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Physical Review Letters

Entanglement, Interference, and Measurement in a Degenerate Parametric Oscillator

Hua Deng, Daniel B. Erenso, Reeta Vyas, Surendra Singh

Published Mar 26, 2001• 24 citations
Publisher

Abstract

Quantum dynamical equations of motion for homodyne detection of the degenerate optical parametric oscillator are solved exactly. Nonclassical photon statistics are shown to be a consequence of interference of probability amplitudes, entanglement of photon pairs from such an oscillator, and the role of measurement in quantum evolution.
DOI
10.1103/physrevlett.86.2770

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The nonclassical nature of light from a degenerate parametric oscillator is discussed in terms of criteria based on direct photon counting probabilities of light. These criteria do not rely on phase sensitive detection and reveal the nonclassical nature of the field where the conventional criteria based on moments of light intensity (like sub-Poissonian statistics or anti-bunching) fail. We also consider the effect of detector efficiency on the signature of nonclassicality and find that under certain circumstances inefficient detection can enhance nonclassical behavior.
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We consider intensity-field correlation functions for a two-level atom in a degenerate optical parametric oscillator (OPO), which would result from a conditioned homodyne measurement. Analytic results are obtained in the limit of weak driving fields using quantum trajectory methods for both the transmitted and fluorescent fields. This system is unique in that after detection of a photon, it is known that one excitation is in the system, in either the atom or cavity mode. We find large violations of inequalities satisfied by classical fields, for both transmitted and fluorescent fields. This is in contrast to the usual cavity QED system of an atom in a driven cavity where we do not find nonclassical behavior in the intensity-field correlation function in fluorescence. This is understood in terms of a relationship between the intensity-field correlation function and the second-order intensity correlation function, as well as the different amount of field-atom entanglement in the two systems. We show that for weak-field cavity QED one must have photon bunching to have nonclassical behavior in the intensity-field correlation function. We compare our results to those of an ordinary OPO. Finally, we also consider cross correlations, where we examine the transmitted (fluorescent) field conditioned by detection of a fluorescent (transmitted) photon.