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Soviet Journal of Quantum Electronics

Calculation method for many-level systems interacting with a resonant field of a high-power light wave

Vladimir Leonardovich Derbov, Mikhail A. Kovner, Sergey K. Potapov

Published Apr 30, 1975• 1 citation
Publisher

Abstract

A theoretical analysis is made of the interaction of a quantum system characterized by two groups of closely spaced levels with a strong resonant field of a steady-state pump wave and a weak field of a "verifying signal." The strong field is allowed for by the canonical transformation and the weak field by the perturbation theory. The first-order susceptibilities are obtained for the weak field in the form which can be used to study the dependences of the frequencies, intensities, and widths of lines in the scatteredradiation spectrum on the frequency and intensity of the strong wave.

DOI
10.1070/qe1975v005n04abeh011073

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A theoretical analysis is made of the interaction of a quantum system characterized by two groups of closely spaced levels with a strong resonant field of a steady-state pump wave and a weak field of a "verifying signal." The strong field is allowed for by the canonical transformation and the weak field by the perturbation theory. The first-order susceptibilities are obtained for the weak field in the form which can be used to study the dependences of the frequencies, intensities, and widths of lines in the scatteredradiation spectrum on the frequency and intensity of the strong wave.
An analysis is made of the spectrum of absorption of a weak probe electromagnetic by two-level atoms in a strong resonant laser field, undergoing collision with buffer gas atoms. The analysis is made using an approach that allows for the direct influence of a strong electromagnetic on the dynamics of an elastic collision between an active atom and a buffer gas atom. Rate equations are analyzed for a combined atom–strong electromagnetic field system (an atom dressed by the field) allowing for spontaneous and optical collisional transitions, and also for the interaction with the probe field. In the steady-state case, an expression is derived for the electric susceptibility of the medium at the small-signal frequency. This expression contains the rates of the optical collisional transitions that depend nontrivially on the parameters of the strong electromagnetic field. The phenomenological characteristics of optical collisional transitions generally used are only valid at low intensities and for small frequency detunings of the strong electromagnetic field, i.e., in the impact limit.
The influence of nonlinear interference processes and of changes in populations in strong electromagnetic fields, and also of the Doppler broadening on resonant four-wave frequency mixing is investigated for a system of Raman-type transitions. The case in which a quantum system interacts with one weak field and two strong fields is considered. Each of the energy levels is assumed to be perturbed by just one strong field. It is shown that the Doppler broadening alters drastically the contributions of the populations of the various levels to the investigated process and that this can alter by several orders of magnitude and nonlinear susceptibilities averaged over the velocities and influence significantly the selection of optimal configurations of the transitions and of the experimental conditions for effective resonant four-wave conversion of the radiation frequencies. A numerical analysis of the derived expressions is used to account for the experimentally observed considerable differences between the spectral dependences of the output power and the conclusions drawn from perturbation theory.
The propagation of a strong coherent "pump" wave traveling through a resonant medium is discussed. The medium is assumed to consist of identical stationary atoms, and the pump-wave frequency is assumed to coincide exactly with the resonance frequency for transitions between a particular pair of atomic states. A previously developed theory of the response of a strongly driven atom to a weak nearly resonant "signal" field is used to deduce the existence of a coupling between any two waves travelling parallel to the pump wave whose (nearly equal) frequencies sum to twice the pump-wave frequency. In the limit of very intense (highly saturating) pump fields, the coupling between the two waves of nearby frequencies leads to amplification of both waves if their frequencies lie within an interval about the pump-wave frequency equal to the Rabi frequency of population inversion. The basic process, which is roughly described by travelling-wave parametric-amplifier equations of motion, consists of the absorption of two pump-field photons followed by their emission at different nearby frequencies, and thus implies a frequency instability of the initially coherent pump wave.
A nonlinear response theory of a quantum-mechanical system undergoing arbitrary relaxation and interacting with fields, some of which may be strong enough to saturate optical transitions, is developed. Explicit expressions for second-order and third-order susceptibilities are obtained. If the fields are weak, then these expressions show the existence of additional resonant contributions to ${\ensuremath{\chi}}^{(n)}$ which arise due to inelastic collisions. Various applications of these ${\ensuremath{\chi}}^{(n)}$'s to modulation spectroscopy, four-wave mixing, and pump-probe experiments are discussed. The general structure suggests how the additional resonances can be used to determine inelastic rates in a Doppler-broadened medium. For saturating fields, ${\ensuremath{\chi}}^{(n)}$'s become dependent on the intensity of such fields and can be formally obtained from weak-field ${\ensuremath{\chi}}^{(n)}$'s, provided proper identification of unperturbed eigenfunctions, eigenvalues, and relaxation times is made. Such intensity-dependent ${\ensuremath{\chi}}^{(n)}$'s have resonant denominators which lead to resonances at Rabi frequencies and submultiples of these frequencies, the widths of which are also dependent on the strength of the field. In the special cases intensity-dependent ${\ensuremath{\chi}}^{(1)}$ agrees with the work of Cohen-Tannoudji and co-workers.
Abstract The interaction of three and two-level atomic systems with two electromagnetic fields, a weak near resonant high-frequency and a strong off-resonant low-frequency ones, is analyzed by applying the method of multiple-scale perturbation theory. We consider two examples: (1) a three-level Λ system interacting with a weak XUV field at the high-energy transition and a strong IR field at the adjacent low-energy transition. The IR field will periodically Stark modulate the energy of the most excited state, which will result in generation of sidebands of the XUV field at the frequencies multiple of the IR field modulation frequency; (2) a two-level atom interacting with a weak near-resonant high-frequency and an off-resonant low-frequency field, which is related to the quantum amplification by superradiant emission of radiation problem.