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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum tomography of squeezed-vacuum for measuring the transmittivity of materials in the dark

A. Porzio, A. Chiummo, Virginia D’Auria, Salvatore Solimeno, Matteo G. A. Paris

Published Oct 19, 2004• 0 citations
Publisher

Abstract

Quantum tomography of cw homodyne detected field quadratures (QHT) is used for investigating quantum states of radiation fields. We apply QHT to the measurement of the transmittance of optical samples illuminated by vacuum squeezed radiation produced by a type-I degenerate OPO operating below threshold. The field reconstructed by QHT contains information about the transmittance of different absorbers illuminated by a very small number of photons.

DOI
10.1117/12.561829

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Quantum tomography of cw homodyne detected field quadratures (QHT) is used for investigating quantum states of radiation fields. We apply QHT to the measurement of the transmittance of optical samples illuminated by vacuum squeezed radiation produced by a type-I degenerate OPO operating below threshold. The field reconstructed by QHT contains information about the transmittance of different absorbers illuminated by a very small number of photons.
We have exploited pattern function quantum homodyne tomography (QHT) to enlight deviations from the Gaussian state for a squeezed vacuum field generated by a type-I below threshold OPO. This tomographic method allows to fully characterize the state without any a--priori assumption on its statistics. Applying pattern function QHT to the radiation outing a type-I below threshold OPO, we have measured photon number distributions different from those expected for a Gaussian field. Being the Wigner function and the quadrature marginal distribution Gaussian for a Gaussian field, the actual state has been analysed by looking at data variance and Kurtosis (0 for a Gaussian distribution) as a function of the quadrature angle θ. A clear deviation of the Kurtosis from zero has been found for different OPO cavities. This deviation increases as the threshold is approached.
A method for measuring the transmittivity of optical samples by using squeezed--vacuum radiation is illustrated. A squeezed vacuum field generated by a below--threshold optical parametric oscillator is propagated through a nondispersive medium and detected by a homodyne apparatus. The variance of the detected quadrature is used for measuring the transmittivity. With this method it is drastically reduced the number of photons passing through the sample during the measurement interval. The results of some tests are reported.
We report measurements of the Wigner distribution and the density matrix of an electromagnetic field mode, for both vacuum and quadrature-squeezed states. As proposed by Vogel and Risken,1 we obtained the Wigner distribution by tomographic inversion of a set of probability distributions of field-quadrature amplitudes measured by using balanced homodyne detection. A Fourier transform of the Wiener function yields the density matrix, which, according to the standard interpretation of quantum mechanics, contains all knowable information about a given quantum system.
From the experimental measurement of probability distributions of quadrature-field amplitudes, followed by numerical inversion (optical homodyne tomography), we have determined distributions and/or moments of the optical phase of small-photon-number fields for several definitions of the phase variable, including those based on Hermitian operators and on quasiprobability distributions. These measurements were performed on a vacuum field, and a weakly squeezed field. It is found that each definition of phase yields different distributions and/or moments for the experimental data. In addition, all of the experimentally determined quantities agree with the corresponding theoretical predictions.