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Physical Review A

Probability of photoassociation from a quasicontinuum approach

Juha Javanainen, Matt Mackie

Published Aug 1, 1998• 64 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.58.r789

Related papers

Reply to “Comment on ‘Quasicontinuum modeling of photoassociation’ ”

Juha Javanainen, Matt Mackie

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.

Physical Review A•Jan 4, 2002•13 citations

Quasicontinuum modeling of photoassociation

Matt Mackie, Juha Javanainen

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.

Physical Review A•Oct 1, 1999•53 citations

Photoassociation: From a quasicontinuum model to coherent matter optics

Matthew Mackie

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. ^

•Oct 1, 1999•1 citation

Bose-Stimulated Raman Adiabatic Passage in Photoassociation

Matt Mackie, Ryan Kowalski, Juha Javanainen

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.

arXiv:physics/9909060•Physical Review Letters•Apr 24, 2000•160 citations

Role of Bose enhancement in photoassociation

Matt Mackie, Juha Javanainen

We discuss the role of Bose enhancement of the dipole matrix element in photoassociation, using stimulated Raman adiabatic passage as an example. In a non-degenerate gas the time scale for coherent optical transients tends to infinity in the thermodynamic limit, whereas Bose enhancement keeps this time scale finite in a condensate. Coherent transients are therefore absent in photoassociation of a thermal non-degenerate gas, but are feasible if the gas is a condensate.

arXiv:physics/0006078•Journal of Modern Optics•Nov 1, 2000•5 citations

Comment on “Quasicontinuum modeling of photoassociation”

Amichay Vardi, Moshe Shapiro, J. R. Anglin

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.

Physical Review A•Jan 4, 2002•24 citations
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 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 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 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 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.