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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Theory of frequency-modulation spectroscopy of coherent dark resonances

Julia Vladimirova, B. A. Grishanin, Victor N. Zadkov, V. Biancalana, G. Bevilacqua, Evelina Breschi, Yordanka V. Dancheva, L. Moi

Published Mar 1, 2006• 0 citations
Publisher

Abstract

Theoretical model for the frequency-modulation spectroscopy of dark resonances is discussed in detail on example of a three-level quantum system in A-configuration driven by resonant laser field(s) with and without frequency modulation using two simulation techniques-the density matrix and quantum trajectories analysis.
DOI
10.1117/12.677920

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The interaction of a three-level atom in the A configuration with a frequency-modulated (FM) field is analyzed theoretically for the first time. The two-frequency model for solving the problem of frequency modulation spectroscopy of coherent dark resonances is described and analyzed for a three-level A system. The effectiveness of the two-frequency model is demonstrated by comparing the results obtained using this model with the results of solving the exact problem of interaction of a A system with an FM field, which can be solved by the density matrix method. It is shown that the simple two-frequency model corresponds to the exact solution and is in qualitative agreement with experimental data.
The results of frequency-modulation (FM) spectroscopy of coherent dark resonances from the Zeeman sublevels of the transition F=2 ↔ F=1 of D1 line in absorption of 87Rb atoms are presented and discussed in detail. By contrast with the conventional spectroscopy of coherent dark resonances employing two laser beams, relative frequency of which can be varied, these data has been obtained with the help of a single frequency-modulated laser field. Variation of the modulation frequency plays then similar role with variation the relative frequency in conventional spectroscopy. Experimental data are fit to the theoretical calculations, which are based on the theory of FM spectroscopy of coherent dark resonances recently developed by us. Feasibility of using such experimental technique for accurate measurements of magnetic fields is also discussed.
Theoretical study and computer modeling results of the spectra of coherent dark resonances resulted from excitation of Zeeman sublevels of the Fg=2→Fe=1 transition of the D1 line in 87Rb atoms by a frequency-modulated laser field are presented and discussed in detail. The influence of the nonlinear Zeeman effect on the structure of the coherent dark resonances is observed. It is shown that calculated for different values of the magnetic field spectra are in a good agreement with the experimental data.
Abstract We develop a theory of modulation response of the coherent population trapping (CPT) resonance. We consider the simplest three-level atom, but take into account the polychromatic spectrum of the pumping and probing light produced by pure FM modulation of single frequency field. The analysis based on the density matrix equations rigorously includes the most important for applications range of modulation parameters where modulation frequency and deviation are comparable with or greater than the CPT linewidth, so the response of the atomic medium is not adiabatic. Some theoretical results, in particular the possibility of using a quadrature response to modulation to suppress light shift, are compared with the experiment carried out with a diode laser (VCSEL) and 87 Rb atoms.
Frequency-modulated spectra of coherently driven quantum systems are calculated using the density-matrix formulation. The modulated spectra are shown to be related to the two-time correlation functions of the polarization operators of the system. In the limit of modulation frequencies small compared to the width of the spectral features under study, the in-phase signal (quadrature signal) is shown to be related to the derivative of absorption (second derivative of dispersion) in the absence of any modulation. Modulation spectra in strong fields are calculated explicitly for two-level systems; such spectra are shown to yield useful information concerning light shifts and Rabi splittings. The influence of laser temporal fluctuations on such modulation spectra is also discussed.