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Latin America Optics and Photonics Conference

Autler-Townes Splitting in a Doppler-Broadened Four-Wave Mixing: Theoretical Results

Marco Polo Moreno de Souza, A. A. C. de Almeida, S. S. Vianna

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We present theoretical results on the forward four-wave mixing in Doppler-broadened media. Our results reveal an Autler-Townes splitting in the nonlinear signal re-gardless of which input field, strong or weak, is scanned.
DOI
10.1364/laop.2022.tu4a.8

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In nonlinear atomic gaseous media the interference between independent macroscopic polarizations of different ensembles within the atomic velocity distribution can lead to anomalous behavior of the multiwave mixing spectra. For phase-conjugate six-wave mixing (SWM) in a Doppler-broadened N-type four-level system, it is found that the SWM spectrum can be either Doppler-free or very broad, depending on the directions of the incident beams and the ratios between the magnitudes of the wave vectors. This polarization interference can be controlled by the strong coupling field which, on the other hand, can induce Autler-Townes (AT) splitting when the SWM spectrum is Doppler-free. This technique may find special applications as an improved form of AT spectroscopy with higher resolution.
This work presents a theoretical analysis of the Autler-Townes splitting pattern in the four-wave mixing signal generated in a three-level cascade Doppler-broadened system. We employ the density matrix formalism to write the Bloch equations and solve them numerically. The solutions allow us to compare the response of the upper level population and the generated signal coherence for homogeneously and nonhomogeneously broadened systems. Our results reveal an AC Stark shift in the nonlinear signal when the frequency of the strong or weak laser beam is scanned, in contrast to what is observed in the fluorescence. Furthermore, we present experimental data for the four-wave mixing signal in a hot rubidium vapor for the copropagating configuration of the laser beams that drive the $5S\ensuremath{\rightarrow}5P\ensuremath{\rightarrow}5D$ transition. The behavior of the AC Stark displacement and signal amplitude as a function of laser power indicates a good agreement between the model and the experimental results.
The effects of Doppler broadening on Autler-Townes (AT) splitting in six-wave mixing (SWM) are investigated by the dressed-state model. We analyze the velocities at which the atoms are in resonance with the dressed states through Doppler frequency shifting and find that, depending on the wave-number ratio, there may be two resonant velocities which can originate from resonance with one of the dressed states or from resonance with two different dressed states. Based on this model, we discuss a novel type of AT doublet in the SWM spectrum, where macroscopic effects play an important role. Specifically, the existence of resonant peaks requires polarization interference between atoms of different velocities in addition to a change in the number of resonant atoms involved. Our model can also be employed to analyze electromagnetically induced transparency resonance and other types of Doppler-free high-resolution AT spectroscopy.
Theoretical analysis of the Autler-Townes splitting pattern in a three-level cascade excitation of a Doppler-broadened sample reveals that the observed Autler-Townes splitting is not only a function of the coupling-laser Rabi frequency, as in the homogeneously broadened case, but can also strongly depend on the wavenumber ratio of the coupling and probe lasers. Utilizing a steady-state density matrix formalism, we derive exact expressions for the populations of the intermediate and upper levels for a homogeneously broadened system. In the limit of a weak probe field, analytical expressions for Doppler-broadened excitation spectra from the intermediate and upper levels are derived. Using these expressions, we investigate the critical role of Doppler broadening on the observation of Autler-Townes splitting and its asymptotic behavior as a function of the coupling Rabi frequency for counterpropagating and copropagating configurations for different wavenumber ratios of the lasers.
We demonstrate Autler-Townes (AT) splitting of four-wave mixing in an electromagnetically induced transparency window, which results from the destructive interference between a three-photon process and a five-photon process. The primary and secondary AT splittings are achieved via induced atomic coherence in a four-level Y-type atomic system. Theoretical calculations fit well with the experimentally measured results. Such controlled multichannel splitting of nonlinear optical signals can have potential applications in optical communication and quantum information processing.
Nowadays degenerate four wave mixing (DFWM) with forward geometry (FDFWM) has found increasing usage, for example, in the gas phase detection. In the fields of theoretical development of DFWM, most of the studies have been concentrated on the understanding of phase-conjugated DFWM. However, few theories have dealt with FDFWM. These models calculated the signal directly from the off-diagonal element of the density matrix by assuming optically thin medium. In the paper we obtain a theoretical model for FDFWM in Doppler broadened two-level absorbers including propagation effect and discuss the Doppler effect on the signal intensity and lineshape. Assuming that probe and signal field amplitudes are small compared with those of the pump fields and pump field amplitudes are constant in the interaction volume, we obtain the following coupled equations from the Maxwell equation using the slowly varying envelope approximation and the paraxial approximation.