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arXiv:quant-ph/9612004 · Europhysics Letters (EPL)

Density matrix from photon number tomography

Stefano Mancini, Paolo Tombesi, Vladimir I. Man’ko

Published Jan 10, 1997• 83 citations
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Abstract

We provide a simple analytic relation which connects the density operator of the radiation field with the number probabilities. The problem of experimentally “sampling” a general matrix element is studied, and the deleterious effects of nonunit quantum efficiency in the detection process are analyzed showing how they can be reduced by using the squeezing technique. The obtained result is particularly useful for intracavity field reconstruction states.

DOI
10.1209/epl/i1997-00115-8

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We provide a simple analytic relation which connects the density operator of the radiation field with the number probabilities. The problem of experimentally “sampling” a general matrix element is studied, and the deleterious effects of nonunit quantum efficiency in the detection process are analyzed showing how they can be reduced by using the squeezing technique. The obtained result is particularly useful for intracavity field reconstruction states.
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We propose an alternative method for detecting the density matrix of a radiation field via optical homodyne tomography. The method needs no assumption on the state, and the density matrix is recovered directly from averages on data. The tomographic reconstruction is very fast and provides very reliable statistics on line with detection. As a test of the method we present numericla results for a set of computer-simulated experiments, corresponding to different quantum states of the radiation source. Then a tomographic reconstruction is given for experimental data provided by Smithey etal. [Phys. Rev. Lett. 70, 1244 (1993)].
The problem of optical homodyne tomography is considered in the context of a Bayesian model-fitting or inverse problem approach. An algorithm is formulated, based on matrix computation rather than the numerical approximation of an analytic inverse transform. This automatically takes into account the effects of noise, detector inefficiencies and incomplete sampling of the data. The relationships with conventional reconstruction schemes, methods for including various forms of prior information and for calculating error estimates are discussed. The process of reconstructing the photon number distribution and the density matrix are illustrated using both simulated and experimental data.