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Journal of Physics B Atomic and Molecular Physics

Nonstationary two-level resonance fluorescence

B. Renaud, R. M. Whitley, Carlos R. Stroud

Published Jan 11, 1977• 55 citations
Publisher

Abstract

Analytic expressions are obtained for the spectrum of the light scattered when a collimated atomic beam is illuminated at right angles to its path by a CW monochromatic laser beam tuned to resonance with a two-level transition. The spectra vary depending on the portion of the interaction region from which the scattered light emanates. The spectrum of the light from a finite sub-region of the interaction volume is described as a function of the location and length of the sub-region, and of the intensity and frequency of the laser. Several interesting features related to the turn-on of the interaction as well as to the finite observation interval are found.

DOI
10.1088/0022-3700/10/1/010

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Analytic expressions are obtained for the spectrum of the light scattered when a collimated atomic beam is illuminated at right angles to its path by a CW monochromatic laser beam tuned to resonance with a two-level transition. The spectra vary depending on the portion of the interaction region from which the scattered light emanates. The spectrum of the light from a finite sub-region of the interaction volume is described as a function of the location and length of the sub-region, and of the intensity and frequency of the laser. Several interesting features related to the turn-on of the interaction as well as to the finite observation interval are found.
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 distribution of light scattered by a two-level atom in a laser beam with phase modulation has been calculated. The spectrum has been obtained via numerical solution of the optical Bloch equations using the algorithm of Wilkens and Rza\ifmmode \mbox{\c{}}\else \c{}\fi{}\ifmmode \dot{z}\else \.{z}\fi{}ewski [Phys. Rev. A 40, 3164 (1989)]. The modulation produces additional sidebands in both coherent and incoherent parts of the spectrum; the location of the added components depends on the modulation depth. In the case of two-frequency phase modulation with incommensurate frequencies, wild, ``chaotic'' behavior of the spectrum has been observed, similar to the case of bichromatic amplitude modulation. The intensity distribution is practically insensitive to the chosen constant value of the phase of modulation.
The problem of resonance fluorescence from a two-level atom that is driven near resonance by a laser beam of finite bandwidth is tackled via the Heisenberg equations of motion, by a simple generalization of our previous treatment. It is found that the two-time intensity correlation function is again factorizable into a product of the mean light intensities at the two times, each of which is slightly modified under broad-band excitation from its value under monochromatic excitation. The spectrum of the fluorescence is affected rather more drastically, and, in general, becomes asymmetric under broad-band excitation.