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.
We have studied the excitation spectrum arising from the optical mixing of the frequencies of a strong bichromatic field interacting with a three-level atom, where the two initially populated modes ωa and ωb are equal to the two atomic transition frequencies, respectively. In the limit of high photon densities, the excitation spectrum near the frequency ω = ωa – 2ωb has been calculated as a function of the parameter η = Ωa2/Ωb2, where Ωa and Ωb are the Rabi frequencies of the two laser fields, respectively. For [Formula: see text] and for weak fields for which [Formula: see text], the spectral function describes a Lorentzian line peaked at the frequency ω = ωa – 2ωb and has a width of the order of γ0, where γ0/2 is the natural width for a two-level atom. When Ωb2 > γ02 and [Formula: see text], the band at ω = ωa – 2ωb splits into two bands described by two Lorentzian lines peaked at ω = ωa – 2ωb ± Ωb/√2 and have spectral widths of the order of 3γ0/4. The ratio of the height of the band ω = ωa – 2ωb to the height ω = ωa – 2ωb ± Ωb/2 is 3:2. The probability amplitudes for both bands take large negative values indicating that optical amplification of the signal field may be expected to occur at these frequencies. When Ωa = Ωb = Ω, η = 1, and for Ω2 < γ02, the spectral function describes a single band at ω = ωa – 2ωb while for Ω2 > γ02, the single band splits into five pairs of bands which are separated from the frequency ω = ωa – 2ωb by frequency shifts which are equal to: ± Ω/√2, [Formula: see text], ± Ω, ± Ω√2, and ± Ω√3, respectively, and have spectral widths of the order of 3γ0/4. For [Formula: see text] and for laser fields for which Ωa2 > γ02 and Ωb2 > γ02, the spectral function consists of three pairs of bands. The probability amplitudes for these bands vary linearly with η and may take large values for [Formula: see text]. A complete discussion of the excitation spectrum as well as a graphical representation of the derived results has been given.