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Journal of Physics B Atomic and Molecular Physics

Theoretical analysis of the phase shift measurement of lifetimes using monochromatic light

L Armstrong, S. Feneuille

Published Mar 11, 1975• 36 citations
Publisher

Abstract

It is shown that, if one uses an essentially monochromatic but weakly modulated light source to excite atoms or molecules in a resonant way, the phase shift of the scattered light is strongly dependent on the strength of the excitation. However, for low values of the excitation strength, this dependence disappears but a result which differs by a factor of two from the result obtained for broad-band light excitation is found. In addition, the strength of the modulated component of the scattered light displays a resonant behaviour in the modulation frequency, this response being directly related to the well-known Autler-Townes effect.

DOI
10.1088/0022-3700/8/4/013

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The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.

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We have investigated the interaction between bichromatic optical fields and atomic transitions. We have considered both the interaction of a saturating bichromatic field in the form of a 100% amplitude-modulated field resonantly interacting with a single atomic transition as well as the interaction of a pair of 100% amplitude-modulated fields with two coupled atomic transitions. In our studies of a single atomic transition resonantly excited by a 100% amplitude-modulated field we have used a fully quantum-electrodynamical analysis to model the Autler-Townes effect induced by a bichromatic optical field. We find that the effect induced by a bichromatic field is markedly different from the effect produced by a monochromatic exciting field. We have derived analytic expressions for the bichromatic Autler-Townes absorption spectrum. The absorption spectrum consists of equally spaced lines spaced by the modulation frequency. The linewidths of neighboring lines alternate as functions of the field strength. Experimentally, we observed this spectrum for both resonant and detuned 100% amplitude-modulated driving fields by monitoring the absorption of a weak monochromatic field as it was tuned about the resonance frequency of the 3²P₃/₂(F = 3, mF = 3) ↔ 4²D₅/₂(F = 4, mF = 4) transition while driving the 3²S₁/₂(F = 2, mF = 2) ↔ 3²P₃/₂(F = 3, mF = 3) transition with a saturating 100% amplitude-modulated field. We found excellent agreement between our predicted and measured spectra. We then investigated the resonant interaction between a pair of 100% amplitude-modulated fields and two atomic transitions sharing a common atomic level. We considered both a three-level atomic cascade system and a three-level atomic lambda system. We examined the effect that the relative phase between the two modulations has on the rate at which the modulated fields are absorbed. We find that the saturated time-averaged field absorption exhibits parametric resonances in both the cascade and lambda systems. The time-averaged absorption is strongly dependent upon the relative phase of modulation between the two fields and for certain phase differences the time-averaged absorption can be enhanced over the maximum saturated absorption experienced by cw fields of the same time-averaged intensities. We also find that the stationary atomic response exhibits periodic oscillations and for the cascade system periodic two-photon inversions of up to 40% can be achieved. We further find dark absorption resonances as a function of phase in the lambda system. We analyze the results from the point of view of semi-classical adiabatic dressed states.

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Monitoring quantum transitions in a three-level atom

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In a recent publication1 the question of the possibility of observing directly the quantum jumps associated with the excitation and deexcitation of an atomic electron in a three-level transition was considered. While the analysis of Ref. 1 reveals the manner in which the fluorescence from a strong transition of a lifetime T1 is modulated by the absorption and emission processes of a weak transition of lifetime T2 (T1 ≪ T2), it was restricted to the case of incoherent excitation of the two transitions. The purpose of the present work is to reconsider this problem for monochromatic excitation in which a variety of coherent effects come into play. The analysis proceeds in a straightforward fashion in the Heisenberg representation to yield expressions for field and atomic correlation functions representing probabilities for the detection of successive photons from the same transition as well as for cross correlations of emission probabilities. In the limit of T1 ≪ T2, a coarse graining of time with respect to the strong transition produces expressions analogous to those presented in Ref. 1. The roles of Autler-Townes splitting, frequency detuning, and saturation of the weak transition are discussed.

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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
It is shown that, if one uses an essentially monochromatic but weakly modulated light source to excite atoms or molecules in a resonant way, the phase shift of the scattered light is strongly dependent on the strength of the excitation. However, for low values of the excitation strength, this dependence disappears but a result which differs by a factor of two from the result obtained for broad-band light excitation is found. In addition, the strength of the modulated component of the scattered light displays a resonant behaviour in the modulation frequency, this response being directly related to the well-known Autler-Townes effect.
The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.
The lifetime of atoms and molecules can be measured by using modulated resonant single-mode laser field. A theoretical mode for this method is presented. It is shown that the laser induced fluorescence, a resonance flourescence is modulated at the same frequency, but phase shift from the exciting laser. The phase shift is mainly due to three processes (1) coherent excitation process characterized by transverse relaxation rate and line width of the laser, (2) population damping process characterized by the decay time of excited levels and other populated levels, (3) collision process characterized by the relaxation time by which the system to be in equilibrium state. The effect of these processes on measurement result is discussed. The Doppler broading is considered also.
We have investigated the interaction between bichromatic optical fields and atomic transitions. We have considered both the interaction of a saturating bichromatic field in the form of a 100% amplitude-modulated field resonantly interacting with a single atomic transition as well as the interaction of a pair of 100% amplitude-modulated fields with two coupled atomic transitions. In our studies of a single atomic transition resonantly excited by a 100% amplitude-modulated field we have used a fully quantum-electrodynamical analysis to model the Autler-Townes effect induced by a bichromatic optical field. We find that the effect induced by a bichromatic field is markedly different from the effect produced by a monochromatic exciting field. We have derived analytic expressions for the bichromatic Autler-Townes absorption spectrum. The absorption spectrum consists of equally spaced lines spaced by the modulation frequency. The linewidths of neighboring lines alternate as functions of the field strength. Experimentally, we observed this spectrum for both resonant and detuned 100% amplitude-modulated driving fields by monitoring the absorption of a weak monochromatic field as it was tuned about the resonance frequency of the 3²P₃/₂(F = 3, mF = 3) ↔ 4²D₅/₂(F = 4, mF = 4) transition while driving the 3²S₁/₂(F = 2, mF = 2) ↔ 3²P₃/₂(F = 3, mF = 3) transition with a saturating 100% amplitude-modulated field. We found excellent agreement between our predicted and measured spectra. We then investigated the resonant interaction between a pair of 100% amplitude-modulated fields and two atomic transitions sharing a common atomic level. We considered both a three-level atomic cascade system and a three-level atomic lambda system. We examined the effect that the relative phase between the two modulations has on the rate at which the modulated fields are absorbed. We find that the saturated time-averaged field absorption exhibits parametric resonances in both the cascade and lambda systems. The time-averaged absorption is strongly dependent upon the relative phase of modulation between the two fields and for certain phase differences the time-averaged absorption can be enhanced over the maximum saturated absorption experienced by cw fields of the same time-averaged intensities. We also find that the stationary atomic response exhibits periodic oscillations and for the cascade system periodic two-photon inversions of up to 40% can be achieved. We further find dark absorption resonances as a function of phase in the lambda system. We analyze the results from the point of view of semi-classical adiabatic dressed states.
In a recent publication1 the question of the possibility of observing directly the quantum jumps associated with the excitation and deexcitation of an atomic electron in a three-level transition was considered. While the analysis of Ref. 1 reveals the manner in which the fluorescence from a strong transition of a lifetime T1 is modulated by the absorption and emission processes of a weak transition of lifetime T2 (T1 ≪ T2), it was restricted to the case of incoherent excitation of the two transitions. The purpose of the present work is to reconsider this problem for monochromatic excitation in which a variety of coherent effects come into play. The analysis proceeds in a straightforward fashion in the Heisenberg representation to yield expressions for field and atomic correlation functions representing probabilities for the detection of successive photons from the same transition as well as for cross correlations of emission probabilities. In the limit of T1 ≪ T2, a coarse graining of time with respect to the strong transition produces expressions analogous to those presented in Ref. 1. The roles of Autler-Townes splitting, frequency detuning, and saturation of the weak transition are discussed.
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.