A Three Level Atom with Quantized Field Modes and Coherent Trapping

Abstract

A coherent trapping phenomenon for the level population of a three-level atom, which takes place on two-photon resonance, has been noted and well studied by a semi-classical approach where the classical electro-magnetic fields are regarded as given [1]. In this article we deal with a closed system of one or two quantized field modes and a three-level (∧-type) atom interacting to each other via the non-vanishing atomic dipole matrix elements d₁₂ and d₂₃ (see Fig. 1). We show that the condition for the coherent trapping determines not only the atomic state but also the field state for the two mode case. In the two mode case (see Fig. 1A), mode ℓ (left) couples with the atom by d₁₂ and mode r (right) by d₂₃. The one mode case with its frequency can be regarded as a special case of the two modes with ω_ℓ = ω_r = ω (see Fig. 1 B).