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Physical review. B, Solid state

Time-Dependent Phenomena Associated with the Resonant Scattering of Light by Perturbed Atoms

David L. Huber

Published Apr 15, 1970• 29 citations
Publisher

Abstract

We report theoretical studies of the resonant scattering of light by perturbed atoms under conditions where the amplitude of the incident electric field varies with time. Adiabatic perturbations are simulated by a randomly fluctuating term in the energy separation between the resonant levels; lifetime effects are accounted for by adding a small imaginary term to the separation. Assuming linearity, we derive a general expression giving the intensity of the scattered light as a function of time. Explicit calculations are carried out in the motional narrowing limit for a variety of cases. Interference and inhomogeneous broadening are assessed. A brief analysis is made of recent scattering experiments involving ${\mathrm{Cr}}^{3+}$ in ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. Incoherence in the source and the motion of the target atoms are also considered.

DOI
10.1103/physrevb.1.3409

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Journal of the Physical Society of Japan•Mar 1, 1984•4 citations
We report theoretical studies of the resonant scattering of light by perturbed atoms under conditions where the amplitude of the incident electric field varies with time. Adiabatic perturbations are simulated by a randomly fluctuating term in the energy separation between the resonant levels; lifetime effects are accounted for by adding a small imaginary term to the separation. Assuming linearity, we derive a general expression giving the intensity of the scattered light as a function of time. Explicit calculations are carried out in the motional narrowing limit for a variety of cases. Interference and inhomogeneous broadening are assessed. A brief analysis is made of recent scattering experiments involving Cr3+{\mathrm{Cr}}^{3+}Cr3+ in {\mathrm{Al}}_{2}$${\mathrm{O}}_{3}. Incoherence in the source and the motion of the target atoms are also considered.
The resonant scattering of photons from a perturbed two-level system is studied in detail. Adiabatic perturbations are approximated by a randomly fluctuating term in the level splitting. Off-diagonal perturbations are accounted for in the linewidth and the time dependence of the correlation functions. Explicit expressions for the cross section are obtained in the statistical and motional-narrowing limits. The detailed-balancing symmetry of the scattering is established. Minor modifications of the approximate expressions for the cross sections are proposed in order to preserve this symmetry. The effects of off-diagonal perturbations, which couple the atom to a thermal bath, are investigated at length for a model interaction.
Some typical resonance nonlinear-optics phenomena taking place when light interacts with atoms are considered. The multitude of such phenomena reduces to scattering of the perturbing light, perturbation of the atomic spectrum, excitation of an atom and its ionization. In all these cases the investigations are carried out using the simplest model—an isolated atom in a monochromatic external field. Such a model enables one to give an exact description of many elementary processes. On the other hand it is sufficiently realistic. A detailed investigation is carried out of resonance fluorescence, spontaneous Raman scattering, multiphoton excitation of atoms, resonance shifts and splitting of atomic levels and resonance lonication of atoms. The nature of these processes is investigated as a function of the intensity of the external field, its frequency, a specific atomic spectrum, the nature of polarization of the perturbing field, and the degree of its nonlinearity. The role played by the field of the electromagnetic vacuum is analyzed. Theoretical predictions are compared with the results of many experiments describing resonance processes of the interaction of an intense light field with atoms.
We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.
The authors present a weak light field, scattering theoretical description of the intensity autocorrelation function for the scattered light from a many-atom (molecule) system. The theory considers both resonant and near-resonant scattering for atoms with many sublevels in both the ground and electronically excited states, and it incorporates the effects of the finite coherence time of the incident radiation. The theory is derived using incident two-photon wave packets with spatial dispersion among the target atoms. Purely anti-bunching contributions arise from single-atom-two-photon scattering and from successive two-atom-two-photon scattering events. However, there are interleaved two-atom-two-photon scattering processes which provide purely bunching contributions since both atoms may be scattering at the same time. Path length differences in the successive two-atom scatterings can also induce some bunching character to the correlation function. The dependence of the risetime and decay of the intensity correlation function upon the atomic excited state lifetimes and the coherence time of the incident light emphasises the correlation between photons which have been coherently and/or incoherently scattered.
A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a ccc number. It is thus proved quite rigorously and generally that the use of a ccc-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.
In order to investigate the effect of perturbation caused by the interaction of a two-level atom with its environment on the coherency of light scattered by the atom when it is irradiated by an intense radiation, Mollow's theory is generalized to include a random modulation of the resonance frequency as well as fluctuations of the incident field. Expressions for the power spectrum, the total intensity, the coherent scattering intensity and the broad Rayleigh scattering intensity are derived. Some general aspects of the problem are discussed.