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International Journal of Quantum Chemistry

Symmetry effects in the radiation damping of degenerate states

Lawrence N. Craft

Published Nov 1, 1969• 0 citations
Publisher

Abstract

Abstract Radiation damping of three atoms in a radiation field is studied for both a linear and closed‐chain configuration. One atom of the system is initially excited. Use is made of the Heitler‐Ma perturbation procedure up to second order. The discussion is developed in terms of the symmetry of the interactions within the system. The interactions arising from dipole transitions perpendicular to the plane of the closed chain are shown to be similar to the interactions in a two‐atom system, and the results are extended to cover larger rings.

DOI
10.1002/qua.560030605

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Abstract Radiation damping of three atoms in a radiation field is studied for both a linear and closed‐chain configuration. One atom of the system is initially excited. Use is made of the Heitler‐Ma perturbation procedure up to second order. The discussion is developed in terms of the symmetry of the interactions within the system. The interactions arising from dipole transitions perpendicular to the plane of the closed chain are shown to be similar to the interactions in a two‐atom system, and the results are extended to cover larger rings.
The radiative decay of an atom with two excited states coupled by an external perturbation is investigated. The differential equations of motion are Fourier transformed and the probability amplitudes are obtained by contour integration. The real parts of the poles in the complex plane are the perturbed energies of the excited states, and the imaginary parts yield the decay characteristics. The decay probabilities of the excited states contain three different decay terms; two exponential decays and one modulated exponential decay. The probabilities of the final states give the frequency distribution of the emitted photons as a function of time. In an Appendix, the Heitler-Ma formalism is used to eliminate the final states of the system, and the resulting equations which contain damping terms are compared with the phenomenological method.
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The problem of resonance between light and an atom is treated by solving the wave equation through the method of variation of constants. It is found that an initial degeneracy is removed by the action of the light, and that there occur fluctuations between the two states involved. Calculation of the electric moment of the perturbed atom on the Schr\"odinger density hypothesis shows that when the incident light is linearly polarized the radiation has the same degree of polarization as though the atom were in a weak magnetic field parallel to the electric vector of the light. In the case of circular polarization this fictious field is perpendicular to the plane of polarization. These results confirm the Heisenberg rule deduced from the correspondence principle.
We calculate the radiative properties for a linear dipole-coupled chain of qubits. Using the explicit energy eigenstates of the system, we find the radiation patterns for spontaneous transitions from the one-photon eigenstates to the ground state of the system. We show that depending on the excitation of a specific atom, the radiation tends to be focused either along or perpendicular to the chain. We conclude with a derivation of the total decay rate of the one-photon eigenstates, and find the interesting result that for systems where the photon wavenumber is not much larger than the interatomic spacing, up to 94% of the eigenstates are subradiant, that is, they decay significantly slower than a single atom in isolation.
Abstract The total radiation rate of the cooperative spontaneous emission from an initially single‐quantum excited three‐atom system is calculated using Lehmberg's master equation and taking into account dipole‐dipole near field interaction. We find a strong influence of the precise configuration of the atomic dipoles and of the position of the initially excited atom on the temporal behaviour of the total radiation rate, especially if the atoms are separated by distances much smaller than the resonance wavelength.