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arXiv:cond-mat/0406629 · Physical Review A

Photoassociation dynamics in a Bose-Einstein condensate

Thomas Gasenzer

Published Oct 20, 2004• 9 citations

Abstract

A dynamical many-body theory of single color photoassociation in a Bose-Einstein condensate is presented. The theory describes the time evolution of a condensed atomic ensemble under the influence of an arbitrarily varying near-resonant laser pulse, which strongly modifies the binary scattering properties. In particular, when considering situations with rapid variations and high light intensities the approach described in this article leads, in a consistent way, beyond standard mean-field techniques. This allows one to address the question of limits to the photoassociation rate due to many-body effects which has caused extensive discussions in the recent past. Both the possible loss rate of condensate atoms and the amount of stable ground-state molecules achievable within a certain time are found to be stronger limited than according to mean-field theory. By systematically treating the dynamics of the connected Green's function for pair correlations the resonantly driven population of the excited molecular state as well as scattering into the continuum of noncondensed atomic states are taken into account. A detailed analysis of the low-energy stationary scattering properties of two atoms modified by the near resonant photoassociation laser, in particular of the dressed state spectrum of the relative motion prepares for the analysis of the many-body dynamics. The consequences of the finite lifetime of the resonantly coupled bound state are discussed in the two-body as well as in the many-body context. Extending the two body description to scattering in a tight trap reveals the modifications to the near resonant adiabatic dressed levels caused by the decay of the excited molecular state.

DOI: 10.1103/physreva.70.043618

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A dynamical many-body theory of single color photoassociation in a Bose-Einstein condensate is presented. The theory describes the time evolution of a condensed atomic ensemble under the influence of an arbitrarily varying near-resonant laser pulse, which strongly modifies the binary scattering properties. In particular, when considering situations with rapid variations and high light intensities the approach described in this article leads, in a consistent way, beyond standard mean-field techniques. This allows one to address the question of limits to the photoassociation rate due to many-body effects which has caused extensive discussions in the recent past. Both the possible loss rate of condensate atoms and the amount of stable ground-state molecules achievable within a certain time are found to be stronger limited than according to mean-field theory. By systematically treating the dynamics of the connected Green's function for pair correlations the resonantly driven population of the excited molecular state as well as scattering into the continuum of noncondensed atomic states are taken into account. A detailed analysis of the low-energy stationary scattering properties of two atoms modified by the near resonant photoassociation laser, in particular of the dressed state spectrum of the relative motion prepares for the analysis of the many-body dynamics. The consequences of the finite lifetime of the resonantly coupled bound state are discussed in the two-body as well as in the many-body context. Extending the two body description to scattering in a tight trap reveals the modifications to the near resonant adiabatic dressed levels caused by the decay of the excited molecular state.

We investigate theoretically the molecular yield in photoassociation of Bose-Einstein condensed sodium atoms for light intensities of the order of and above those applied in a recent experiment. Our results show that the rate at which ground-state molecules may be formed saturates at high light intensities whereas the loss rate of condensate atoms does not. This is caused by the opposing roles of the short- and long-range pair correlations present near resonance under the influence of the laser and is crucial for the development of efficient photoassociation procedures in a condensate.

We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found, and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett. 88, 090403 (2002)10.1103/PhysRevLett.88.090403], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms.

We revisit the mean-field treatment of photoassociation and Feshbach resonances in a Bose-Einstein condensate previously used by various authors. Generalizing the Cherny and Shanenko approach [Phys. Rev. E 62, 1646 (2000)] where the finite size of the potentials is explicitly introduced, we develop a two-channel model for a mixed atomic-molecular condensate. Besides the individual dynamics of the condensed and noncondensed atoms, the model also takes into account their pair dynamics by means of pair wave functions. We show that the resulting set of coupled equations can be reduced to the usual coupled Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} equations when the time scale of the pair dynamics is short compared to that of the individual dynamics. Such time scales are discussed in the case of typical photoassociation experiments with cw lasers. We show that the individual dynamics plays a minor role, demonstrating the validity of the rates predicted by the usual models describing photoassociation in a nondegenerate gas.

In this paper we formulate the time-dependent many-body theory of photoassociation in an atomic Bose-Einstein condensate with realistic interatomic interactions, using and comparing two approximations: the first-order cumulant approximation [Phys. Rev. A 65, 033601 (2002)], and the reduced pair wave approximation [Phys. Rev. A 68, 033612 (2003)]. The two approximations differ only by the way a pair of condensate atoms is influenced by the mean field at short interatomic separations. In both cases we identify two different regimes of photoassociation: the adiabatic regime and the coherent regime. The threshold for the so-called ``rogue dissociation'' [Phys. Rev. Lett. 88, 090403 (2002)] (where the Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} model breaks down) is found to be different in each regime, shedding new light on the experiment of McKenzie et al. [Phys. Rev. Lett. 88, 120403 (2002)]. Comparing numerical solutions for the two approximations with the Gross-Pitaevski\ifmmode \breve{\imath}\else \u{\i}\fi{} predictions, we find two different effects: reduction of the photoassociation rate at short times, and creation of correlated pairs of atoms when the laser intensity is switched on rapidly. We also observe effects on the symmetry of the photoassociation line shapes, giving the possibility to experimentally distinguish between the two approximations.

Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold

(<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK})

temperatures allows photoassociation spectroscopy to be performed with very high spectral resolution. Of particular interest is the investigation of molecular states whose properties can be related, with high precision, to the properties of their constituent atoms with the ``complications'' of chemical binding accounted for by a few parameters. These include bound long-range or purely long-range vibrational states in which two atoms spend most or all of their time at large internuclear separations. Low-energy atomic scattering states also share this characteristic. Photoassociation techniques have made important contributions to the study of all of these. This review describes what is special about photoassociation spectroscopy at ultracold temperatures, how it is performed, and a sampling of results including the determination of scattering lengths, their control via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular spectra, limits on photoassociation rates in a Bose-Einstein condensate, and briefly, production of cold molecules. Discussions are illustrated with examples on alkali-metal atoms as well as other species. Progress in the field is already past the point where this review can be exhaustive, but an introduction is provided on the capabilities of photoassociation spectroscopy and the techniques presently in use.

We demonstrate coherent one-color photoassociation of a Bose-Einstein condensate, which results in Rabi oscillations between atomic and molecular condensates. We attain atom-molecule Rabi frequencies that are comparable to decoherence rates by driving photoassociation of atoms in an ^{88}Sr condensate to a weakly bound level of the metastable 1S0+3P1 molecular potential, which has a long lifetime and a large Franck-Condon overlap integral with the ground scattering state. Transient shifts and broadenings of the excitation spectrum are clearly seen at short times, and they create an asymmetric excitation profile that only displays Rabi oscillations for blue detuning from resonance.