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

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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 Ω 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 Ω, 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 Ω 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 2π/Ω) 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.