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Optics and Spectroscopy

Macroscopic manifestations of specific features of quantum statistics of the radiation field in the spectrum of resonance fluorescence

A. D. Gazazyan, Б. В. Крыжановский

Published Apr 1, 2000• 0 citations
Publisher

Abstract

The fluorescence spectrum of a two-level atom excited by the field, whose state represents a superposition of the coherent states, is investigated. It is shown that to each mode of the quantum-statistical distribution of the incident field, a spectral mode of the scattered radiation corresponds, and one can determine the number of statistical modes of the incident field from the number of spectral modes of the scattered field. This result is a consequence of the fact that in the quasi-classical limit, statistical modes of the superimposed state interact with the atom independently of one another.

DOI
10.1134/1.626838

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The fluorescence spectrum of a two-level atom excited by the field, whose state represents a superposition of the coherent states, is investigated. It is shown that to each mode of the quantum-statistical distribution of the incident field, a spectral mode of the scattered radiation corresponds, and one can determine the number of statistical modes of the incident field from the number of spectral modes of the scattered field. This result is a consequence of the fact that in the quasi-classical limit, statistical modes of the superimposed state interact with the atom independently of one another.
The quasi-energy wave functions of a two-level atom in an electromagnetic field, the state of which represents a superposition of coherent states, were found. The fluorescence spectrum of an atom excited by such a field was investigated. It was shown that a spectral fluorescence mode corresponds to each mode of the quantum-statistical distribution of the field incident on the atom. This means that the number of statistical modes of the incident field may be recorded as the number of data bits of the information carried by the light pulse.
The problem of the interaction between a two-level atom and a quantum electromagnetic field is treated without the use of perturbation theory, without introduction of classical fields or factorization conditions for the states, and without assumptions about loss of memory. The calculation is carried out in the Heisenberg picture, without mode decomposition, and the conclusions all refer to physically measurable quantities, such as the fluorescence detected in the far field of the atom. It is shown that in a coherent field of constant amplitude the system always settles down to a quasistationary state, and that the stationarity is a manifestation of the quantum fluctuations. A solution for the growth of the fluorescent light intensity is presented that holds for any coherent exciting field. The two-time correlation function and the spectral density of the fluorescence are calculated, and are found to agree in the long-time limit with earlier results of Mollow. The two-time intensity correlation function of the field is derived, which corresponds to measurable photoelectric pair correlations, and it is found that this reflects several quantum features of the field. It is shown that quantum fluctuations are manifest more explicitly in two-time correlations in the steady state than in transient effects, like spontaneous emission in the vacuum. The measurement of such correlations therefore presents an opportunity for further experimental tests of quantum electrodynamics.
The phenomenon of resonance fluorescence provides an interesting manifestation of the quantum theory of light and is a “real world” application of the material of the Chapters 8 and 9. In this process, a two-level atom is typically driven by a resonant continuous-wave laser field and the spectral and quantum statistical properties of the fluorescent light emitted by the atom are measured. Experimentally this can be achieved by scattering a laser off a collimated atomic beam such that the directions of the laser beam, atomic beam, and detector axis are mutually perpendicular as shown in Fig. 10.1. If the driving field is monochromatic, then at low excitation intensity the atom absorbs a photon at the excitation frequency and reemits it at the same frequency as a consequence of conservation of energy. The spectral width of the fluorescent light is therefore very narrow. The situation, however, is considerably more complicated when the excitation intensity increases and the Rabi frequency associated with the driving field becomes comparable to, or larger than, the atomic linewidth. At such intensity levels, the Rabi oscillations show up as a modulation of the quantum dipole moment and sidebands start emerging in the spectrum of the emitted radiation. This so-called dynamic Stark splitting is an interesting feature of the atom–field interaction. In addition to that, the fluorescent light exhibits certain nonclassical properties including photon antibunching and squeezing. In this chapter, we develop a theory of resonance fluorescence to explain these phenomena.
The spectral density of resonance fluorescence from a two-level atom in a monochromatic radiation field of arbitrary strength and detuning is calculated by solution of the wave equation. A basis set in which the strong coupling of the atom and the quantised incident field is diagonal is used, and the resulting infinite set of coupled equations is solved by truncating them to a set of N equations and finally proceeding to the N to infinity limit. The resulting spectral densities of the inelastically scattered field for various levels of intensity of the incident field and degree of detuning are found to be identical with those of Kimble and Mandel (1976, 1977) obtained by solution of the coupled equations of motion of the atom and the radiation field in the Heisenberg picture.