodissociation that is slower than the STIRAP time scale. Moreover, we derive a reduced-parameter model of collisions, and thereby find that a gain in the molecular conversion efficiency can be obtained by adjusting the atom-atom scattering length with off-resonant magnetoassociation. This gain saturates when the atom-atom scattering length is tuned to a specific fraction of either the molecule-molecule or atom-molecule scattering length. We conclude that a fully optimized STIRAP scheme may offer the best chance for achieving coherent conversion from an atomic to a molecular condensate with photoassociation.
The optimum conditions for producing Cs2{\text{Cs}}_{2}Cs2​ molecular condensates from Cs atomic condensates with high transfer efficiency by stimulated Raman adiabatic passage are presented. Under the extended ``two-photon'' resonance condition, including the two-photon process, the mean-field correction, and the tunneling coupling between two upper excited molecular levels, a high and stable conversion efficiency is realized. The high conversion efficiency could be achieved by following two methods under experimentally less demanding conditions (relatively small effective Rabi frequency for pump laser pulse). One is adjusting the detuning difference between two laser pulses for same effective Rabi frequencies with up to 87.2% transfer efficiency. Another one is adjusting the effective Rabi frequency, the detuning of dump laser for given effective Rabi frequency, and the detuning of pump laser with up to 80.7% transfer efficiency.