Non-linear optical mixing of frequencies of a strong bichromatic field interacting with a two-level atom at high proton densities

Abstract

We have studied the excitation spectrum arising from the interaction of a two-level atom with two strong electromagnetic fields whose initially populated modes ω _a and ω _b are near resonance with the atomic transition frequency In the limit of high photon densities the Green's function of the system describing the electronic transition in question has been derived in a closed form and includes processes arising from the interaction of seven photon modes of both laser fields. The spectral function of the system is calculated when the frequency ω _a of the one laser field is in resonance with the atomic transition frequency while the frequency ω _b of the other field is varied. The excitation spectrum is found to consist, apart from the central peak at the excitation frequency ω _a , of several lorentzian lines which are peaked in the neighbourhood of the frequencies ω _a ± Δ, ω _a ± 2Δ, ω _a ± 3Δ and ω _a ± 4Δ, where Δ = ω _a - ω _b and describe the type of optical mixing of light modes which is of the third, fifth, seventh and ninth order, respectively. Additional peaks appear in the spectra, which result from the interaction between the frequency modes in question. The probability amplitudes describing the relative intensities of the peaks in question are expressed as functions of the parameters η _a = Ω _a /Δ and η _b = Ω _b /Δ, where Ω _a and Ω _b are the Rabi Frequencies of the two laser fields, respectively. It is found that when η _a ⩾ 1 and η _b ⩾ 1 the expression for the relative intensities of the bands in question are remarkably enhanced and take extremely large positive or negative values. Results of numerical calculations for a wide range of values of η _a and η _b when η _a = η _b ⩾ 1 are presented graphically and the complete excitation spectrum is discussed in detail. The method may be useful to investigate the behaviour of excited states as well as those close to the limit of ionization.