Abstract: In this paper, the system of a A-type three-level atom interacting with two-mode SU(1,1) coherent states in a Kerr-like medium is studied by means of the quantum theory, and the state function for the resonant or non-resonant interaction is derived. Using the state function, the Kerr effect on the quantum dynamics and nonclassical properties in the system is investigated; and the influences of the detuning and initial atomic on the quantum and nonclassical properties in the non-resonant interaction study system. It has been shown that whether resonant or non-resonant interaction system, the Kerr effect weakens the coupling of the field-atom, shortens the cycle of quantum collapses and revivals of the atomic level occupation and makes the nonclassical correlation properties steady. Kerr effects on the properties of the correlation, on the correlation intensity between the two-mode, on the photon-number distribution and on the bunching or antibunching effect of the two-mode SU(1,1) coherent states produce obviously different characters when it is changed the initial intensity of the light field. That is to say, Kerr effect on the two interaction systems is accorded.In the non-resonant interaction system, the detuning lengthens the cycle of collapse-and-reclaim of the atomic Rabi oscillation, induces steady nonclassical correlation and affects the photon statistical properties. With increasing the photon difference of the two-mode cavities, the influences of the detuning on them become weak, at the same time, Kerr effects become evident and make the correlation and photon statistical properties steady. The detuning makes the influence of initial atomic state on the cavity 1 weak and on the cavity 2 strong. The initial atomic state affects obviously on the nonclassical coherence degree between the two mode cavities, while the influence on the atomic population is not evident. And the initial atomic state affects on the second-order coherence degree for each mode, but the effect on the cavity 1 is stronger than that on the cavity 2.The state function for the interaction of a A-type three-level atom withtwo-mode squeezing vacuum field is derived in the paper. The influences of detuning 8 and initial squeezed light-field factor r on the Cauchy-Schwartz inequality, light squeezing and nonclassical properties are investigated. The results show that the light field is squeezed regularly, and that the collapse-and-revival of the atomic Rabi oscillation appears under the detuning. When the initial squeezed light-field factor r is weak, photon bunching alternates with photon antibunching, and the detuning leads to the reduction of photon antibunching; to the contrary, the factor r is strong, photon statistical properties are steady bunching, and the detuning makes two-mode correlation properties steady…

Key words: A-type three-level atom; SU(1; 1)coherent states; Kerr-like medium; Two-mode intensity correlation function; Cauchy-Schwartz inequality; Second-order coherence degree; Photon statistical properties; Two-mode Squeezing Vacuum Field; Light squeezing

# Two-Mode Correlation Field Interacting with a ∧-type Three-level Atom

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