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arXiv:2412.16767 · Physical Review A

Fundamental and second-subharmonic Autler-Townes splitting in classical systems

Ahmed A. Barakat, Avishek Chowdhury, Anh Tuan Le, Eva Maria Weig

Published Mar 12, 2026• 1 citation
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Abstract

The dynamic Stark effect and Autler-Townes splitting (ATS) are hallmarks of driven two-level systems. We establish a direct correspondence between these quantum phenomena and the parametric normal mode splitting in coupled classical oscillators. This identifies a second-subharmonic ATS under a two-tone parametric drive. We find excellent agreement between the theory and the vibrations of a nanomechanical two-mode system, capturing both the fundamental and second-subharmonic ATS, and allowing quantitative extraction of the modal coupling irrespective of the degree of modal hybridization.

DOI
10.1103/m4m8-fkrr

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The dynamic Stark effect and Autler-Townes splitting (ATS) are hallmarks of driven two-level systems. We establish a direct correspondence between these quantum phenomena and the parametric normal mode splitting in coupled classical oscillators. This identifies a second-subharmonic ATS under a two-tone parametric drive. We find excellent agreement between the theory and the vibrations of a nanomechanical two-mode system, capturing both the fundamental and second-subharmonic ATS, and allowing quantitative extraction of the modal coupling irrespective of the degree of modal hybridization.
In this thesis the effect of Autler-Townes splitting is revisited and the dynamics of a 2- and 3-level quantum systems, exhibiting this effect, is studied. This effect is a special case of the Stark effect, where the spectral lines of an atom are modified due to an external driving electromagnetic field. Two different articles, describing the Autler-Townes splitting, are studied, where one solves the time-dependent equations of the semi-classical model and the other studies the time-independent Hamiltonian for the system, which is described completely quantum mechanically. In our work, we proceed by employing the semi-classical model but transforming the Hamiltonian into a time-independent form, which makes the model easier to study. Subsequently, we also study the atom as an open quantum system and investigate the effect that the decay of an atom to a vacuum field has on the Autler-Townes splitting. Throughout the thesis, we present the density matrices, and hence the time-evolution of the dynamics, in the Bloch-vector description in an attempt to understand the geometrical nature of the dynamics and, in effect, the Autler-Townes phenomenon.
Summary form only given.It is well known that a strongly driven transition exhibits a doublet splitting when probed by a weak field, commonly known as AC Stark splitting. It can be observed either by probing the driven two-level itself (Mollow-type spectrum) or via a third level (Autler-Townes-type spectrum). These two type splittings can have very different characteristics, particularly when driven resonantly. The absorptive Mollow spectrum consists of two dispersion-like features, whereas for the Autler-Townes spectrum there is a simple doublet splitting. In this paper we report the observation of both Mollow and Autler-Townes spectrum simultaneously by applying two strong driving fields in a three-level configuration.
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two phenomena that can affect the transmission of a probe field in the presence of a stronger field, both yielding transparency in the absorption profile. Being able to discriminate these two similar but distinct phenomena is of vital importance. Here we propose a scheme to describe the EIT and ATS phenomena in a plasmonic system. The proposed system consists of one radiative resonator and one subradiant resonator in metal-insulator-metal waveguide, and the transition is observed from the ATS model to the EIT model through three qualitative regions as the coupling strength decreases. In addition, we apply the method proposed by Anisimov to the induced transparency spectrum in our model, and numerically discerning EIT from ATS based on the Akaike's information criterion in a clear way.
We present an experimental study of Autler-Townes splitting of non-linear selective reflection spectroscopy in a A-type driven three-level system. The sub-Doppler reflection spectroscopy is observed and the Autler-Townes splitting is measured as functions of the different coupling laser intensity and detuning. The coherent drive splits the excited state into two dressed states and an Autler-Townes splitting emerges in the probe reflection. The experimental results are in good agreement with theoretical fit.
The atom-light interaction in a three-level system has shown significant physical phenomena, such as electromagnetically induced transparency and Autler{Townes splitting (ATS), for broad applications in classical and quantum information techniques. Here, we optimally demonstrated the ATS with a quantum state manipulation method. The ATS in the dephasing-dominated diamond NV center system was successfully recovered by coherent microwave control, which cannot be observed with traditional method. The dynamical process of ATS was investigated in detail, revealing a nontrivial quantum interference with geometric phase modulations. Based on the quantum interference, the signal of the optimal ATS is twice as intense as those with traditional observation method.