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Canadian Journal of Physics

PHOTON CROSS CORRELATIONS IN A COUPLED BIMODAL SYSTEM

Roscoe C. Williams

Published Sep 1, 1967• 1 citation
Publisher

Abstract

When two atoms are coupled by an interaction potential, they can emit electrons simultaneously into different modes. For a coupled bimodal system, this effect (coupling) causes the line widths and amplitudes of the modes to differ.
DOI
10.1139/p67-256

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A theory on interference effects at high photon densities has been developed for two types of a single three-level atom for which transitions occur: (i) from two different upper levels to a common lower one and (ii) from a common upper level to two different lower levels. The excitation spectrum for the interference effects for the two types of atoms results from the symmetric and antisymmetric interference between the two electronic transitions of the system, respectively. The spectral function for the symmetric modes consists of three Lorentzian lines peaked at the frequencies ω = Δ and ω = Δ ± Ω and having spectral widths of the order of γ0 and 3γ0/4, respectively, where Δ is the beat frequency, Ω is the Rabi frequency, and γ0/2 is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. The antisy mmetric spectrum consists of the peak of ω = Δ, which has a delta-function distribution indicating the stability of the mode in question, and two Lorentzian lines peaked at ω = Δ ± Ω with radiative widths of the order of γ0/2. The excitation spectrum of each type of atom contains also a Lorentzian line describing the very low frequency mode of the system, respectively.
We consider the excitation spectrum of a three-level atom interacting with an electromagnetic field whose two initially populated modes ω a and ω b are in resonance with two atomic transition frequencies while the remaining unpopulated modes are simultaneously coupled to the atomic states. It is found that at high photon densities, the Green's functions describing the lower and upper systems corresponding to the transition frequencies ω a and ω b respectively are-independent of each other. The spectral functions for the lower and upper systems consist of seven lorentzian lines describing the central peak and three pairs of sidebands where each pair is symmetrically located with respect to the transition frequency. For the lower system, the lines are peaked at frequencies ω = ω a , ω = ω a ± Ω a , ω = ω a ± Ω b and ω = ω a ± Ω ab with radiative widths γa 0/2, 3γa 0/4, (γa 0 + γb 0)/4 and (γa 0 + 3γb 0)/4 respectively, where Ω a and Ω b are the energy shifts of the populated modes ω a and ω b , Ω ab 2 = Ω b 2 + Ω a 2/4 and γa 0/2 is equal to the natural width of a photon spontaneously emitted from an isolated atom. For the upper system, the lines occur at ω = ω b , ω = ω b ± Ω b , ω = ω b ± Ω a and ω = ω b ± Ω ba with radiative widths (γa 0 + γb 0)/2, (γa 0 + 3γb 0)/4, (γa 0 + 2γb 0)/4, and 3γa 0/4 respectively. Relations between Ω a and Ω b are derived for which the heights of the lorentzian lines of the corresponding bands become positive or negative indicating attenuation or amplification of the signal field respectively. It is also shown that when certain relations exist between Ω a and Ω b , the signal field is attenuated in the lower system while it is simultaneously amplified in the upper system at different frequencies and vice versa. Spectral functions of the lower and upper systems are derived and discussed for equally spaced levels and equally populated modes Ω a = Ω b , as well as for the limiting case when Ω b 2 = 3Ω a 2/4 or Ω a 2 = 3Ω b 2/4.