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Journal of Physics B Atomic and Molecular Physics

Transitions at the Rabi frequency in the AC Stark effect: a dressed-molecule description

Helen S. Freedhoff

Published Mar 14, 1978• 22 citations
Publisher

Abstract

Studies are made of a system consisting of a molecule interacting with both an intense electromagnetic field resonant with a molecular transition frequency and a weak RF probe field at the Rabi frequency. An earlier study of this system (Freedhoff et al., ibid., vol.8, p.L209 (1975)) is extended to include the effects of photon cascades and of laser detuning. The method of calculation is the dressed-atom description and master-equation approach of Cohen-Tannoudji and Reynaud (1977). Unlike the earlier study, the present treatment produces quantitatively correct expressions for the emission and absorption spectra both in the visible and in the RF regions. More importantly, however, the predicted absorption intensity is greatly enhanced over that in the earlier study, and, for negative detuning of the laser, amplification of the RF signal is predicted.

DOI
10.1088/0022-3700/11/5/015

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AC Stark effect and fluorescence in modulated laser beams. II. Two-photon stepwise excitations

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For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.

Journal of Physics B Atomic and Molecular Physics•Feb 14, 1980•21 citations
Studies are made of a system consisting of a molecule interacting with both an intense electromagnetic field resonant with a molecular transition frequency and a weak RF probe field at the Rabi frequency. An earlier study of this system (Freedhoff et al., ibid., vol.8, p.L209 (1975)) is extended to include the effects of photon cascades and of laser detuning. The method of calculation is the dressed-atom description and master-equation approach of Cohen-Tannoudji and Reynaud (1977). Unlike the earlier study, the present treatment produces quantitatively correct expressions for the emission and absorption spectra both in the visible and in the RF regions. More importantly, however, the predicted absorption intensity is greatly enhanced over that in the earlier study, and, for negative detuning of the laser, amplification of the RF signal is predicted.
Preliminary studies have been made of a system which consists of a molecule placed in an intense electromagnetic field resonant with a molecular transition frequency, and a probe field containing frequencies in the neighbourhood of the resulting dynamic Stark splitting frequency 2 epsilon . In these studies, only a single decay process was considered. Both emission and absorption of radiation by the system are predicted at frequencies near 2 epsilon , provided that the molecule has different permanent dipole moments in its lower and its upper states. A correct treatment, which allows for a cascade of emitted photons, is expected to bring about some quantitative changes in the shape of the predicted spectrum, but to leave unchanged the basic prediction of transitions at frequency 2 epsilon .
We study the interaction of a two-level atom with two lasers of different frequencies and amplitudes: a strong laser of Rabi frequency $2{\ensuremath{\Omega}}_{1}$ on resonance with the atomic transition, and a weaker laser detuned by subharmonics $(2{\ensuremath{\Omega}}_{1}/n)$ of the Rabi frequency of the first. We find that under these conditions the second laser couples the dressed states created by the first in an nnn-photon process, resulting in ``doubly dressed'' states and in a ``multiphoton ac Stark'' effect. We calculate the eigenstates of the doubly dressed atom and their energies, and illustrate the role of this multiphoton ac Stark effect in its fluorescence, absorption, and Autler-Townes spectra.
In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.
Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.
A dressed-atom approach to resonance fluorescence in intense laser fields is presented. Simple and general results are derived which include the now well known predictions concerning two-level atoms but are not restricted to such simple cases. The positions of the various components of the fluorescence and absorption spectra are given by the allowed Bohr frequencies of the total system: atom+laser mode (dressed atom). The master equation, describing spontaneous emission from the dressed atom is solved in the limit of high intensities. Simple expressions, taking into account the effect of cascades, are derived for the widths of the components.
For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.