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Physica Scripta

Occurrence of Split Spectra in Doppler-free Two-photon Spectroscopy

Rainer Salomaa

Published Apr 1, 1977• 10 citations
Publisher

Abstract

This paper discusses the origin of splitting of two-photon spectra of three-level cascade configurations having a near resonant intermediate level. A clear distinction between splitting mechanisms in homogeneously and inhomogeneously broadened systems is demonstrated. When one of the laser fields is a weak probe the velocity averaged two-photon response is primarily caused by two resonantly excited velocity groups; the absence of these implies a split spectrum as suggested by Chebotaev and collaborators. A simple derivation of the probe response is presented. When both fields have non-negligible intensities resonant excitation is inhibited and instead all level populations pulsate. Still a split spectrum can appear. A simple graph showing the regions where this occurs is given and analyzed.

DOI
10.1088/0031-8949/15/4/005

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Rainer Salomaa

Discusses within a simple statistical model modifications of two-photon spectra caused by finite bandwidths of the light sources used for excitation. Field fluctuations are shown to affect the two-photon and step-wise contribution differently which provides a way of distinguishing them. The rate equation approximation, which ignores coherent two-photon processes, is shown to be accurate only when the frequency spread of the fields exceeds the detuning parameters and relaxation rates of the three-level system. In an inhomogeneous system satisfying the Doppler-limit criteria the step-wise contribution is efficiently cancelled away demonstrating the poor applicability of a rate description. Only when the field bandwidths are much larger than the Doppler widths are the coherence effects negligible.

Journal of Physics B Atomic and Molecular Physics•Nov 14, 1978•21 citations
This paper discusses the origin of splitting of two-photon spectra of three-level cascade configurations having a near resonant intermediate level. A clear distinction between splitting mechanisms in homogeneously and inhomogeneously broadened systems is demonstrated. When one of the laser fields is a weak probe the velocity averaged two-photon response is primarily caused by two resonantly excited velocity groups; the absence of these implies a split spectrum as suggested by Chebotaev and collaborators. A simple derivation of the probe response is presented. When both fields have non-negligible intensities resonant excitation is inhibited and instead all level populations pulsate. Still a split spectrum can appear. A simple graph showing the regions where this occurs is given and analyzed.
For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.
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.
For pt.II see ibid., vol.9, p.1221 (1976). Discusses the steady-state response of a three-level atom in two-photon absorption. The applied laser fields can have arbitrary intensities (within the rotating-wave approximation (RWA)). A general expression is derived for the population excited on the uppermost energy level. Two special cases which allow a trivial Doppler averaging are treated in detail. For an off-resonant intermediate state the two-photon spectrum is a simple Lorentzian showing a power shift and modest cross power broadening. The same features are retained when several off-resonance intermediate levels are assumed. For very strong laser fields the Doppler shifts can be neglected in the first approximation. The corresponding spectra are analysed.
Polarization and Rayleigh type optical mixing spectra of a homogeneously and inhomogeneously broadened two-level system are calculated. We show that the nonlinear signal has contributions from the population pulsation and saturation effect. In the homogeneous system these effects can induce an asymmetric spectrum when the probe frequency is different from the resonant value. In the inhomogeneous system the spectral response is always symmetric independent of the probe frequency value. Line saturation and dynamic stark splitting are substantially reduced in the inhomogeneous case. The mentioned differences can be used to identify the type of broadening of a given spectral line.
Discusses within a simple statistical model modifications of two-photon spectra caused by finite bandwidths of the light sources used for excitation. Field fluctuations are shown to affect the two-photon and step-wise contribution differently which provides a way of distinguishing them. The rate equation approximation, which ignores coherent two-photon processes, is shown to be accurate only when the frequency spread of the fields exceeds the detuning parameters and relaxation rates of the three-level system. In an inhomogeneous system satisfying the Doppler-limit criteria the step-wise contribution is efficiently cancelled away demonstrating the poor applicability of a rate description. Only when the field bandwidths are much larger than the Doppler widths are the coherence effects negligible.