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Physical Review A

Comment on “Quasicontinuum modeling of photoassociation”

Amichay Vardi, Moshe Shapiro, J. R. Anglin

Published Jan 4, 2002• 24 citations
Publisher

Abstract

We maintain that the reservations against the use of stimulated Raman adiabatic photoassociation in a nondegenerate gas, expressed by Mackie and Javanainen in a recent manuscript [Phys. Rev. A 60, 3174 (1999)], do not account for the coherence induced by the photoassociating laser. The authors treat the problem of two-color stimulated photoassociation using a set of decoupled three-mode problems, each containing a box eigenstate and the two bound states. We argue that such decomposition is not justified, since in the limit of a very large box all three-mode problems are, in fact, coherently coupled. The three-mode condition can only be met with a set of wave packets whose bandwidth matches the spectral width of the photoassociating pulse. Using this basis set, we show that by the authors' own formalism; stimulated Raman photoassociation is a viable process in the thermal ensemble.

DOI
10.1103/physreva.65.027401

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In the preceding Comment [Phys. Rev. A 65, 027401 (2002)], the authors maintain that we have used incorrect initial conditions in our calculations on photoassociation of a thermal, nondegenerate gas [Phys. Rev. A 58, R789 (1998)], and that our conclusion that stimulated Raman adiabatic passage (STIRAP) is absent in two-color photoassociation is therefore invalid. We refute the technical argument of the Comment. Nonetheless, corresponding to the fact that in quantum mechanics the decomposition of a mixed state into pure states is not unique, the question of the presence or absence of STIRAP turns out to be a matter of semantics.

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We maintain that the reservations against the use of stimulated Raman adiabatic photoassociation in a nondegenerate gas, expressed by Mackie and Javanainen in a recent manuscript [Phys. Rev. A 60, 3174 (1999)], do not account for the coherence induced by the photoassociating laser. The authors treat the problem of two-color stimulated photoassociation using a set of decoupled three-mode problems, each containing a box eigenstate and the two bound states. We argue that such decomposition is not justified, since in the limit of a very large box all three-mode problems are, in fact, coherently coupled. The three-mode condition can only be met with a set of wave packets whose bandwidth matches the spectral width of the photoassociating pulse. Using this basis set, we show that by the authors' own formalism; stimulated Raman photoassociation is a viable process in the thermal ensemble.
In the preceding Comment [Phys. Rev. A 65, 027401 (2002)], the authors maintain that we have used incorrect initial conditions in our calculations on photoassociation of a thermal, nondegenerate gas [Phys. Rev. A 58, R789 (1998)], and that our conclusion that stimulated Raman adiabatic passage (STIRAP) is absent in two-color photoassociation is therefore invalid. We refute the technical argument of the Comment. Nonetheless, corresponding to the fact that in quantum mechanics the decomposition of a mixed state into pure states is not unique, the question of the presence or absence of STIRAP turns out to be a matter of semantics.
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.
Collective two-color photoassociation of a freely interacting 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate is theoretically examined, focusing on stimulated Raman adiabatic passage (STIRAP) from an atomic to a stable molecular condensate. In particular, Drummond et al. [Phys. Rev. A. 65, 063619 (2002)] have predicted that particle-particle interactions can limit the efficiency of collective atom-molecule STIRAP, and that optimizing the laser parameters can partially overcome this limitation. We suggest that the molecular conversion efficiency can be further improved by treating the initial condensate density as an optimization parameter.
We analyze coherent two-color photoassociation of a Bose-Einstein condensate, focusing on stimulated Raman adiabatic passage (STIRAP) in free-bound-bound transitions from atoms to molecules. This problem raises an interest because STIRAP has been predicted to be absent in the nondegenerate case [Javanainen and Mackie, Phys. Rev. A 58, R789 (1998)]. Nevertheless, we find that Bose stimulation enhances the free-bound dipole matrix element for an atomic condensate, and photoassociative STIRAP turns out to be a viable mechanism for converting an atomic condensate to a molecular condensate with near-unit efficiency.
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 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)].