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Physical Review A

Simultaneously forbidden resonances in the Autler-Townes effect with a modulated pump

V. N. Smelyanskiy, R. S. Conti, G. W. Ford

Published Mar 1, 1997• 12 citations
Publisher

Abstract

It was shown recently that systems subject to a strong modulating interaction can exhibit a new property in their response to a probe field. Under certain conditions an infinite number of resonances are simultaneously forbidden [V. N. Smelyanskiy, G. W. Ford, and R. S. Conti, Phys. Rev. A 53, 2598 (1996)]. In the present paper we investigate this effect in the case of a three-state system in which a strong pump field with a periodic frequency modulation \ensuremath{\Omega} couples a pair of excited levels while the complex Autler-Townes spectrum is probed via a weak field that connects one of the coupled states to the ground state. Under certain conditions a half-infinite comb of spectral lines, spaced by \ensuremath{\Omega}, simultaneously disappear from the Autler-Townes spectrum. These lines are positioned above or below a unique edge frequency, which is that of the probe transition in the absence of the strong field. It is shown that the aforementioned effect results from a special factorization property of the corresponding Floquet Hamiltonian that describes the Autler-Townes spectrum. Detailed analysis of this property is presented. In particular, it is found that the subset of the parameter space of the system where the factorization occurs consists of an infinite number of quasiperiodic manifolds. These manifolds exhibit some universal features related to the degeneracy of the dressed states. The line shapes of the probe resonances near the degeneracy points are derived. The intensities of the probe resonances are investigated in the limit of \ensuremath{\Omega} small compared with the modulation depth and the strength of the pump field. In the latter case, effects related to the avoided crossings of the dressed-state levels are considered. The Floquet Hamiltonian that describes the Autler-Townes spectrum in the case considered, effectively corresponds to a special model of a periodically driven system (with period 2\ensuremath{\pi}/\ensuremath{\Omega}) in which an external perturbation has the form of an operator projecting onto a single-quantum state. We generalize this model to the case of an N-level periodically driven system where the simultaneous vanishing of a half-infinite number of the dressed-state Fourier harmonics are analyzed. Possible experimental tests of the effect are suggested.

DOI
10.1103/physreva.55.2186

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It was shown recently that systems subject to a strong modulating interaction can exhibit a new property in their response to a probe field. Under certain conditions an infinite number of resonances are simultaneously forbidden [V. N. Smelyanskiy, G. W. Ford, and R. S. Conti, Phys. Rev. A 53, 2598 (1996)]. In the present paper we investigate this effect in the case of a three-state system in which a strong pump field with a periodic frequency modulation \ensuremath{\Omega} couples a pair of excited levels while the complex Autler-Townes spectrum is probed via a weak field that connects one of the coupled states to the ground state. Under certain conditions a half-infinite comb of spectral lines, spaced by \ensuremath{\Omega}, simultaneously disappear from the Autler-Townes spectrum. These lines are positioned above or below a unique edge frequency, which is that of the probe transition in the absence of the strong field. It is shown that the aforementioned effect results from a special factorization property of the corresponding Floquet Hamiltonian that describes the Autler-Townes spectrum. Detailed analysis of this property is presented. In particular, it is found that the subset of the parameter space of the system where the factorization occurs consists of an infinite number of quasiperiodic manifolds. These manifolds exhibit some universal features related to the degeneracy of the dressed states. The line shapes of the probe resonances near the degeneracy points are derived. The intensities of the probe resonances are investigated in the limit of \ensuremath{\Omega} small compared with the modulation depth and the strength of the pump field. In the latter case, effects related to the avoided crossings of the dressed-state levels are considered. The Floquet Hamiltonian that describes the Autler-Townes spectrum in the case considered, effectively corresponds to a special model of a periodically driven system (with period 2\ensuremath{\pi}/\ensuremath{\Omega}) in which an external perturbation has the form of an operator projecting onto a single-quantum state. We generalize this model to the case of an N-level periodically driven system where the simultaneous vanishing of a half-infinite number of the dressed-state Fourier harmonics are analyzed. Possible experimental tests of the effect are suggested.
A general Floquet approach is used to investigate the nonlinear response of a multilevel quantum system driven by a strong, in general off-resonance, pump field. The response to a weak probe field is studied near the quasienergy interval resonances. A general condition is derived for a phenomenon in which the transition matrix elements for a given pair of Floquet states simultaneously vanish for an infinite number of equally spaced resonances beyond a unique frequency edge. This phenomenon is illustrated with several models involving modulating interactions and possibilities for its observation are analyzed. \textcopyright{} 1996 The American Physical Society.
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.
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.
In this paper we study the nonlinear behavior of an electromagnetically induced transparency (EIT) resonance subject to a coherent driving field. The EIT is associated with a $\ensuremath{\Lambda}$ three-level system where two hyperfine levels within an electronic ground state are coupled to a common excited state level by a coupling field and a probe field. In addition there is an radio-frequency (rf) field driving a hyperfine transition within the ground state. The paper contrasts two different situations. In one case the rf-driven transition shares a common level with the probed transition and in the second case it shares a common level with the coupled transition. In both cases the EIT resonance is split into a doublet and the characteristics of the EIT doublet are determined by the strength and frequency of the rf-driving field. The doublet splitting originates from the rf-field induced dynamic Stark effect and has close analogy with the Autler-Townes effect observed in three-level pump-probe spectroscopy study. The situation changes when the rf field is strong and the two cases are very different. One is analogous to two $\ensuremath{\Lambda}$ three-level systems with EIT resonance associated with each. The other corresponds to a doubly driven three-level system with rf-field-induced electromagnetically induced absorption resonance. The two situations are modeled using numerical solutions of the relevant equation of motion of density matrix. In addition a physical account of their behaviors is given in terms of a dressed state picture.
We study the effects of driving a two-level atom by two intense field modes that have equal frequencies but are otherwise distinguishable; the intensity of one mode is also assumed to be greater than that of the other. We calculate first the dressed states of the system, and then its resonance fluorescence and Autler-Townes absorption spectra. We find that the energy spectrum of the doubly dressed atom consists of a ladder of doublet continua. These continua manifest themselves in the fluorescence spectrum, where they produce continua at the positions of the Mollow sideband frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathrm{L}}$ \ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega} of the strong field, and in the Autler-Townes absorption spectrum, which becomes a two-continuum doublet.