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arXiv:0811.4115

A possible experimental check of the uncertainty relations by means of homodyne measuring photon quadrature

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni, F. Ventriglia

Published Nov 25, 2008• 4 citations
arXivHTMLPDF

Abstract

We suggest to use the photon homodyne detection experimental data for checking the Heisenberg and Schrödinger-Robertson uncertainty relations, by means of measuring optical tomograms of the photon quantum states.
DOI
10.48550/arxiv.0811.4115

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We have experimentally determined all of the quantities involved in the uncertainty relation for the phase and photon number of a mode of the electromagnetic field when the field mode is in a coherent state of small average photon number. This is accomplished by determining the quantum state of the field using optical homodyne tomography, which uses measured distributions of electric-field quadrature amplitude to determine the Wigner function and hence the density matrix. The measured state is then used to calculate the uncertainty product for the number and phase, as well as the expectation value of the commutator of the number and phase operators. The experimental results agree with the quantum-mechanical predictions. We also present measured phase- and photon-number distributions for these weak coherent states, as well as their measured complex wave functions.