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Journal of Experimental and Theoretical Physics

Dispersion Relation for a Four-Level Atom with an Equidistant Energy Spectrum at a High Excitation Level

О. В. Коровай

Published May 1, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776122030062

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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.
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.
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.
We have investigated the dispersive properties of excited-doublet four-level atoms interacting with a weak probe field and an intense coupling laser field. We have derived an analytical expression of the dispersion relation for a general excited-doublet four-level atomic system subject to a one-photon detuning. The numerical results demonstrate that for a typical rubidium Dl line configuration, due to the unequal dipole moments for the transitions of each ground state to double excited states, generally there exists no exact dark state in the system. Close to the two-photon resonance, the probe light can be absorbed or gained and propagate in the so-called superluminal form. This system may be used as an optical switch.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.