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arXiv:0909.3726 · Journal of the Optical Society of America B

Self-consistent phase determination for Wigner function reconstruction

Maria Bondani, Alessia Allevi, Alessandra Andreoni

Published Jan 22, 2010• 14 citations
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Abstract

We present the reconstruction of the Wigner function of a classical phase-sensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid photodetector operated above its photon-resolving regime, we obtain both the statistics at different values of the probe field and the values of the probe phase required to reconstruct the Wigner function.

DOI
10.1364/josab.27.000333

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We present the reconstruction of the Wigner function of a classical phase-sensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid photodetector operated above its photon-resolving regime, we obtain both the statistics at different values of the probe field and the values of the probe phase required to reconstruct the Wigner function.
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We present an experimental scheme for the reconstruction of the Wigner function of optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. We mix, at a beam-splitter, the signal state with a set of coherent probes of known complex amplitudes, and measure the probability distribution of the detected photons for each probe. The Wigner function is given by a suitable sum of those probability distributions. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.
We present the experimental reconstruction of the Wigner function of some optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. The signal state is mixed at a beam-splitter with a set of coherent probes of known complex amplitudes and the probability distribution of the detected photons is measured. The Wigner function is given by a suitable sum of these probability distributions measured for different values of the probe. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.
We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state 1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+/-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.