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Journal of Physics C Solid State Physics

The dynamic Zeeman effect in the two-photon resonance condition

M. Guccione, M. Li Vigni, G. Vetri

Published Apr 20, 1986• 2 citations
Publisher

Abstract

The frequency distribution of the second harmonic radiated by a two-level system in the presence of a two-photon resonant electromagnetic field is investigated. It is shown that the interaction of a permanent dipole with the driving field causes, in the second harmonic spectra, effects analogous to those belonging to the resonance fluorescence. The effects (dynamic Zeeman or Stark effects) are, however, of the second order in the amplitude of the driving field. The results are illustrated by using the vectorial model of Feynman, Vernon and Hellwarth (1957). Numerical results based on realistic parameters of a paramagnetic system are given.

DOI
10.1088/0022-3719/19/11/018

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The frequency distribution of the second harmonic radiated by a two-level system in the presence of a two-photon resonant electromagnetic field is investigated. It is shown that the interaction of a permanent dipole with the driving field causes, in the second harmonic spectra, effects analogous to those belonging to the resonance fluorescence. The effects (dynamic Zeeman or Stark effects) are, however, of the second order in the amplitude of the driving field. The results are illustrated by using the vectorial model of Feynman, Vernon and Hellwarth (1957). Numerical results based on realistic parameters of a paramagnetic system are given.
It is suggested that the combined effect of a resonant magnetic field (dynamic Zeeman effect) and of the fluctuations due to spin-spin and spin-lattice interactions could give rise to inelastic components in the emission spectrum of a paramagnetic system. It is also shown that a similar effect can be expected in the second harmonic emission. It is found that if the Rabi frequency is much larger than the relaxation rates, both the resonant and the second harmonic spectra show the two side lines typical of the atomic resonant fluorescence. The results are illustrated by means of a semiclassical model. Plots of expected spectra as a function of the frequency are given for some realistic parameters of paramagnetic samples.
The theory of coherent radiation emission in two-level quantum systems with permanent dipole moments at the multiphoton resonant excitation by moderately strong laser fields is presented. A simple analytic formula for the expectation value of a dipole moment operator is obtained. The spectrum corresponding to harmonic generation and low-frequency radiation on the generalized Rabi frequency is investigated both analytically and numerically. The effect of dynamic Stark shift on a dipole spectrum under direct multiphoton resonant excitation is considered.
In this thesis, we investigate the effect of the dynamical Stark shift on the quantum electrodynamics of an atom undergoing two-photon transitions, interacting with a quantized radiation field in an ideal cavity. To begin with, we discuss the dynamics of the electromagnetic field and the atom in the presence of the Stark shift. We derive closed expressions for the second-order coherence function, quadrature variances, atomic population inversion and dipole squeezing under the approximation of a large initial photon number and coherent or squeezed field input. We show that for an atom initially in the ground state, the inclusion of Stark shift reduces the field squeezing as well as the antibunching. Both the population inversion and the dipole squeezing exhibit phase sensitivity in the presence of Stark shift and for a particular choice of the relative phase of the two atomic levels "trapping" occurs in a two-level atom and the dipole is modified in such a way that it is permanently squeezed. We then discuss the effect of the stark shift on the emission spectrum of an atom and the cavity field spectrum. The inclusion of Stark shift results in asymmetric vacuum field Rabi splitting. We also study the dynamics of the combined atom-field wave function in the presence of the Stark shift and show that both the electromagnetic field and the atom periodically evolve to pure states which are radically different from those in the absence of the Stark shift. Finally, we study the nondegenerate two-photon Jaynes-Cummings model (NTPJCM) in the presence of the Stark shift and show that the dynamics of the NTPJCM in the presence of Stark shift is qualitatively different from the case of the absence of the Stark shift and radically different from the case of degenerate two-photon JCM in the presence of Stark shift.
The resonance two-photon interaction of the broadband squeezed field (without coherent displacement) with the dipole-forbidden two-level atoms via nonresonant virtual levels is investigated. It is demonstrated that the broadband squeezed field excites coherently the system of radiators (atoms, molecules) that have dipole-forbidden transitions. The two-photon Rabi frequency, in this case, is amplified due to the large number of couples of correlated modes of the broadband squeezed field involved. It should be mentioned that this coherent excitation is not specific for optical allowed dipole transitions. In the high-field limit, the quantum statistics of the photon pairs generated in the process of resonance fluorescence is analysed. As the fluorescence spectrum consists of three bands of the correlated photon pairs we analysed the second-order fluctuations in the central and sideband peaks of the triplet. It is shown that the amplitude-squared squeezing that is presented in the sidebands arises from the interaction of the spontaneously radiated photon pairs with the vacuum of the electromagnetic field.
A formalism is developed to calculate radiative processes, and applied to the shift of resonance frequency due to the radiation field itself. The zeroth approximation gives the Bohr resonance condition, while the next approximation gives a shift proportional to the photon density. The first-order shift is made of two terms: electric and magnetic. They can be interpreted as second-order Stark effect and Zeeman effect due to the oscillating field, respectively. A comparison with experimental data on the Cs atom is made. A good agreement is obtained by choosing the value of parameters suitably. These values of parameters can be checked by a future experiment.