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Journal of Physics B Atomic and Molecular Physics

Time-dependent optical Autler-Townes theory using finite bandwidth lasers

Kariman I. Osman, S. Swain

Published Jun 28, 1980• 31 citations
Publisher

Abstract

Time-dependent spectra are calculated for the optical Autler-Townes effect in a three-level system without Doppler broadening and in the probe field approximation. Analytic expressions are also given for the steady-state spectra taking account of the finite laser linewidths, which are assumed to be due to phase diffusion. Comparison is made with time-dependent spectra in the related phenomenon of resonance fluorescence, and the differences pointed out. The effects of laser linewidths on the amplitude of the spectra are also discussed, and found to be marked. The method used in the calculations is that of generalised multiphoton rate equations.

DOI
10.1088/0022-3700/13/12/016

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Time-dependent aspects of the Autler-Townes effect in a four-level system

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Time-dependent optical Autler-Townes spectra are calculated for a four-level system in which the ground state is a doublet with frequency separation much larger than any of the Rabi frequencies. The finite linewidths of the lasers are taken into account in the phase-diffusion model. Optical-pumping effects cause a transfer of population with a resulting significant change in the spectra with time. Numerically evaluated spectra are presented, and it is found that the nature of the asymmetry can change drastically with time.

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Some features of the optical Autler-Townes effect as observed in Doppler-broadened three-level systems, including the physical significance of the observed line splitting, the conditions for the observation of the doublet, the doublet separation and the detuning effects, are discussed in this paper. A graphical illustration of the phenomenon, based on a search for on-resonance velocity groups, is proposed which allows a complete qualitative discussion of the effect and shows that the observed doublet is not really a splitting of the resonance as for the atom at rest but rather corresponds to a frequency hole where the laser probe does not see any resonant velocity group. The method is applied to real three-level systems of neon as typical cases. A semi-classical density-matrix calculation is performed numerically and definitely confirms the results of the qualitative graphical discussion ; furthermore it shows that, for many experimental situations, the first order approximation is inadequate. The observation of the Autler-Townes doublet in a new experiment using two dye lasers is reported. The experimental results and that of one of our previous experiments are compared with the theoretical predictions ; the agreement is quite satisfactory.

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Effect of Doppler broadening on Autler-Townes splitting in the molecular cascade excitation scheme

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A dressed-state rate-equation model is used to describe the Autler-Townes effect that is produced by a resonant 100% amplitude-modulated field driving a two-level resonance. The purpose of using this model is to give an intuitive interpretation of the rather complex absorption spectra that are produced when a weak probe field couples this strongly driven transition to a third atomic state. We obtain analytic expressions for the positions, strengths, and widths of the components of the absorption spectra, which are in excellent agreement with experimentally obtained spectra presented in the accompanying paper [S. Papademetriou, following paper, Phys. Rev. A 53, 997 (1996)]. \textcopyright{} 1996 The American Physical Society.

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This paper presents a theory of lineshapes for molecular Optical-Optical Double Resonance (DR) Spectroscopy with arbitrary strength for both pump and probe fields using the steady-state solutions for the 3-level density matrix. When Doppler broadening can be neglected, the results are analytical, and the probe spectrum is a pair of Lorentzian lines that display Autler-Townes splitting, each with an angular frequency half-width half maximum equal to the relaxation rates, which are assumed to be equal. When Doppler broadening is introduced, one must resort to numerical integration except for the limit of weak pump and probe fields. When the Doppler width is assumed to be much larger than the pump and probe Rabi frequencies and the probe frequency is higher than that of the pump, the calculated DR lineshapes are found to be Lorentzian with a strong pump field limit width that is proportional to the pump Rabi frequency, which is commonly known as power broadening. However, the width does not equal that Rabi frequency and is different for co- and counter-propagating pump and probe fields. Furthermore, that broadening is largely inhomogeneous, despite the Lorentzian shape. The saturation power is found to be about 4 times higher than for the bare probe transition with the same relaxation rate, dramatically lower than that expected if the width is interpreted as homogeneous.

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Autler-Townes effect for an atom in a 100% amplitude-modulated laser field. II. Experimental results

Stephanos Papademetriou, Michael F. Van Leeuwen, Carlos R. Stroud

We report the observation of the Autler-Townes absorption spectrum of a two-level atom in a 100% amplitude-modulated optical field. Two frequency-stabilized dye lasers interact with a three-level atomic cascade system. One of the two lasers is used to create the bichromatic field that saturates the lower transition, while the second one is tuned in the frequency between the second and third levels to probe the absorption line shape. We investigate the dependence of the spectrum on the detuning between the average frequency of the bichromatic field and the lower atomic resonance. In order to study the effects of saturation, for every value of the detuning we take a series of data for different intensity levels of the bichromatic field. There is very good agreement between theory and experiment and profound differences from the conventional Autler-Townes results with a monochromatic pump field. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Feb 1, 1996•42 citations
Time-dependent spectra are calculated for the optical Autler-Townes effect in a three-level system without Doppler broadening and in the probe field approximation. Analytic expressions are also given for the steady-state spectra taking account of the finite laser linewidths, which are assumed to be due to phase diffusion. Comparison is made with time-dependent spectra in the related phenomenon of resonance fluorescence, and the differences pointed out. The effects of laser linewidths on the amplitude of the spectra are also discussed, and found to be marked. The method used in the calculations is that of generalised multiphoton rate equations.
Time-dependent optical Autler-Townes spectra are calculated for a four-level system in which the ground state is a doublet with frequency separation much larger than any of the Rabi frequencies. The finite linewidths of the lasers are taken into account in the phase-diffusion model. Optical-pumping effects cause a transfer of population with a resulting significant change in the spectra with time. Numerically evaluated spectra are presented, and it is found that the nature of the asymmetry can change drastically with time.
Some features of the optical Autler-Townes effect as observed in Doppler-broadened three-level systems, including the physical significance of the observed line splitting, the conditions for the observation of the doublet, the doublet separation and the detuning effects, are discussed in this paper. A graphical illustration of the phenomenon, based on a search for on-resonance velocity groups, is proposed which allows a complete qualitative discussion of the effect and shows that the observed doublet is not really a splitting of the resonance as for the atom at rest but rather corresponds to a frequency hole where the laser probe does not see any resonant velocity group. The method is applied to real three-level systems of neon as typical cases. A semi-classical density-matrix calculation is performed numerically and definitely confirms the results of the qualitative graphical discussion ; furthermore it shows that, for many experimental situations, the first order approximation is inadequate. The observation of the Autler-Townes doublet in a new experiment using two dye lasers is reported. The experimental results and that of one of our previous experiments are compared with the theoretical predictions ; the agreement is quite satisfactory.
Theoretical analysis of the Autler-Townes splitting pattern in a three-level cascade excitation of a Doppler-broadened sample reveals that the observed Autler-Townes splitting is not only a function of the coupling-laser Rabi frequency, as in the homogeneously broadened case, but can also strongly depend on the wavenumber ratio of the coupling and probe lasers. Utilizing a steady-state density matrix formalism, we derive exact expressions for the populations of the intermediate and upper levels for a homogeneously broadened system. In the limit of a weak probe field, analytical expressions for Doppler-broadened excitation spectra from the intermediate and upper levels are derived. Using these expressions, we investigate the critical role of Doppler broadening on the observation of Autler-Townes splitting and its asymptotic behavior as a function of the coupling Rabi frequency for counterpropagating and copropagating configurations for different wavenumber ratios of the lasers.
A dressed-state rate-equation model is used to describe the Autler-Townes effect that is produced by a resonant 100% amplitude-modulated field driving a two-level resonance. The purpose of using this model is to give an intuitive interpretation of the rather complex absorption spectra that are produced when a weak probe field couples this strongly driven transition to a third atomic state. We obtain analytic expressions for the positions, strengths, and widths of the components of the absorption spectra, which are in excellent agreement with experimentally obtained spectra presented in the accompanying paper [S. Papademetriou, following paper, Phys. Rev. A 53, 997 (1996)]. \textcopyright{} 1996 The American Physical Society.
This paper presents a theory of lineshapes for molecular Optical-Optical Double Resonance (DR) Spectroscopy with arbitrary strength for both pump and probe fields using the steady-state solutions for the 3-level density matrix. When Doppler broadening can be neglected, the results are analytical, and the probe spectrum is a pair of Lorentzian lines that display Autler-Townes splitting, each with an angular frequency half-width half maximum equal to the relaxation rates, which are assumed to be equal. When Doppler broadening is introduced, one must resort to numerical integration except for the limit of weak pump and probe fields. When the Doppler width is assumed to be much larger than the pump and probe Rabi frequencies and the probe frequency is higher than that of the pump, the calculated DR lineshapes are found to be Lorentzian with a strong pump field limit width that is proportional to the pump Rabi frequency, which is commonly known as power broadening. However, the width does not equal that Rabi frequency and is different for co- and counter-propagating pump and probe fields. Furthermore, that broadening is largely inhomogeneous, despite the Lorentzian shape. The saturation power is found to be about 4 times higher than for the bare probe transition with the same relaxation rate, dramatically lower than that expected if the width is interpreted as homogeneous.
We report the observation of the Autler-Townes absorption spectrum of a two-level atom in a 100% amplitude-modulated optical field. Two frequency-stabilized dye lasers interact with a three-level atomic cascade system. One of the two lasers is used to create the bichromatic field that saturates the lower transition, while the second one is tuned in the frequency between the second and third levels to probe the absorption line shape. We investigate the dependence of the spectrum on the detuning between the average frequency of the bichromatic field and the lower atomic resonance. In order to study the effects of saturation, for every value of the detuning we take a series of data for different intensity levels of the bichromatic field. There is very good agreement between theory and experiment and profound differences from the conventional Autler-Townes results with a monochromatic pump field. \textcopyright{} 1996 The American Physical Society.