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Journal of Experimental and Theoretical Physics

Polariton-Type Dispersion Laws for Three-Level Atoms Interacting with Two Laser Radiation Pulses

P. I. Khadzhi, О. В. Коровай, L. Yu. Nad’kin

Published Apr 1, 2019• 3 citations
Publisher

Abstract

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 $$1 \leftrightarrows 2$$ and $$2 \leftrightarrows 3$$ , 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.

DOI
10.1134/s1063776119030075

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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.
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.
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.
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.
We have considered the excitation spectra arising from stimulated two-photon transitions between two atomic levels of the same parity. The system consists of a three-level atom in the cascade configuration interacting with two strong electromagnetic fields whose initially populated modes ωa and ωb are in resonance with the two atomic transition frequencies, respectively. The Green function formalism is used to calculate the spectral function of the system near the frequencies ω=ωa+ωb, in the limit of high photon densities. The excitation spectra consist of Lorentzian lines peaked at the frequencies ω−ωa−ωb=0, ±Ωa/√2, ±Ωb/√2, ±Ω, and ±2Ω, where Ω2=(Ω2a+Ω2b)/2 and Ωa,Ωb are the Rabi frequencies of the two laser fields, respectively. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. The computed two-photon spectra are compared with those arising from the third-order nonlinear mixing of frequencies near ω=ωa+2ωb and ωb+2ωa, respectively, as well as with those of the stimulated Raman spectra near ω=±(ωa−ωb).
The authors develop a theoretical analysis which describes coherent nonlinear resonant effects where two optical pulses of different frequencies undergo two-photon self-induced transparency (two-photon SIT) in an inhomogeneously broadened three-level system. The field (Maxwell) and atomic (Schrodinger; density matrix representation) equations are coupled in a self-consistent manner by virtue of the resultant macroscopic polarizations at the two frequencies. This treatment is accomplished under circumstances where atomic coherence plays a predominant role. The resulting equations yield a new two-photon area theorem which gives first the intensity dependent, two-photon absorption law analogous to Beer's law for the one-photon transition. Secondly, a 2 pi Lorentzian pulse solution is derived which propagates without loss at the modified pulse velocity.