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Journal of Experimental and Theoretical Physics

Polariton-Type Dispersion Laws for Four-Level Atoms with Nonequidistant Energy Spectrum That Interact with Three Laser Pulses

О. В. Коровай

Published Sep 1, 2021• 1 citation
Publisher

Abstract

Characteristic features of polariton dispersion laws are studied for four-level atoms interacting with three pulses of coherent laser radiation with frequencies that are in resonance with optically allowed one-photon transitions 1 $$\leftrightarrows$$ 2, 2 $$\leftrightarrows$$ 3, and 3 $$\leftrightarrows$$ 4 with regard to two-photon transitions 1 $$\leftrightarrows$$ 3 and 2 $$\leftrightarrows$$ 4, as well as a direct three-photon transition 1 $$\leftrightarrows$$ 4. The approximation of a given photon density of three pulses is used. It is shown that the dispersion law consists of four branches the position and shape of which are specified by the Rabi frequencies of the above transitions and the photon densities of the three pulses. The direct consideration of all six optical transitions leads to the dependence of the dispersion law of atomic polaritons on quantum parameters—the phase differences between the Rabi frequencies of the transitions under consideration. Parameter values are found for which the branches of the dispersion law may intersect.

DOI
10.1134/s1063776121080033

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Characteristic features of polariton dispersion laws are studied for four-level atoms interacting with three pulses of coherent laser radiation with frequencies that are in resonance with optically allowed one-photon transitions 1 ⇆\leftrightarrows⇆ 2, 2 ⇆\leftrightarrows⇆ 3, and 3 ⇆\leftrightarrows⇆ 4 with regard to two-photon transitions 1 ⇆\leftrightarrows⇆ 3 and 2 ⇆\leftrightarrows⇆ 4, as well as a direct three-photon transition 1 ⇆\leftrightarrows⇆ 4. The approximation of a given photon density of three pulses is used. It is shown that the dispersion law consists of four branches the position and shape of which are specified by the Rabi frequencies of the above transitions and the photon densities of the three pulses. The direct consideration of all six optical transitions leads to the dependence of the dispersion law of atomic polaritons on quantum parameters—the phase differences between the Rabi frequencies of the transitions under consideration. Parameter values are found for which the branches of the dispersion law may intersect.
Behavioral features of polariton dispersion laws are studied for three-level atoms interacting with two coherent laser radiation pulses with frequencies ω1 and ω2 that are in resonance with optically resolved one-photon transitions between levels 1⇆21 \leftrightarrows 21⇆2 and 2⇆32 \leftrightarrows 32⇆3 , respectively, and with regard to the direct two-photon transition between levels 1 and 3. The approximation of given photon densities of both pulses compared with the densities of atoms is used. It is shown that the dispersion law consists of three branches whose position and shape are determined by the Rabi frequencies of the above three optical transitions and the photon densities in both pulses. The direct consideration of all three optical transitions leads to the dependence of the dispersion law of atomic polaritons on a new quantum parameter—the phase difference between the three Rabi frequencies. The values of the system parameters are found for which the branches of the dispersion law may intersect. The concept of the surface of the dispersion law is introduced in the dependence of the eigenfrequencies of atomic polaritons on the photon wave vectors in both pulses.
A dispersion law for the system of three-level atoms with an equidistant energy spectrum interacting with resonant laser radiation has been obtained taking into account two successive optically allowed one-photon transitions and an optically allowed two-photon transition between the lower and upper levels. It has been shown that the dispersion law consists of three polariton branches. The effects of repulsion and attraction of branches of the dispersion law and their intersection, as well as the self-consistent variation of the photon–atom coupling constant, have been predicted.
Abstract The dispersion relation is obtained for a system of four-level atoms with an equidistant energy spectrum, which interact with resonant laser radiation, with account for three sequential one-photon optically allowed transitions, two-photon transitions, as well as a direct three-photon transition. It is shown that the dispersion relation consists of four polariton branches. The divergence and convergence of the dispersion relation branches, their intersection, and a self-consistent change in the binding force of photons with atoms are predicted using the fixed photon concentration approximation.
A dispersion law for the system of three-level atoms with an equidistant energy spectrum interacting with resonant laser radiation has been obtained taking into account two successive optically allowed one-photon transitions and an optically allowed two-photon transition between the lower and upper levels. It has been shown that the dispersion law consists of three polariton branches. The effects of repulsion and attraction of branches of the dispersion law and their intersection, as well as the self-consistent variation of the photon– atom coupling constant, have been predicted.
We theoretically study the coherent interaction of a tripod-type atomic system with three laser fields, i.e., one probe and two coupling, or two probe and one coupling field. Our analytical and numerical results show that, when all three fields are on two-photon resonance, in addition to the Rabi frequencies of the coupling fields, the probe group velocities also depend on the spontaneous decay rates and the initial population distribution. So we can manipulate the probe pulses to achieve controllable ultraslow group velocities by preparing different initial atomic states. With an incoherent pump field applied, a narrow transparent window accompanied by abnormal dispersion may occur in the probe absorption spectrum, which then allows us to switch a probe pulse from ultraslow to superluminal propagation.
The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.