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Optics Letters

Ultranarrow extraresonant holes and antiholes in pump–probe and four-wave mixing spectroscopy of a two-level system interacting with two fields of arbitrary intensity

S. Hochman, A. D. Wilson‐Gordon, Harry Friedmann

Published May 15, 1990• 6 citations
Publisher

Abstract

We study pump–probe and four-wave mixing spectroscopy for moderately intense copropagating pump and probe beams (Rabi frequencies 2|V1,2|) interacting with an open two-level system where the lower state of an optical transition relaxes faster to reservoir states than the upper state does. The probe absorption spectrum displays an ultranarrow extraresonant antihole (ERA) when |V1| ≥ |V2| and a ultranarrow dip when |V1| < |V2|. The pump and probe absorption profiles display opposite tendencies except for the case of |V1| = |V2| when identical ERA’s are produced. The four-wave mixing spectrum shows an extraresonant dip for |V1| ≥ |V2| and an ERA when |V1| < |V2| The subnatural features are not power broadened.

DOI
10.1364/ol.15.000631

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Physical Review A•Dec 1, 1988•17 citations
We study pump–probe and four-wave mixing spectroscopy for moderately intense copropagating pump and probe beams (Rabi frequencies 2|V1,2|) interacting with an open two-level system where the lower state of an optical transition relaxes faster to reservoir states than the upper state does. The probe absorption spectrum displays an ultranarrow extraresonant antihole (ERA) when |V1| ≥ |V2| and a ultranarrow dip when |V1| < |V2|. The pump and probe absorption profiles display opposite tendencies except for the case of |V1| = |V2| when identical ERA’s are produced. The four-wave mixing spectrum shows an extraresonant dip for |V1| ≥ |V2| and an ERA when |V1| < |V2| The subnatural features are not power broadened.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
In this paper we present theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrary strong pump field drives a given transition and a probe (weak) field drives the same transition. We have studied the influence of level degeneracy and field polarization on pump-probe and four-wave mixing signals. Our results indicate that for some closed systems (no population loss to the reservoir) it is possible to observe resonances that are characterized by the ground state width. Previous calculations indicate that for a nondegenerate system this resonance can appear only for an open system, the so-called "pressure induced resonances.”1 Our result, which contradicts this conclusion, can be understood by noting the fact that there are in general three irreducible tensor2 (in general) contributions to the line shape (K = 0 population, K = 1 orientation, and K = 2 alignment). Thus, even if the system is closed for the population it may still remain open for orientation or alignment; this effect is responsible for the narrow resonance. Specific calculations are presented for J = 1/2 → 1/2 and J = 1→2 transitions.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave mixing, population modulation, and Zeeman optical pumping are derived. On all these observables, subnatural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited-state population modulation in the D2{D}_{2}D2​ line of Rb vapor are presented in good agreement with the calculations.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations
A nonperturbative theoretical study of four-wave-mixing processes in four-level systems is presented. Using the density-matrix formalism, numerical results are obtained for two arbitrarily intense pump fields with the third field a weak probe. The fourth wave, radiated by the system, is obtained analytically for some special cases. We find, for different frequency detunings, Rabi frequencies, and relaxation rates that the line shapes exhibit: (i) dynamic Stark splitting and shifting, and merging of resonances; (ii) power broadening with two-photon antiresonance behavior resulting from a destructive interference between different contributions to the optical polarization; and (iii) extra resonances induced by field intensities and saturation processes.