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Physical Review A

Quantum interference and radiative coupling in two-atom single-photon emission

Gershon Kurizki, A. Ben‐Reuven

Published Oct 1, 1985• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.32.2560

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Physical Review A•Mar 1, 1985•5 citations
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.
The time-resolved cooperative emission from a system of correlated neutral dissociation fragments, or molecular collision products in beams, is investigated. The investigation is focused on emission at large fragment separations (between 1 nm and a few emission wavelengths), exceeding the domain of short-range interactions within the reactive or collisional molecular complex. A master-equation approach is used to obtain a general expression for the cooperative emission rate, which consists of nonexponential decay factors multiplied by temporal ringing patterns. These features result from the time-dependent radiative coupling between the receding fragments; they depend in an essential manner on the initial electronic state of the parent molecular complex and its symmetry which determine the correlations between the fragments. In the model system of a pair of identical two-level fragments two cases are considered separately. (a) A single photon shared by the fragments, where the emission is initially superradiant or subradiant (radiation trapping), depending on the spin and inversion symmetry of the parent molecular system and of the nascent fragments. The ringing pattern depends on the electronic angular momentum state of the parent molecule and on the polarization of the emitted light. (Such a ringing has been observed recently by Grangier, Aspect, and Vigu\'e [Phys. Rev. Lett. 54, 418 (1985)] in the emission of photodissociated Ca2{\mathrm{Ca}}_{2}Ca2​.) (b) Two initially excited fragments, where the ringing pattern is of smaller amplitude, and is weakly dependent on the electronic angular momentum of the parent molecule. All the aforementioned cooperative features generally last until the fragments recede several radiation wavelengths away from each other. The application of this time-resolved analysis to various diagnostic problems is discussed, especially with regard to the identification of excited electronic states of the parent molecular complex, and the stereospecificity of the fragmental orbitals.
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.
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.
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 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.