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Journal of Physics B Atomic and Molecular Physics

Multiphoton scattering processes

S.C. Yeh, P. Stehle

Published Jun 14, 1981• 8 citations
Publisher

Abstract

A direct, completely quantum mechanical method of calculating transition probabilities involved in multiphoton scattering processes is described. It is applied to the often treated problem of resonance fluorescence of a two-level atom and is used to give a completely general description of the resonance scattering from an atom with two nearly degenerate excited states coupled to a ground state. Other applications of the method are indicated.

DOI
10.1088/0022-3700/14/11/011

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Physical Review A•May 1, 1974•14 citations
A direct, completely quantum mechanical method of calculating transition probabilities involved in multiphoton scattering processes is described. It is applied to the often treated problem of resonance fluorescence of a two-level atom and is used to give a completely general description of the resonance scattering from an atom with two nearly degenerate excited states coupled to a ground state. Other applications of the method are indicated.
Resonance fluorescence, the process in which a single two-level quantum emitter interacts with a near-resonant coherent light, is a cornerstone of quantum optics as a paradigmatic light-matter interaction. Quantum phenomena in resonance fluorescence have been accounted for in terms of one- and two-photon processes; however, the physical processes arising from the interaction of a single two-level atom with higher photon numbers remain unexplored experimentally. Here we experimentally reveal the multiphoton scattering nature of resonance fluorescence, which intrinsically gives rise to multiphoton entanglement. By accessing quantum fluctuations in the field emitted from a cavity-quantum electrodynamics system, we resolve third- and fourth-order photon scattering events from a single two-level atom. In the three-photon component, the scattered photons are shown to be genuinely energy-time entangled, as verified by a violation of Svetlichny's inequality. As a demonstration of an application, a quantum secret sharing protocol (QSS) is implemented using this entangled photon source. Our study refines the descriptive framework of resonance fluorescence and broadens the scope of its investigation. It also establishes a fundamentally simple route for generating multiphoton entangled states for quantum information processing and quantum metrology.
In a phenomenological two-level model, by using Floquet method, we directly calculate the multiphoton transition probability between the Rydberg states of an alkali-metal atom in strong microwave fields. The convergence of the truncated Floquet matrix, and the influences of parameters upon the multiphoton resonant spectra are discussed. The results show that our method can give clearer physical picture and better results about the multiphoton transition than indirect methods. Moreover, our method can easily be generalized to treat multi-level models.
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.
Abstract If and only if spontaneous resonance Raman scattering is excited by irradiation upon a single, discrete and non‐degenerate energy level sufficiently distant from other levels can it be interpreted as resonance fiuorescence, i.e. a sequence of two independent one‐photon processes, an absorption and an emission in definte order of succession. This decomposition of the resonance scattering process is independent of the bandwidth of the exciting radiation relative to the widths of the combining levels. These widths however determine quantitatively the temporal decay of the resonance scattering (= resonance fluorescence) probability given explicitly in the paper.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.