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Journal of Physics B Atomic and Molecular Physics

Resonant fluorescence: Zeeman and AC Stark effect

J. Kourlas

Published May 14, 1981• 1 citation
Publisher

Abstract

Resonant fluorescent spectra are calculated in cases where the incident laser radiation is linearly polarised and the fluorescent radiation circularly polarised. The incident radiation is coherent, monochromatic and sufficiently intense to enable AC Stark splitting of the atomic levels. The long-time limit spectra are calculated when the atom consists of two magnetically degenerate levels. In addition, the spectra are derived when the degeneracy is removed by a constant magnetic field.

DOI
10.1088/0022-3700/14/9/008

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Journal of Physics B Atomic and Molecular Physics•Jan 28, 1980•102 citations
Resonant fluorescent spectra are calculated in cases where the incident laser radiation is linearly polarised and the fluorescent radiation circularly polarised. The incident radiation is coherent, monochromatic and sufficiently intense to enable AC Stark splitting of the atomic levels. The long-time limit spectra are calculated when the atom consists of two magnetically degenerate levels. In addition, the spectra are derived when the degeneracy is removed by a constant magnetic field.
In the intense radiation fields with power density from 104W/cm2 to 109W/cm2 the essential modification of electronic states of atoms occurs displaying, in particular, in modifications of resonant fluorescence (rf) spectra. We use 'Fermi golden rule' for calculations of relative intensities and frequencies for rf multiplet for real multilevel initially unexcited atoms in two monochromatic laser fields of arbitrary intensity resonant to adjacent transitions of (Xi) or (Lambda) types and magnetic field, giving the level splittings of different values from Zeeman to Paschen-Back effect. The dependence of quasienergies on parameters obtained with the help of a sorting program permits us to define the values of parameters for which the states of the system are mixed and so to receive the correct probability amplitudes for instantaneous or adiabatic regimes of switching the perturbation. The analysis of the quasienergies and form of rf spectra permits us to get relations between the form of the spectra and modifications of electronic structure of the atom due to radiation fields and external magnetic field.
The resonance fluorescence from a three-level atom irradiated by a monochromatic laser is studied. Detailed spectra are calculated by using the Heisenberg source-field approach, and introducing Liouvillian space techniques. It is predicted that in the steady-state limit the fluorescence from an atom having two closely spaced excited states will have an anisotropically polarised seven-line spectrum. Graphs are shown of the predicted spectra in the case of on-resonance excitation and of far off-resonance excitation.
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.
The effect of a dc magnetic field on the rate at which a ground-level, Zeeman-degenerate atom is photoionized via a short-lived autoionizing level is calculated. We consider single-step as well as two-step photoionization; in the latter case we allow the light to be either resonant or far from resonance with an intermediate level. In all cases we find that the magnetic field may raise the fraction of the atoms available for photoionization and consequently increase the photoion fraction produced by a light pulse of given fluence. In the resonant case we find that if the magnetic-field Zeeman splitting of the ground and intermediate level is much larger than the rate at which population enters or leaves that level then the Zeeman-state populations are decoupled from one another and there exist simple conditions under which they obey rate equations. In the nonresonant case an additional condition for two-photon rate equations is that the optical Stark shift of the ground state be much smaller than the magnetic Zeeman splitting. These results apply specifically to excitation by lasers whose spectral widths are narrow compared to the homogeneous linewidths of the corresponding atomic transitions, but appear to be generalizable to the opposite limit, in which the laser spectral widths are much broader than the homogeneous linewidths.
Theory and methods of computer simulations permit investigation of the interaction of high-power laser radiation, up to GW/cm2, with atoms having both small and large fine-structure intervals compared with interactions with a laser field and an external magnetic field. The modifications of the energies and population of atomic levels due to such interactions lead to nonlinear effects. Besides modifications in the Raman effect and new effects of rotation of the plane of polarization and circular dichroism that were investigated earlier, there are such nonlinear effects as the modification of the number, positions, intensities, and polarizations of the lines in the resonant fluorescence spectrum. Numerical experiments permit investigation of the characteristics of resonant fluorescence and comparison with known experimental results.PACS Nos.: 32.50, 78.20.L, 42.65, 42.50.H
Attention is focused on the dynamic evolution of the emission spectrum following abrupt excitation of a near-resonant two-level absorber by a strong laser field. The multiphoton character of the absorption-emission process is evident in the AC Stark splitting of the spectrum, which begins approximately half an atomic lifetime after excitation, if the laser field is strong enough. Analytic expressions for the spectra are given of arbitrary laser field strength, atomic lifetime, laser-atom detuning, and the bandwidth of the spectrometer used to analyse the spectrum. Selected graphs are included to illustrate various time-dependent features of the spectrum. The influence on the transient spectrum of three different states of atomic excitation prior to laser irradiation and the effect on the spectrum of irradiation by a phase-noisy laser are also considered. Comparison of the transient spectra from atoms initially prepared in ' pi /2' and '3 pi /2' states show clearly that phase relationships between the irradiating field and the emitting dipole are important even in fluorescence.