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Journal of Physics B Atomic and Molecular Physics

Optical resonances in a strong modulated laser beam

P. Thomann

Published Mar 28, 1980• 43 citations
Publisher

Abstract

The fluorescent intensity of two-level atoms irradiated by a near-resonant amplitude-modulated light wave is calculated in the Bloch model. The analogy with magnetic resonance in a strong oscillating field making an arbitrary angle with the static field is pointed out. Experimental evidence of the predicted parametric and multiple quantum resonances has been obtained with an atomic beam of sodium. Optical pumping was used to prepare the sodium atoms as two-level systems.

DOI
10.1088/0022-3700/13/6/017

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The fluorescent intensity of two-level atoms irradiated by a near-resonant amplitude-modulated light wave is calculated in the Bloch model. The analogy with magnetic resonance in a strong oscillating field making an arbitrary angle with the static field is pointed out. Experimental evidence of the predicted parametric and multiple quantum resonances has been obtained with an atomic beam of sodium. Optical pumping was used to prepare the sodium atoms as two-level systems.
The resonance behavior of magnetic and optical two-level systems under the influence of strong modulated fields is studied in detail by solving the Bloch equations in the limit of vanishing damping, namely, in terms of matrix continued fractions. Thus both analytical and numerical results are obtained for the positions of the various multiple quantum resonances in the time-averaged as well as modulated interaction components. Specifically, the role of the orientation of the optical pump beam in magnetic-resonance configurations is investigated, and it is shown that there are several classes of resonances for which the behavior of the system is independent of the orientation of the pump beam. These are the geometries in which the static and oscillating magnetic fields are either orthogonal or parallel, the geometries leading to Haroche-like resonances (which, however, play a special role in modulated interaction components also), and a previously unknown class, labeled saddle-point resonances. However, other than for these special classes, the behavior of the system depends generally on the orientation of the optical pump beam, unlike as implied in some previous work on this problem. As in the recently studied case of a fully amplitude-modulated optical interaction [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], it is found that the resonances in modulated interaction components are generally doubly branched, with one branch duplicating the resonances found in the time-averaged component. A new feature found for not-fully-amplitude-modulated and phase-modulated, off-resonance optical excitation (or magnetic resonance with nonparallel or nonorthogonal static and oscillating magnetic fields) is the occurrence of an extra type of resonance in modulated components of the interaction that cannot, like all other resonances of the system, be classified as power-shifted multiple quantum transitions.
The interaction of a strong bichromatic field with a two-level atom has been the subject of numerous experimental and theoretical investigations. We performed an experimental study of the Interaction of an intense 100% amplitude-modulated (AM) field with an ensemble of homogeneously broadened two-level atoms. An optically pumped sodium atomic beam is used as the atomic medium. The field is created by interfering two intense frequency-stabilized laser fields. The frequency of one field is held fixed while another field of equal amplitude is scanned in frequency. The beat frequency produced by interfering the two laser fields is equal to twice the modulation frequency of a 100% AM field. We monitor the time-averaged fluorescent intensity of the atoms as the frequency separation between the two fields is varied. A similar experiment was done in the past in the rf regime.1 For the first time, we report the observation of multiple, well-resolved resonances in the absorption spectrum of the field in the optical regime. We present data and theory for several values of detuning between the fixed field and atomic resonance. The experimental results are in good agreement with theory.
The parametric resonances and the quasi-level structure of an atom strongly driven by a near-resonant amplitude-modulated optical field are studied theoretically. An approximate analytical solution of the density-matrix equations of motion is obtained for two-level and three-level atoms. Based on this solution the quasi-level shifts are analyzed, and the conditions for the quasi-levels to cross each other are derived. Expressions are given for the probe-wave absorption/gain spectrum near the parametric resonance and far from it. It is pointed out that the parametric resonances appear when the pumping field sidebands are tuned to resonance with some transitions among the quasi-levels.
We present a detailed theoretical treatment of the response of a two-level atom to a fully-amplitude-modulated, narrow-band optical field. Specifically, we calculate the resonance behavior of modulated fluorescence and susceptibility components from the scalar continued-fraction solution of the optical Bloch equations. In the limit of vanishing damping the resonances are generally doubly branched: One set of branches reproduces the resonances of the time-averaged fluorescence, while the second set is different for each harmonic component. However, each branch is uniquely associated with an odd multiple quantum resonance. In analogy with magnetic resonance work, we derive analytical expressions for the generalized Bloch-Siegert shifts of the additional resonances. We discuss also the possibility of experimental verification of the theory.