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Journal de physique

Coherence effects in the polarization of the light emitted by photofragments

J. Vigué, Juan Alberto Beswick, Michel Broyer

Published Jan 1, 1983• 59 citations
Publisher

Abstract

In this paper a general quantum mechanical treatment of photodissociation and fluorescence from the fragments in the case of direct dissociation as well as in the case of photo-predissociation is presented. This formulation takes into consideration all the possible coherence effects coming from quantum interference between photodissociation amplitudes to different magnetic sublevels of the fragments. This results in large differences between classical and quantum results for the degree of polarization of the light emitted from photofragments. The theory is applied to the case of Ca2 which constitutes a striking experimental example of coherence effects in direct photodissociation. For this case the classical calculation predicts a polarization degree of 14 % while the experiment shows 64 %. The maximum theoretical value when coherence is taken into account is 78 %. The difference between the experimental result and the theoretical value is attributed to depolarization by saturation, although some other minor contribution may also be present.

DOI
10.1051/jphys:0198300440110122500

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The Journal of Chemical Physics•Jul 1, 1986•0 citations
In this paper a general quantum mechanical treatment of photodissociation and fluorescence from the fragments in the case of direct dissociation as well as in the case of photo-predissociation is presented. This formulation takes into consideration all the possible coherence effects coming from quantum interference between photodissociation amplitudes to different magnetic sublevels of the fragments. This results in large differences between classical and quantum results for the degree of polarization of the light emitted from photofragments. The theory is applied to the case of Ca2 which constitutes a striking experimental example of coherence effects in direct photodissociation. For this case the classical calculation predicts a polarization degree of 14 % while the experiment shows 64 %. The maximum theoretical value when coherence is taken into account is 78 %. The difference between the experimental result and the theoretical value is attributed to depolarization by saturation, although some other minor contribution may also be present.
The optical magnetic birefringence (Faraday) technique that can be used to study the anisotropy distributions of the angular momenta of photofragments produced in molecular photodissociation is compared theoretically and experimentally with the magnetic dichroism technique. The frame independent tensor form of the general expression describing the difference between an initial and a final polarization matrix of a probe light beam passing through the photofragment vapor is presented and analyzed. The procedure of detection of the photofragment electron orientation and alignment angular distributions by Doppler spectroscopy using each of the techniques is studied theoretically. The angular independent anisotropy orientation and alignment parameters describing photodissociation dynamics that can be determined from these studies are presented. It is shown that in principle each of the techniques can give the same information about the photodissociation dynamics; however, the birefringence technique has an undeniable advantage since it leads to an increase in accuracy of the experimental data. Both magnetic birefringence and magnetic dichroism techniques were used experimentally to study the spin orientation of ground state Rb atoms produced in photodissociation of RbI at 266 nm by circularly polarized laser light. The experiment was not of the Doppler spectroscopy type, but use of different 85 Rb and 87 Rb isotopes in the dissociation cell and in the probe light source allows detection of the oriented atomic photofragments separately by each of the techniques. Obtained experimental results are in agreement with the theoretical predictions. Contribution of the orientation of the Rb hyperfine structure energy states to the observed signals were also studied and treated theoretically. The initial degree of the electron spin orientation of the Rb atoms produced in the reaction was found to be P e = 0.11 ± 0.02.
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.
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.
The rotational coherence of an ensemble of photodissociation fragments is studied in the absence of collisions. Formulas for quantum orientation correlation functions are obtained for the case when parent molecules and their fragments are asymmetric tops and the predissociation time is much shorter than the characteristic time of rotational reorientation. It is shown that photodissociation does not affect periods of a rotational echo, but the structure of the echo pulses (their shape and width) depends substantially on the features of rotational excitation of photofragments upon photodissociation.
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.