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arXiv:cond-mat/0504114 · Physical Review A

Photoassociation and optical Feshbach resonances in an atomic Bose-Einstein condensate: Treatment of correlation effects

Pascal Naidon, Françoise Masnou-Seeuws

Published Apr 18, 2006• 21 citations

Abstract

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.

DOI: 10.1103/physreva.73.043611

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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.

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.

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.

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 study coherent photoassociation, phenomena analogous to coherent optical transients in few-level systems, which may take place in photoassociation of an atomic Bose-Einstein condensate but not in a nondegenerate gas. We develop a second-quantized Hamiltonian to describe photoassociation, and apply the Hamiltonian both in the momentum representation and in the position representation (field theory). The solution of the two-mode problem, including only one mode each for the atomic and molecular condensates, displays analogs of Rabi oscillations and rapid adiabatic passage. A classical version of the field theory for atoms and molecules is used to demonstrate that, in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of density fluctuations. Experimental complications, including spontaneous emission and unwanted ``rogue'' photodissociation from a photoassociated molecule, are analyzed. A two-color Raman scheme is studied as a method to set up an effective two-mode scheme with reduced spontaneous-emission losses. We discuss photoassociation rates and photoassociation Rabi frequencies for high-lying vibrational states in alkali dimers both on the basis of molecular-structure calculations, and by comparing with an experiment [Wynar et al., Science 287, 1016 (2000)].

We theoretically investigate the effect of anomalous quantum correlations on the light-induced frequency shift in the photoassociation spectrum of a Bose-Einstein condensate. Anomalous quantum correlations arise because, although formed from a pair of zero-momentum condensate atoms, a condensate molecule need not dissociate back to the atomic condensate, but may just as well form a noncondensate atom pair with equal and opposite momentum, i.e., due to rogue photodissociation. The uncorrelated frequency shift of the photoassociation spectrum is to the red and linearly dependent on the laser intensity I. In contrast, anomalous correlations due to rogue dissociation lead to a blueshifted photoassociation spectrum. For sufficiently low light intensities, the rogue blueshift is dominant and proportional to sqrt[I].

We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient dynamics occuring for each pair of atoms. This transient dynamics can be summarised into a time-dependent shift and broadening of the molecular state. A simple Gross-Pitaevskii picture including this shift and broadening is proposed to describe the system in the three regimes. Finally, we suggest how to explore these regimes experimentally.