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Physical Review A

Quasicontinuum modeling of photoassociation

Matt Mackie, Juha Javanainen

Published Oct 1, 1999• 53 citations
Publisher

Abstract

We analyze photoassociation theoretically by treating the dissociation continuum of a molecule as a quasicontinuum (QC) of discrete states. In this manner, free-bound transitions are reduced to a few-level problem. The correct continuum limit is deduced from an explicit analysis of the density of QC states. Besides giving the usual photoassociation rate, the QC model facilitates the analysis of the steady-state molecular yield. Moreover, complications such as velocity redistribution and line broadening due to atom-atom collisions may be treated basically in the same way as in connection with the customary two-level atom. Next we adapt the standard three-level quantum optics to describe free-bound-bound photoassociation for both continuous-wave and pulsed two-color excitation. For a quantum degenerate gas of atoms, a proper two-photon resonant scheme may transform atoms to ground state molecules with near-unit efficiency even in the presence of spontaneous losses from the intermediate state.

DOI
10.1103/physreva.60.3174

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We analyze photoassociation theoretically by treating the dissociation continuum of a molecule as a quasicontinuum (QC) of discrete states. In this manner, free-bound transitions are reduced to a few-level problem. The correct continuum limit is deduced from an explicit analysis of the density of QC states. Besides giving the usual photoassociation rate, the QC model facilitates the analysis of the steady-state molecular yield. Moreover, complications such as velocity redistribution and line broadening due to atom-atom collisions may be treated basically in the same way as in connection with the customary two-level atom. Next we adapt the standard three-level quantum optics to describe free-bound-bound photoassociation for both continuous-wave and pulsed two-color excitation. For a quantum degenerate gas of atoms, a proper two-photon resonant scheme may transform atoms to ground state molecules with near-unit efficiency even in the presence of spontaneous losses from the intermediate state.
We consider the process of photoassociation (PA) that occurs when a pair of colliding atoms interacts with a photon, thereby making a transition from the two-atom continuum to a bound molecular state. Such free-bound transitions are described by quantizing the molecule's dissociation continuum, and coupling each of these quasicontinuum (QC) levels to a similarly discrete molecular level. The correct free-atom results are recovered no later than at the end of a given calculation by taking the limit as the QC spacing tends to zero. From the quasicontinuum model, we are led to adapt the few-level and second-quantization methods of photon optics to analyze free-bound transitions. In particular, we establish the PA density parameter as nearly identical to the phase-space parameter as a Bose-Einstein condensate (BEC), illustrate the near-unit efficiency of one- and two-color photoassociation of a BEC, and develop coherent atom-molecule transitions as the matter optics version of second-harmonic generated photons. ^
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 examine photoassociation by using a quasicontinuum to describe the colliding atoms. The quasicontinuum system is analyzed using methods adapted from the theory of laser spectroscopy and quantum optics, and a continuum limit is then taken. In a degenerate gas the equilibrium probability of photoassociation may be close to unity. In the continuum limit, for a thermal atomic sample, the stimulated Raman adiabatic passage (STIRAP) mechanism cannot be employed to eliminate unwanted spontaneous transitions.
In the molecular photoassociation process, two free cold atoms absorb one photon by a resonant way, to create an excited molecule in a well defined ro-vibrational state. The photoassociative spectroscopy of alkaline dimers yields accurate determinations for the long-range parts of molecular potential curves correlated to the first s + p asymptote. In contrast to atoms, laser cooling of molecules is very difficult because of the lack of a closed two-level scheme for recycling the population. The molecular photoassociation of cold atoms opens also a promising alternative for the formation of cold ground state molecules. Photoassociation of cold cesium atoms has permitted the first observation of translationally cold ground state molecules. The case of the cesium atom is very favorable because the 0 g - and 1 u purely long-range states below the dissociation limit 6s 1/2 +6p 3/2 present Condon points at intermediate distances. Such configurations offer rather efficient channels for the creation of singlet or triplet ground state Cs 2 molecules after spontaneous decay.
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.
Bound-state molecules can be photoassociated directly from ultracold free-atom pairs by excitation to a purely repulsive electronic state. The process is explained on the basis of quantum unitarity: the initially free-scattering state is transformed by an impulsive light pulse to a deformed superposition which contains bound-state components. For pulse durations which are short compared to the ultracold dynamics, the maximal rate of photoassociation was found to be determined by the initial stationary distribution of scattering states of the atom pairs. The process was simulated for an ultracold gas of 87Rb^{87}\text{R}\text{b}87Rb with a temperature of $T=44\text{ }\ensuremath{\mu}\text{K}$ and a density of $\ensuremath{\approx}{10}^{11}\text{ }{\text{cm}}^{\ensuremath{-}3}$. Transform-limited pulses maximize the photoassociation, yielding $\ensuremath{\sim}1$ bound molecule per pulse. Coherent control calculated by a local control scheme can increase the photoassociation yield by two orders of magnitude.