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Physical Review A

Effect of recoil in resonance fluorescence

Juan Francisco Lam, P. R. Berman

Published Nov 1, 1976• 19 citations
Publisher

Abstract

The effect of recoil on the frequency of the spontaneously emitted photons in resonance fluorescence processes is examined. The rate of fluorescence is calculated in the limit of a weak external field. It is found that conservation of energy and linear momentum for the entire scattering process determines the frequency spectrum of the fluorescence. A simple experiment is proposed to measure the frequency shifts due to recoil.

DOI
10.1103/physreva.14.1683

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The effect of recoil on the frequency of the spontaneously emitted photons in resonance fluorescence processes is examined. The rate of fluorescence is calculated in the limit of a weak external field. It is found that conservation of energy and linear momentum for the entire scattering process determines the frequency spectrum of the fluorescence. A simple experiment is proposed to measure the frequency shifts due to recoil.
The effect of the specific anisotropy of the environment on the dynamics of a resonantly fluorescing atom is analyzed in a one-dimensional model. The environmental anisotropy, which is manifested as different spectral selectivities of the absorption of spontaneous photons emitted by the atom in different directions, results in the anisotropy of the photon emission rate giving rise to a nonzero recoil force on the atom. The effect under optimal conditions can reach one-quarter of the recoil momentum per single photon emission. This force is directed toward the weaker spectral selectivity.
We present calculations of the spontaneous-emission spectrum from a two-photon two-level system in the presence of an arbitrarily intense monochromatic field at half of the two-photon transition frequency. The single-photon counterpart to this is called resonance fluorescence. Because of the complexity of the two-photon two-level model, many effects arise that are absent in the one-photon problem. In particular, we show how the Rayleigh scattering from this system is markedly different and discuss the role of Stark shifts on the emission spectrum.
A simple theoretical model is formulated which describes dynamical features of the interaction of two-level atoms with a continuum of radiation oscillators. In particular, this paper is concerned with resonance scattering by single atoms in the presence of an external classical field, and spontaneous emission by a system of identical atoms. In the case of resonance scattering, the response of an atom to rapid changes of the amplitude of the external field is studied. The model for spontaneous emission by a system of atoms is based on the assumptions that all atoms have the same resonance frequency, and that the atoms are contained in a volume whose extension is small compared with the wavelength of the emitted radiation. The complete evolution of a system of mmm atoms is determined by a set of coupled first-order linear differential equations, and explicit solutions are presented for the values m=1,2,3,4,and8m=1,2,3,4, \mathrm{and} 8m=1,2,3,4,and8. Pair correlations of the atoms and photon-number fluctuations are discussed. An approximation for resonance fluorescence by a system of atoms with a broad distribution of resonance frequencies is included in an Appendix.
We present a theory of two-photon resonance fluorescence of an atom or molecule in which the excitation by an external electromagnetic field as well as fluorescence emission is mediated by two-photon processes. The treatment is based on first dressing the atom or molecule by the external field and then evaluating perturbatively the effect of the interaction with the vacuum or fluorescent field and so resonance fluorescence can be considered as spontaneous emission from the dressed atom. The introduction of the combined system of atom and external field via dressed states leads to simpler calculations and more transparent physics. The fluorescence spectrum derived by us has similarities as well as differences with that of one-photon resonance fluorescence and earlier theoretical predictions for the two-photon case.
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.
We suggest that the statistical properties of the scattered radiation in resonance-fluorescence experiments may be affected significantly by the existence of atomic correlations. The scattered light spectrum from two- and three-atom collective systems has been calculated and compared with the one-atom spectrum. The differences are quite significant for weak fields, but become less pronounced as the intensity of the driving field is increased. In addition, we have calculated the scattered intensity correlation function for collectively interacting systems, and found that its behavior is very different from that of the single-atom intensity correlation function, both for weak and strong incident fields. The implications of our findings for the observation of photon antibunching are also discussed.