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Physical Review A

Autler-Townes effect for an atom in a 100% amplitude-modulated laser field. I. A dressed-atom approach

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

Published Feb 1, 1996• 31 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.53.990

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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.

•Jan 1, 1998•0 citations

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

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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.

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Strongly driven Stark coupled three-level systems and transitions at the Rabi frequency

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Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.

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Hyperfine interaction in the Autler-Townes effect: The formation of bright, dark, and chameleon states

Teodora Kirova, A. Cinins, Dmitry K. Efimov +6 more

This paper is devoted to clarifying the implications of hyperfine (HF) interaction in the formation of adiabatic (i.e., ``laser-dressed'') states and their expression in the Autler-Townes (AT) spectra. We first use the Morris-Shore model [J. R. Morris and B. W. Shore, Phys. Rev. A 27, 906 (1983)] to illustrate how bright and dark states are formed in a simple reference system where closely spaced energy levels are coupled to a single state with a strong laser field with the respective Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{S}$. We then expand the simulations to realistic hyperfine level systems in Na atoms for a more general case when non-negligible HF interaction can be treated as a perturbation in the total system Hamiltonian. A numerical analysis of the adiabatic states that are formed by coupling of the $3{p}_{3/2}$ and $4{d}_{5/2}$ states by the strong laser field and probed by a weak laser field on the $3{s}_{1/2}\ensuremath{-}3{p}_{3/2}$ transition yielded two important conclusions. Firstly, the perturbation introduced by the HF interaction leads to the observation of what we term ``chameleon'' states---states that change their appearance in the AT spectrum, behaving as bright states at small to moderate ${\mathrm{\ensuremath{\Omega}}}_{S}$, and fading from the spectrum similarly to dark states when ${\mathrm{\ensuremath{\Omega}}}_{S}$ is much larger than the HF splitting of the $3{p}_{3/2}$ state. Secondly, excitation by the probe field from two different HF levels of the ground state allows one to address orthogonal sets of adiabatic states; this enables, with appropriate choice of ${\mathrm{\ensuremath{\Omega}}}_{S}$ and the involved quantum states, a selective excitation of otherwise unresolved hyperfine levels in excited electronic states.

Physical Review A•Oct 26, 2017•11 citations
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.
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.
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.
We study the Autler-Townes absorption spectrum of the upper and intermediate levels of a three-level cascade atom in which the intermediate and ground levels are strongly driven by a laser field as well as weakly coupled by a cavity mode [Phys. Rev. 100, 703 (1955)]. Surprisingly, one of the Autler-Townes peaks may be greatly suppressed or enhanced by tuning the cavity resonant frequency. The larger the Rabi frequency, the more pronounced the cavity-induced suppression or enhancement. The Autler-Townes spectrum carries full information on the cavity-induced modification of the strongly driven levels. A physical interpretation is presented in the dressed-state basis.
The damped and coherently-driven JaynesndashndashndashCummings model
We investigate the influence of a single-mode cavity on the Autler–Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler–Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom–cavity coupling strength g and the cavity damping κ. For an increasing g and/or decreasing κ the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double-dressing' model.
Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.
This paper is devoted to clarifying the implications of hyperfine (HF) interaction in the formation of adiabatic (i.e., ``laser-dressed'') states and their expression in the Autler-Townes (AT) spectra. We first use the Morris-Shore model [J. R. Morris and B. W. Shore, Phys. Rev. A 27, 906 (1983)] to illustrate how bright and dark states are formed in a simple reference system where closely spaced energy levels are coupled to a single state with a strong laser field with the respective Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{S}$. We then expand the simulations to realistic hyperfine level systems in Na atoms for a more general case when non-negligible HF interaction can be treated as a perturbation in the total system Hamiltonian. A numerical analysis of the adiabatic states that are formed by coupling of the 3p3/23{p}_{3/2}3p3/2​ and 4d5/24{d}_{5/2}4d5/2​ states by the strong laser field and probed by a weak laser field on the $3{s}_{1/2}\ensuremath{-}3{p}_{3/2}$ transition yielded two important conclusions. Firstly, the perturbation introduced by the HF interaction leads to the observation of what we term ``chameleon'' states---states that change their appearance in the AT spectrum, behaving as bright states at small to moderate ${\mathrm{\ensuremath{\Omega}}}_{S}$, and fading from the spectrum similarly to dark states when ${\mathrm{\ensuremath{\Omega}}}_{S}$ is much larger than the HF splitting of the 3p3/23{p}_{3/2}3p3/2​ state. Secondly, excitation by the probe field from two different HF levels of the ground state allows one to address orthogonal sets of adiabatic states; this enables, with appropriate choice of ${\mathrm{\ensuremath{\Omega}}}_{S}$ and the involved quantum states, a selective excitation of otherwise unresolved hyperfine levels in excited electronic states.