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Journal of Nonlinear Optical Physics & Materials

NON-LINEAR INTERACTION OF TWO INTENSE FIELDS WITH A THREE-LEVEL ATOMIC SYSTEM

N. A. Ansari, Zlatko Jovanoski, Harvinder Singh Sidhu, Isaac N. Towers

Published Dec 1, 2006• 2 citations
Publisher

Abstract

The interaction between two intense fields with a closed three-level atomic system in the cascade configuration is considered. We derive the steady-state expressions for the field-induced susceptibilities which are valid for all field strengths for the two fields. In particular, we show that each field influences the steady-state susceptibility and absorption experienced by the other field.

DOI
10.1142/s0218863506003402

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The interaction between two intense fields with a closed three-level atomic system in the cascade configuration is considered. We derive the steady-state expressions for the field-induced susceptibilities which are valid for all field strengths for the two fields. In particular, we show that each field influences the steady-state susceptibility and absorption experienced by the other field.
General expressions for the steady-state population distribution and complex susceptibilities of a three-level system interacting with two strong near-resonant electromagnetic fields are obtained using a density-matrix formalism. A complete treatment of the steady-state population distribution established in the three-level system, under the action of two strong fields with arbitrary resonance detunings is presented. The criterion for maximal populations of the exciting levels, as well as conditions in which the population of the exciting levels exceeds the population of the ground state are found. The modification of the absorption and emission lines with increasing intensity of the second (probe) field is considered. The emphasis in the present treatment, as distinct from Panock and Temkin (see IEEE J. Quantum Electron., vol.QE-13, p.476 (1977)) is on the consideration of the arbitrary distribution of the equilibrium populations of the system which exhibits a number of interesting features which have not been previously discussed.
We have considered the excitation spectra of three-photon processes arising from the interaction of a three-level atom, in the cascade configuration, with two strong electromagnetic fields whose initially populated modes ω a and ω b are near resonance with the atomic transition frequencies ω21 and ω32, respectively. In the limit of high photon densities, expressions for the Green's functions are derived in a closed form describing third order nonlinear processes in the region of frequencies ω = ω a + 2ω b and ω = ω b + 2ω a , respectively. Numerical calculations are then performed and the computed spectra are presented graphically for different values of the Rabi frequencies Ω a and Ω b , and detunings ζ a and ζ b , respectively. The excitation spectrum near ω = ω a + 2ω b is calculated as a function of the parameters η a = Ω a /γ0, η b = Ω b /γ0, ζ a = (ω21 - ω a )/γ0 and ζ b = (ω32 - ω b )/γ0 where γ0 is the spontaneous transition probability. With no detuning the spectral intensities vary slowly with respect to variations of the Rabi frequencies and are shifted by amounts governed by the field strengths η a and η b . In the presence of detunings, asymmetries, characteristics of such off-resonance situations, arise enhancing certain spectral peaks while diminishing the intensity of others.
The behaviour of a system of two two-level atoms, both identical as well as non-identical, under the influence of a continuously varying dipole-dipole coupling parameter for a wide range of other parameters such as the atomic level separations and the coupling strength of the external radiation field is explored. A detailed analysis of the behaviour of various level populations and some of the atomic coherences is presented. The influence of the competing effects between the Rabi field strength and the dipole dipole interaction on the two photon absorption probability is explored in detail both for identical as well as non-identical atoms. There are significant variations in the behaviour of identical and non-identical atoms as a function of the dipole coupling strength, even for small amounts of non-identity of the atoms, which in this study is incorporated through the atomic level separations.