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Journal de physique

Quantum interference effect for two atoms excited by molecular photodissociation : a theoretical analysis

Philippe Grangier, J. Vigué

Published Jan 1, 1987• 7 citations
Publisher

Abstract

We present a theoretical analysis of a previous experiment, in which a modulation in the time-resolved atomic fluorescence light following the photodissociation of Ca2 molecules by a pulsed laser was observed. First a calculation is performed on a simple model, involving two atoms coupled with the quantized radiation field. Then the validity of this model is discussed on molecular physics grounds. Finally, a quantitative analysis of the experiment is presented ; a good agreement is obtained if quasi-bound levels of the molecular ground state are taken into account.

DOI
10.1051/jphys:01987004805078100

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Quantum beats in atomic fluorescence excited by molecular photodissociation

Gerald J. Diebold

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The Journal of Chemical Physics•Jul 1, 1986•0 citations
We present a theoretical analysis of a previous experiment, in which a modulation in the time-resolved atomic fluorescence light following the photodissociation of Ca2 molecules by a pulsed laser was observed. First a calculation is performed on a simple model, involving two atoms coupled with the quantized radiation field. Then the validity of this model is discussed on molecular physics grounds. Finally, a quantitative analysis of the experiment is presented ; a good agreement is obtained if quasi-bound levels of the molecular ground state are taken into account.
We present experimental evidence for a modulation in the time-resolved atomic fluorescence light following the photodissociation of Ca2{\mathrm{Ca}}_{2}Ca2​ molecules by a pulsed laser. This modulation is due to an interference effect involving two atoms recoiling in opposite directions, while only one photon is emitted. The period of the modulation is equal to the time for the interatomic distance to increase by an optical wavelength.
Atomic fluorescence that accompanies the photodissociation of Ca2 molecules is modulated in time. This modulation was attributed to an interference between the fields emitted by the two atoms [1,2]. The effect of radiative resonant coupling between the atoms was considered to be negligible. It was suggested that the modulation of emission is analogous to the interaction of a single photon with two slits. However, the present article demonstrates that radiative resonant coupling is the main cause of the modulation, and the effect is not analogous to the interaction of single, space-time separated photons with two slits.
The recent experiment by Grangier, Aspect, and Vigu\'e on interference in the emission from fragments of electronically photodissociated molecules is treated as a special case of cooperative fluorescence (CF) from products of various molecular processes. This general analysis relates time-resolved features of the CF to characteristics (such as orbital symmetry) of the dissociating parent molecule (PM) suggests various PM state preparations (including formation of subradiant states), and discusses the persistence of CF in systems of nonidentical fragments. The diagnostic potentialities of such studies are emphasized.
In photodissociation of a homonuclear diatomic molecule, conservation of linear and angular momenta requires that each atomic fragment follow identical but oppositely directed trajectories with respect to the molecular center of mass. For certain values of the incident photon energy, one of the atoms will be electronically excited while the other will be in its ground state. When a detector records the undispersed fluorescence from the decay of the excited atom it cannot distinguish which trajectory the excited atom followed and hence whether the photon possesses a blue or red Doppler shift corresponding to recoil towards or away from the detector. According to the principle of superposition in quantum mechanics, the wave function of the photon must be a sum over two paths corresponding to emission from an excited atom in either of the two recoil directions. Detection of such photons gives rise to an interference between the probability amplitudes for the two paths that is manifested in the output from the photodetector as a beat frequency. Since photodissociation of an ensemble of molecules gives rise to a distribution of recoil directions relative to the electric vector of the incident radiation, a range of beat frequencies must be present in the detected signal. This paper gives a calculation of expected output voltage waveforms from a photodetector viewing atomic fluorescence excited by molecular photodissociation. Expressions are given for partial Fourier transforms of the photodetector signals. The results show that the shape of the voltage waveforms depends strongly on the asymmetry parameter for recoil of the photofragments and on whether or not the magnetic sublevels of the excited atomic state are created in a coherent superposition.
When a diatomic molecule is photodissociated on a singlet molecular potential energy surface to give two singlet atoms, one of which is electronically excited, the atoms are left in pure angular momentum states referred to the molecular quantization axis. Transformation of such pure states to a laboratory frame of reference gives atomic wave functions that are described as coherent superpositions of states. Application of an external magnetic field to an ensemble of excited atoms causes quantum beats, or, alternately, a Hanle effect to appear in the fluorescence emitted by the atoms. Calculations show that the interference effects are observed only for certain geometrical arrangements of the electric vector of the photodissociating radiation, the external field, and the polarization direction accepted by the fluorescence detector. The expressions for the fluorescence intensity show that the phase and modulation depth of the quantum beat can be used to determine the asymmetry parameter for recoil of the photofragments.