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

Pattern-function quantum tomography: a tool for experimentally investigating the real state of radiation fields

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

Published Aug 18, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.617784

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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.
States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.
We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg–Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.
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.