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Physical Review A

Effect of Doppler broadening on Autler-Townes splitting in the molecular cascade excitation scheme

Ergin H. Ahmed, A. M. Lyyra

Published Nov 9, 2007• 21 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.76.053407

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We have investigated the effects of inhomogeneous Doppler line broadening on the Autler-Townes (AT) splitting in a three-level open molecular cascade system. For moderate Rabi frequencies in the range of $300--600\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, the fluorescence line shape from the uppermost level \ensuremath{\mid}3⟩ in this system depends strongly on the wave-number ratio of the two laser fields. However, the fluorescence spectrum of the intermediate level \ensuremath{\mid}2⟩ appears as expected. We provide a description of the conditions for optimally resolved AT splitting in terms of the ratio of the probe and coupling laser wave numbers, and the laser propagation geometry based on our theoretical analysis of the Doppler integral. The low threshold Rabi frequency region for Autler-Townes splitting is important for high-resolution Autler-Townes spectroscopy since the laser E-field amplitudes are modest in continuous-wave laser experiments.

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Some features of the optical Autler-Townes effect as observed in Doppler-broadened three-level systems, including the physical significance of the observed line splitting, the conditions for the observation of the doublet, the doublet separation and the detuning effects, are discussed in this paper. A graphical illustration of the phenomenon, based on a search for on-resonance velocity groups, is proposed which allows a complete qualitative discussion of the effect and shows that the observed doublet is not really a splitting of the resonance as for the atom at rest but rather corresponds to a frequency hole where the laser probe does not see any resonant velocity group. The method is applied to real three-level systems of neon as typical cases. A semi-classical density-matrix calculation is performed numerically and definitely confirms the results of the qualitative graphical discussion ; furthermore it shows that, for many experimental situations, the first order approximation is inadequate. The observation of the Autler-Townes doublet in a new experiment using two dye lasers is reported. The experimental results and that of one of our previous experiments are compared with the theoretical predictions ; the agreement is quite satisfactory.

Journal de physique•Jan 1, 1978•53 citations
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 have investigated the effects of inhomogeneous Doppler line broadening on the Autler-Townes (AT) splitting in a three-level open molecular cascade system. For moderate Rabi frequencies in the range of 300−−600MHz300--600\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}300−−600MHz, the fluorescence line shape from the uppermost level \ensuremath{\mid}3⟩ in this system depends strongly on the wave-number ratio of the two laser fields. However, the fluorescence spectrum of the intermediate level \ensuremath{\mid}2⟩ appears as expected. We provide a description of the conditions for optimally resolved AT splitting in terms of the ratio of the probe and coupling laser wave numbers, and the laser propagation geometry based on our theoretical analysis of the Doppler integral. The low threshold Rabi frequency region for Autler-Townes splitting is important for high-resolution Autler-Townes spectroscopy since the laser E-field amplitudes are modest in continuous-wave laser experiments.
We describe in this Letter how inhomogeneous line broadening affects the Autler-Townes (AT) splitting in a three level open molecular cascade system. For moderate Rabi frequencies in the range of 300 to 500 MHz the fluorescence line shape from the uppermost level |3> in this system depends strongly on the frequency ratio of the two laser fields. However, the fluorescence spectrum of the intermediate level |2> appears as expected. We provide a description of the conditions for optimally resolved AT splitting in terms of the probe laser/coupling field frequency ratio and laser propagation geometry based on our theoretical analysis of the Doppler integral. This is important for applications such as molecular angular momentum alignment as well as for the measurement of the transition dipole moment matrix element.
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.
This paper presents a theory of lineshapes for molecular Optical-Optical Double Resonance (DR) Spectroscopy with arbitrary strength for both pump and probe fields using the steady-state solutions for the 3-level density matrix. When Doppler broadening can be neglected, the results are analytical, and the probe spectrum is a pair of Lorentzian lines that display Autler-Townes splitting, each with an angular frequency half-width half maximum equal to the relaxation rates, which are assumed to be equal. When Doppler broadening is introduced, one must resort to numerical integration except for the limit of weak pump and probe fields. When the Doppler width is assumed to be much larger than the pump and probe Rabi frequencies and the probe frequency is higher than that of the pump, the calculated DR lineshapes are found to be Lorentzian with a strong pump field limit width that is proportional to the pump Rabi frequency, which is commonly known as power broadening. However, the width does not equal that Rabi frequency and is different for co- and counter-propagating pump and probe fields. Furthermore, that broadening is largely inhomogeneous, despite the Lorentzian shape. The saturation power is found to be about 4 times higher than for the bare probe transition with the same relaxation rate, dramatically lower than that expected if the width is interpreted as homogeneous.
We demonstrate the three-photon Autler-Townes (AT) spectroscopy in a cold cesium Rydberg four-level atom by detecting the field ionized Rydberg population. The ground state |6S1/2〉, two intermediate states |6P3/2〉 and |7S1/2〉 and Rydberg state |60P3/2〉 form a cascade four-level atomic system. The three-photon AT spectra and AT splittings are characterized by the Rabi frequency Ω852 and Ω1470 and detuning δ852 of the coupling lasers. Due to the interaction of two coupling lasers with the atoms, the AT spectrum has three peaks denoted with the letters A, B and C. Positions of the peaks and relative AT splittings, γAB and γBC, strongly depend on two coupling lasers. The dependence of the AT splitting, γAB and γBC, on the coupling laser detuning, δ852, and Rabi frequency, Ω852 and Ω1470 are investigated. It is found that the AT splitting γAB mainly comes from the first photon coupling, whereas the γBC mainly comes from the second photon coupling with the atom. The three-photon AT spectra and relevant AT splittings are simulated with the four-level density matrix equation and show good agreement with the theoretical simulations considering the spectral line broadening. Our work is of great significance both for further understanding the interaction between the laser and the atom, and for the application of the Rydberg atom based field measurement.
Some features of the optical Autler-Townes effect as observed in Doppler-broadened three-level systems, including the physical significance of the observed line splitting, the conditions for the observation of the doublet, the doublet separation and the detuning effects, are discussed in this paper. A graphical illustration of the phenomenon, based on a search for on-resonance velocity groups, is proposed which allows a complete qualitative discussion of the effect and shows that the observed doublet is not really a splitting of the resonance as for the atom at rest but rather corresponds to a frequency hole where the laser probe does not see any resonant velocity group. The method is applied to real three-level systems of neon as typical cases. A semi-classical density-matrix calculation is performed numerically and definitely confirms the results of the qualitative graphical discussion ; furthermore it shows that, for many experimental situations, the first order approximation is inadequate. The observation of the Autler-Townes doublet in a new experiment using two dye lasers is reported. The experimental results and that of one of our previous experiments are compared with the theoretical predictions ; the agreement is quite satisfactory.