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Physical Review A

Strong effective saturation by optical pumping in three-level systems

Jae-Ihn Kim, D. Haubrich, B. Klöter, Dieter Meschede

Published Dec 2, 2009• 5 citations
Publisher

Abstract

We have studied nonlinear absorption from the In ${P}_{1/2,3/2}$ ground-state doublet in a resistively heated high-temperature cell and a hollow cathode lamp. Using probe and pump lasers at 410 and 451 nm, respectively, absorption spectra with nonlinear properties caused by saturated absorption, coherent dark resonances, and optical pumping are observed. A theoretical description in terms of a density-matrix theory agrees very well with the observed spectra and identifies optical pumping as a dominating process of broadening in the stepwise contribution rather than velocity-changing collisions. Our experiments suggest that the theory used here is widely applicable in saturation spectroscopy on three-level $\ensuremath{\Lambda}$ systems.

DOI
10.1103/physreva.80.063801

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We have studied nonlinear absorption from the In P1/2,3/2{P}_{1/2,3/2}P1/2,3/2​ ground-state doublet in a resistively heated high-temperature cell and a hollow cathode lamp. Using probe and pump lasers at 410 and 451 nm, respectively, absorption spectra with nonlinear properties caused by saturated absorption, coherent dark resonances, and optical pumping are observed. A theoretical description in terms of a density-matrix theory agrees very well with the observed spectra and identifies optical pumping as a dominating process of broadening in the stepwise contribution rather than velocity-changing collisions. Our experiments suggest that the theory used here is widely applicable in saturation spectroscopy on three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ systems.
We present a theoretical analysis of high-frequency optical heterodyne saturation spectroscopy in Doppler-broadened coupled three-level systems. The saturating beam, which is assumed to be amplitude modulated at frequency δ (double-sideband suppressed carrier amplitude modulation) is resonant for one of the transitions. Through non-degenerate four-wave mixing processes, this modulation is transferred to a probe beam, resonant for the coupled transition. Saturating and probe fields may be either co-propagating or counter-propagating. The lineshape of the probe modulation is analysed via a third-order perturbation expansion of the atomic density matrix with respect to the incident field amplitudes. The resulting signal is integrated over velocities, in the Doppler limit approximation. Both population saturation effects and coherent (Raman-type, or two-photon) processes contribute to the signal. The various contributions appear as Lorentzian-type resonance doublets. We show that, in the absence of relaxation processes (collisional dephasing, or radiative cascades), destructive interferences between population saturation and coherent two-photon processes are responsible for the disappearance of one resonance doublet. Phase-interrupting collisions are thus predicted to lead to the existence of a « pressure-induced extra-resonance » (PIER) doublet, which could yield information on collisional processes in the impact regime. The properties of the predicted PIER doublets are analysed in relation with other types of PIER signals studied in four-wave mixing, and in time-resolved saturation spectroscopy.
A theory of saturation spectroscopy is developed which accounts for effects of level degeneracy. The theory can be applied to those situations in which a pump laser field of arbitrary strength and polarization acts between two manifolds of degenerate or nearly degenerate atomic levels, while a probe laser field of arbitrary strength and polarization acts between a coupled manifold of levels. As such, this theory of "three-level" systems could, in principle, include effects arising from level degeneracy, optical pumping, atomic motion, transient laser fields, different polarizations and strengths for pump and probe fields, and atomic transit across the laser fields. The present calculation, however, is limited to a study of optical pumping and field polarization effects for pump fields of arbitrary strength and weak probe fields interacting with a single velocity subclass of atoms. Probe absorption line shapes clearly display the effects of pump-field strength (Rabi splittings), pump-field polarization (positions and number of Rabi-split resonance peaks), pump-field detuning (positions of resonance peaks), and optical pumping (relative strengths of the resonance peaks). The calculation is carried out with the use of an irreducible tensor basis for the atomic density matrix although a standard (mmm-basis) calculation is included in an appendix.
The absorption/gain spectrum of a weak probe field is theoretically analyzed for an atomic three-level Λ system driven by a strong pump field and perturbed by collisions with buffer-gas atoms. It is assumed that both pump and probe drive the same transition. When the dark state is sufficiently long lived, the probe spectrum exhibits an extremely narrow (possibly subnatural-width) resonance. It is shown that coherence-preserving collisions drastically (both qualitatively and quantitatively) change the probe absorption spectrum even at a low collision frequency, when Dicke narrowing is negligible. Strong coherence effects on the resonance structure at low gas pressures is explained by a change in refractive index due to coherence-preserving collisions for particles in the resonant velocity group.
Three typical excited-state nonlinear absorption effects in molecular systems with weak ground-state absorption (at 532 nm) are experimentally demonstrated: (a) reverse saturable absorption (RSA) caused by strong triplet first-to-second excited-state absorption in a copper phthalocyanine solution with 15-ns laser pulses; (b) RSA caused by strong singlet first-to-second excited-state absorption in a C60{\mathrm{C}}_{60}C60​ solution with 21-ps laser pulses; (c) the RSA-SA turnover caused by strong singlet first-to-second excited-state absorption and weak singlet second-to-third excited-state absorption in a metallo-porphyrin-like solution with 21-ps laser pulses. To simulate these excited-state nonlinear absorption behaviors we propose a general ten-level density-matrix model and its simplified models for the three cases. All simulations are in good agreement with the experimental results.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
A theoretical analysis of the relative intensities of the Doppler-free signals in saturation spectroscopy, velocity selective optical pumping (VSOP) spectroscopy, polarization spectroscopy and a mixing of saturation and polarization spectroscopies is presented using the approximation of a single cycle of optical pumping in a four-level system. An optical pumping process in the Zeeman sublevels is taken into account owing to the important role of spontaneous emission even if the sublevels are degenerate. Arbitrary polarization combinations are considered for pump and probe beams. The similarities and differences between three kinds of spectroscopy are made clear. Both circular and linear optical anisotropies induced by the pump beam are considered in this theoretical calculation. The magnitude and sign of Doppler-free resonances in each spectroscopy are quite different owing to the polarizations of the pump and probe beams. The four-level system is important as a three-level approximation. The results obtained from the four-level optical pumping theory are in good agreement with experimental reports.