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Quantum Electronics

Saturated two-photon absorption of single-frequency radiation in gaseous media

Victor P. Kochanov

Published Feb 28, 2012• 2 citations
Publisher

Abstract

A saturated nonresonant two-photon absorption (TPA) theory of quasi-monochromatic radiation by an atom is developed in a model of a three-level cascade quantum system. It is shown that doubled-frequency radiation, arising from a multipole interaction of radiation with the dipole-forbidden transition, experiences spatial oscillations at arbitrary intensities of the pump. The influence of the total phase of the waves with the initial and doubled frequencies on TPA is considered under conditions of ring frequency mixing in a medium.

DOI
10.1070/qe2012v042n02abeh014766

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A saturated nonresonant two-photon absorption (TPA) theory of quasi-monochromatic radiation by an atom is developed in a model of a three-level cascade quantum system. It is shown that doubled-frequency radiation, arising from a multipole interaction of radiation with the dipole-forbidden transition, experiences spatial oscillations at arbitrary intensities of the pump. The influence of the total phase of the waves with the initial and doubled frequencies on TPA is considered under conditions of ring frequency mixing in a medium.
Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.
The effect of a double structure of saturated absorption resonance in the field of counterpropagating light waves interacting with an atomic gas is studied. The experimental observation of this effect was first reported in 2011 in a work by our colleagues at the P.N. Lebedev Physical Institute of the Russian Academy of Sciences (Laboratory of Frequency Standards). The essence of the effect lies in the fact that, on exciting an open dipole transition, another, narrower, resonance of an opposite sign can be observed at the center of the ordinary saturated absorption resonance. A theoretical analysis of this effect has also been performed in this work in terms of a simple spectroscopic model of an atom with two nondegenerate energy levels without taking into account higher spatial harmonics of atomic polarization and polarizations of light waves (scalar model). The present work is devoted to the development of a theory of the formation of a central narrow resonance for the example of a real F g = 1 → F e = 1 atomic transition and to the study of its main characteristics (amplitude, width, contrast, and amplitude-to-width ratio). In addition, the theoretical results obtained without taking into account the influence of higher spatial harmonics and with inclusion of the influence of first higher harmonics are compared. This comparison shows that their influence on the parameters of the new nonlinear resonance is strong even in moderately intense light fields (R ~ γ, where R is the Rabi frequency). The results of this study can be of interest for quantum metrology, as well as for many experiments in which the laser-radiation frequency is stabilized by the saturated absorption resonance on open dipole transitions in atoms and molecules.
A general theory of the saturated-absorption phenomenon in a two-level atomic system is developed, in which the phase relationships between the oscillating atomic dipoles as well as the population differences between energy levels are taken into account. The absorbing gaseous medium considered in this theory is subjected to irradiation by a quasi-running-wave composed of a strong pump field and a weak probe field propagating in opposite directions. Some new interesting results, not predicted by the so-called hole-burning or rate-equation model, are obtained. In particular, the probe-field-transmission peak line shape is found to be markedly different from what is expected according to the rate equations. For finite Doppler widths and a strong saturating pump field, absorption of the probe field can even change sign, and amplification of this field can actually occur. All these features are explained by a close inspection of the evolution of each atomic ensemble of given velocity. Detailed comparison with similar phenomena already observed in rf experiments is presented and permits us to clarify the new predicted effects.
The physics of the two-photon absorption process is investigated for a three-state system. The density-matrix equations for the two-photon interaction are solved in the steady-state limit assuming that the pump laser radiation is monochromatic. Collisional broadening, saturation, and Stark shifting of the two-photon resonance are investigated in detail by numerical solution of the steady-state density-matrix equations. Analytical expressions for the saturation intensity and the Stark shift are derived for the case where the single-photon transitions between the intermediate state and the initial and final states are far from resonance with the pump laser. For this case, it is found that the direction of the Stark shift is dependent on the relative magnitudes of the dipole-moment matrix elements for the single-photon transitions that couple the intermediate state with the initial and final states. Saturation and Stark shifting are also investigated for the case where the single-photon transitions between the intermediate state and the initial and final states are close to resonance with the pump laser.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by rNT\frac{\mathrm{rN}}{T}TrN​, where NNN is the total number of atoms, TTT is the average time of coherent interaction of atoms and the radiation field, and rrr is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.
Steady-state interactions of one, two, and three waves with two-photon two-level media are treated semiclassically. Dynamic Stark shifts as well as dynamic Stark splittings are included in the theory. The intermediate levels are assumed to be nonresonant, and one wave is allowed to have arbitrarily large intensity. The theory parallels the one-photon theory of multiwave mixing couched in terms of population pulsations. We find the one-, two-, and three-wave two-photon absorption coefficients and the three-wave coupling coefficients. We find similarities and significant differences between the one- and two-photon polarizations of the medium. The work treats two-photon saturation spectroscopy, laser- and optical-bistability instabilities, and phase conjugation with a unified formalism.