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arXiv:quant-ph/0204103 · Physical Review A

Direct measurement of optical quasidistribution functions: Multimode theory and homodyne tests of Bell’s inequalities

Konrad Banaszek, Andrzej Dragan, Krzysztof Wódkiewicz, Czesław Radzewicz

Published Oct 4, 2002• 32 citations

Abstract

We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase-space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as nonunit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell's inequalities by measuring joint two-mode quasidistribution functions by photon counting under locality conditions. We determine the range of parameters of the experimental setup that enable violation of Bell's inequalities for two states exhibiting entanglement in the Fock basis: a one-photon Fock state divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced in the process of nondegenerate parametric down-conversion.

DOI: 10.1103/physreva.66.043803

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Q

function and the Wigner function. This assigns a novel operational meaning to these two quasidistribution functions in tests of quantum nonlocality and also establishes a direct relationship between two intriguing aspects of quantum mechanics: the nonlocality of entangled states and the noncommutativity of quantum observables, which underlies the nonclassical structure of the phase-space quasidistribution functions.

In this thesis we present a direct scheme for measuring quasidistribution functions of light. This scheme, based on photon counting, is derived from a simple relation linking the Wigner function with photon statistics. We develop a full multimode theory of the scheme, and show that the principle of the measurement can be straightforwardly generalized to the detection of the multimode radiation. We also discuss practical aspects of the scheme, including statistical error, non-unit detection efficiency, and imperfect interference visibility. Next, we report experimental realization of the scheme, and present measurements of the Wigner function for several quantum states of light. Finally, we study the general problem of statistical uncertainty in quantum-optical photodetection measurements.