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Physical Review A

Violation of Bell's inequality in a driven three-level cascade atomic system

Nadeem A. Ansari

Published Mar 1, 1997• 6 citations
Publisher

Abstract

A fully quantum-mechanical theory of multiwave mixing in a three-level cascade atomic system with two field modes is presented. The top and bottom levels are coupled with a strong external field. Certain conditions on the Rabi frequency and detuning of the driving field have been worked out for the violation of Bell's inequality and for when the system may behave as nondegenerate parametric oscillator.

DOI
10.1103/physreva.55.1639

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A fully quantum-mechanical theory of multiwave mixing in a three-level cascade atomic system with two field modes is presented. The top and bottom levels are coupled with a strong external field. Certain conditions on the Rabi frequency and detuning of the driving field have been worked out for the violation of Bell's inequality and for when the system may behave as nondegenerate parametric oscillator.
A theory of two-mode phase-sensitive amplification by a three-level atomic system in the cascade configuration is presented, within the framework of the theory of multiwave mixing. Two photons of a strong external pump field induce coherence between the top and bottom levels. It is shown that both quadratures of the field modes acquire unequal gain and added noise. For large values of the dimensionless pump intensity, with a particular choice of its phase, and zero side-mode detuning, the system behaves as a nondegenerate parametric amplifier.
We investigate violation of Cauchy–Schwarz and Bell inequalities in two-mode three-level cascade system with injected atomic coherence in the framework of quantum theory of multiwave mixing. We show that Cauchy–Schwarz inequality is strongly violated when there is strong entanglement in the system. It also appears that Bell inequality is violated in the region where there is weak entanglement and well-preserved where there is strong entanglement in the system. We thus note that there are states which are entangled but do not violate Bell inequality. We also show that this system can be used to prepare states that exhibit EPR correlations.
We present a fully quantum-mechanical theory of nondegenerate multiwave mixing processes in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong-pump intensities and tunings within the Rabi sidebands. We find good broadband squeezing for low-pump intensities and tunings outside a small region around central tuning. Both cases avoid regions of significant spontaneous emission.