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Physical Review A

Interference in atomic fluorescence excited by molecular photodissociation

Gerald J. Diebold

Published Sep 1, 1985• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.32.1458

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Journal de physique•Jan 1, 1987•7 citations
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 homonuclear diatomic molecule is photodissociated to give one ground state and one electronically excited atom, the wave function of the two-atom systems must reflect an uncertainty as to which atom is excited. Consequently, the wave function of the photon for a photodetector viewing the resulting fluorescence must be written as a superposition of states. Detection of such photons is shown to give rise to an interference signal in the detector voltage at a frequency depending on the Doppler shift from the atomic recoil. Photodissociation of a random distribution of molecules gives rise to a detector voltage whose power spectral density is determined by the angular distribution of photofragments.
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.
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.
A Schrödinger representation approach is used to calculate the atom-field dynamics following spontaneous emission by an atom in its excited state to a superposition of its two ground-state sublevels, in the case where the frequency separation of the ground-state sublevels is large compared to the excited-state decay rate. The emitted radiation is incident on a broadband photodetector. Using a relatively simple model for the photodetector, we show how a measurement of a photo-signal leaves the atom in a coherent superposition of the two ground states. The relative phase between the two ground-state amplitudes can be interpreted in terms of the temporal phase acquired in the time interval between spontaneous emission (viewed as a quantum jump process) and detection. Alternatively, the phase can be associated with a spatial phase of the entangled atom-field system; the source atom is projected into a state containing this spatial phase when the emitted photon is detected.
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.