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The Journal of Chemical Physics

Resonance Radiation from Interacting Atoms

John Wolfgang Czarnik, Peter R. Fontana

Published May 1, 1969• 15 citations
Publisher

Abstract

The frequency distribution of resonant radiation emitted by a system of two identical interacting atoms is calculated. The separation between the atoms is assumed to be much larger than the size of their charge distributions. Initially one atom is excited while the second one is in the ground state. The two atoms are coupled through the radiation field and the electrostatic interaction. For not too large internuclear separations the line shape of the emitted radiation exhibits two distinct peaks, and the general features are identical with the result obtained from resonance fluorescence scattering. In the decay process, however, there is equal probability of scattering through the symmetric and antisymmetric states, and thus the peak heights of the emitted radiation are different from the ones in the resonance fluorescent case. For large internuclear separations the two peaks merge into the one characteristic of the line shape of a single isolated atom.

DOI
10.1063/1.1671666

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The frequency distribution of resonant radiation emitted by a system of two identical interacting atoms is calculated. The separation between the atoms is assumed to be much larger than the size of their charge distributions. Initially one atom is excited while the second one is in the ground state. The two atoms are coupled through the radiation field and the electrostatic interaction. For not too large internuclear separations the line shape of the emitted radiation exhibits two distinct peaks, and the general features are identical with the result obtained from resonance fluorescence scattering. In the decay process, however, there is equal probability of scattering through the symmetric and antisymmetric states, and thus the peak heights of the emitted radiation are different from the ones in the resonance fluorescent case. For large internuclear separations the two peaks merge into the one characteristic of the line shape of a single isolated atom.
The resonance fluorescence of a system of two identical, interacting atoms is investigated when the atoms are separated by distances that are large compared with atomic size. We consider the interactions between the atoms and the radiation field and the electrostatic interaction between the atoms, and find that the line shape of the emitted radiation consists of two peaks whose amplitude, separation, and width are functions of the internuclear distance RRR of the atoms. The peaks are distinct at smaller separations, and, as RRR increases, rapidly merge to the characteristic line shape of a single, isolated atom.
The processes of absorption and emission of radiation by a system of two interacting atoms is investigated. Separation between the atoms is assumed to be much larger than the atomic diameter, and interactions considered are those between the individual atoms and the radiation field and the electrostatic interaction between the atoms. Calculations include those for the time-dependent probability amplitude of the intermediate and final states as well as that of the emission line shape. The line shape of the emitted radiation consists of two peaks whose amplitude, separation, and half-width are functions of both the internuclear separation R of the atoms and the energy difference of the excited states of the two atoms. For a large energy difference, the peaks are distinct; for small energy differences, the peaks are distinct at smaller separations, but merge toward the line shape characteristic of a single, isolated atom as R increases.
Abstract General expressions for the time‐dependent probability amplitudes of the quantum states of two arbitrary, interacting atoms are calculated when one atom is initially in an excited p state and the other atom is in an s ground state. The lifetimes of the excited states and the line shape of the emitted radiation are obtained as functions of both the atomic separation and the energy difference between the excited states of the two atoms. The emission line shape is shown to be doubly peaked and to agree with the line shape of the radiation scattered by a system of two interacting atoms. The expressions for the lifetimes of the excited states are found to be identical to those obtained for the radiation scattering situation.
The excitation and decay probabilities for resonance scattering of radiation from an atom with two coupled excited states in an external static field are calculated as a function of time and frequency. Various oscillatory terms are found in the probabilities. These oscillations depend on the frequency of radiation, the external coupling and the energy difference between the excited states. Two special cases are investigated in detail. In the first case where one of the excited states does not decay a 'hole' appears in the emission line at a frequency equal to the frequency difference between the ground state and the unperturbed non-decaying excited state. In the second case where the two excited states decay with the same rate, one of the two lines in the emission spectrum is suppressed and the other is enhanced.
The excitation spectrum arising from the interaction between two identical atoms (molecules), one of which is excited in the presence of a resonant strong electromagnetic field (pump field), is investigated. The excitation spectrum is found to consist of those describing the symmetric and antisymmetric modes, respectively. The form of both spectra depends on the relation between the distance RRR separating the atoms and the wavelength $\ensuremath{\lambda}$ of the transition from the ground state to the excited state. For $R<\ensuremath{\lambda}$, and when certain conditions prevail, the spectral function for the symmetric modes consists of three Lorentzian lines describing the central peak and the two sidebands whose radiative widths are equal to ${\ensuremath{\gamma}}_{0}$, $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, and $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, which are twice the corresponding ones arising from an isolated single atom interacting with the pump field. For the antisymmetric modes the central peak has a $\ensuremath{\delta}$-function distribution indicating the stability of the mode in question, while, when certain conditions are satisfied, the two sidebands are described by Lorentzian lines each having a radiative width of the order of $\frac{{\ensuremath{\gamma}}_{0}}{2}$, which is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. For both the symmetric and antisymmetric modes, the dipole-dipole interaction between the atoms brings about small energy shifts. For $R>\ensuremath{\lambda}$, apart from the small energy shifts caused by the dipole-dipole interaction, the spectral functions for symmetric and antisymmetric modes are similar to that for the single atom interacting with the pump field.
This paer is concerned with the spontaneous-emision rate of two two-level atoms which have different resonance frequencies and whose spatial separation is much smaller than the corresponding mean resonance wavelength. The total radiation rate of such an atom pair is calculated completely quantum mechanically as a function of time. Explicit results are given for various values of the frequeny difference and the following initial states of the atomic system: (a) both atoms in the excited state, (b) one taom in the excited state the other in the ground state, (c) a symmetric combination of those states, (d) an antisymmetric combination of those states, and product states where each atom is in an equal superposition of its ground and excited states, for which the expectation values of the dipole moments are nonzero and may be considered to be osicillating (e) in phase, (f) in opposite phae, and (g) in random phase. Oscillations are found to appear in the radiation rate in all cases when the frequency difference becomes larger than a certain critical value, viz., the mean half-width of the atomic resonance lines. The oscillations are especially pronounced for the initial atomic states (c), (d), (e), and (f), which exhibit superradiance and radiation trapping. For example, for atoms in the antisymmetric state (d), for which the radiation from two identical atoms is zero (completely self-trapped), a pair of nonidentical atoms begins radiating and even oscillates into the superradiant region at times.