On the basis of a stochastic model of Burshtein et al. (1967) which assumes the phases, frequencies and/or amplitudes of the radiation field to constitute a randomly time-varying jump-like Markoff process, a generalisation of Mollow's theory (1975) of the dynamic Stark effect is formulated leading to predictions for the resonant scattering spectrum for a two-level atom quite similar to those published in the work of Agarwal (1976), of Eberly (1976) and of Kimble et al. (1977) who use a different approach. Apparently, the general form of the resonant scattering spectrum in a modulated radiation field depends less strongly on the particular stochastic model of the laser light than might be expected.
On the basis of a stochastic model of Burshtein et al. (1967) which assumes the phases, frequencies and/or amplitudes of the radiation field to constitute a randomly time-varying jump-like Markoff process, a generalisation of Mollow's theory (1975) of the dynamic Stark effect is formulated leading to predictions for the resonant scattering spectrum for a two-level atom quite similar to those published in the work of Agarwal (1976), of Eberly (1976) and of Kimble et al. (1977) who use a different approach. Apparently, the general form of the resonant scattering spectrum in a modulated radiation field depends less strongly on the particular stochastic model of the laser light than might be expected.
Strong laser fields, when tuned on resonance to an atomic (molecular) transition, give rise to the well-known triplet of resonance fluorescence. The laser field is normally assumed to be strong and monochromatic, even though the spectrum of real lasers is never a \ensuremath{\delta} function. A standard way to treat laser fluctuations has been to assume a well-defined nominal frequency and a randomly fluctuating phase. Recently we introduced the generalized jump model (GJM) for correlated phase fluctuations, where correlated phase jumps are considered, leading to Markovian as well as non-Markovian stochastic behavior. In the GJM, each phase jump may be correlated to the previous jump, and the degree of correlation, the typical jump size, and the mean time between jumps are the three parameters defining the stochastic character of the laser field. In this paper we apply the GJM model to the case of resonance fluorescence from an atom excited by a stochastic field. The ``standard'' Mollow triplet is obtained in the monochromatic limit of small jumps, and several new predictions are made in the different limits of the stochastic parameters. In the small-jump limit, a new ``field effect'' is predicted. The spectral line shape and the triplet separation deviate from the Mollow predictions for a monochromatic field in a substantial way, giving rise to observable differences.In the highly correlated small-jump limit, which is approximated by the Kubo oscillator model, the previous results are corrected to include nonzero line shifts and extended to the case of non-Lorentzian line shapes. In all regions, even input fields of the same line shape (which would be considered identical in the one-parameter linewidth description) give rise to very different output spectra, justifying the more complete stochastic description. Effective relaxation constants ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\mathrm{*}}$ that simplify the description of the spectrum are calculated in all appropriate cases, and ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ is found to equal the input laser linewidth. In addition to predicting the resonance fluorescence spectra, the present analysis provides a way to extract the stochastic parameters from the nonlinear measurement in those cases where the linear characterization of the input field cannot do it. The analytic work is fully supported by extensive numerical simulations.
By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels which is stimulated by a circularly polarized laser and we compute its fluorescence spectrum. Let us stress that, once the model for the unitary atom–field dynamics has been given, then the spectrum is computed without further approximations. If only the absorption/emission term is included in the interaction, we reobtain the Mollow spectrum in the case of a monochromatic laser and the Kimble–Mandel spectrum in the case of a ‘phase diffusion model’ for a non-monochromatic laser. However, our model can also describe another type of light scattering, a ‘direct scattering’ due to the response of the atom as a whole, which we expect to be small but which interferes with the scattering due to the absorption/emission channel. When both the scattering channels are introduced we obtain a modification of the Mollow–Kimble–Mandel spectrum, which shares its main features with the usual case, but which presents some asymmetries even in the case of no detuning.
An experiment was performed recently [Y. Zhu, A. Lezama, Q. Wu, and T. W. Mossberg (unpublished)] in which a two-level atom of transition frequency \ensuremath{\Omega} was placed in a bichromatic laser field with frequencies \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}, of sufficient intensity to produce dynamic Stark splitting. The observed fluorescence spectrum differed qualitatively in almost all its details from the well-known Mollow triplet [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. In this article, we use a dressed-atom model to explain the observed results.
The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.
The authors apply the recently developed theory of multiplicative stochastic correlation functions with Markovian random jumps to the problem of resonance fluorescence from a two-level atom in a strong laser field. The finite bandwidth of a single-mode laser or the appearance of distinct lines in a multimode laser is considered to be brought about by a random mode-switching process. The two-time dipole correlation functions, which determine the spectral distribution of the fluorescence and the temporal correlations between the emitted photons are averaged exactly over the stochastics of the driving field. The authors' explicit expressions only involve single-time averages, which can be easily evaluated for a given probability distribution. These results generalise and modify earlier results. The authors obtain closed expressions, rather than implicit differential equations, which can handle the continuous case as well, and take into account the initial correlations, which always arise when the laser coherence time is finite. They illustrate the dependence on the stochastics of the laser model by comparing the multimode description with the phase-diffusion process and the Lorentz wave, which all give rise to the same laser profile, but to a different fluorescence spectrum.
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.