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Optics Communications

Interaction of a bichromatic field with a two-level system in a cavity

D. Kagan, Harry Friedman, A. D. Wilson‐Gordon

Published Jun 1, 1990• 1 citation
Publisher
DOI
10.1016/0030-4018(90)90460-b

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It is well known that bichromatic excitation on one common transition can tune the emission or absorption spectra of atoms due to the modulation frequency dependent non-linearities. However little attention has been focused on the quantum dynamics of fields under bichromatic excitation. Here we present dissipative effects on noise correlations of fields in bichromatic interactions with atoms in cavities. We first consider an ensemble of two-level atoms that interacts with the two cavity fields of different frequencies and considerable amplitudes. By transferring the atom-field nonlinearities to the dressed atoms we separate out the dissipative interactions of Bogoliubov modes with the dressed atoms. The Bogoliubov mode dissipation establishes stable two-photon processes of two involved fields and therefore leads to two-mode squeezing. As a generalization, we then consider an ensemble of three-level Λ atoms for cascade bichromatic interactions. We extract the Bogoliubov-like four-mode interactions, which establish a quadrilateral of the two-photon processes of four involved fields and thus result in four-mode squeezing.
We present a numerical study of the interaction of a two-level atom with a frequency-modulated cavity mode described by the Jaynes-Cummings Hamiltonian. In particular, we explore how the population of the atomic levels changes for monochromatic and bichromatic modulations of the cavity field. The primary goal is to find sets of boundary conditions for which the evolution of the system exhibits nonlinear dynamic behavior, by solving the equations of motion of the atomic system using embedded and semi-implicit numerical algorithms. We find that the system shows quasiperiodicity when the monochromatic frequencies or ratio of the bichromatic frequencies of the field are irrational (incommensurate) numbers. In addition, when the modulated frequencies are overtones of the Rabi frequency a nearly single dominant frequency becomes apparent for the evolution of the atomic level population of the system.