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Optics Express

Tomographic characterization of OPO sources close to threshold

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

Published Jan 1, 2005• 32 citations
Publisher

Abstract

Pattern function quantum homodyne tomography (QHT) has been used for characterizing the output of a degenerate below-threshold type-I OPO. The recovered photon number distributions deviated from those relative to Gaussian thermal states. The Kurtosis of the homodyne data confirmed these deviations, thus proving the power of QHT to highlight unexpected features of quantum states.

DOI
10.1364/opex.13.000948

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Pattern function quantum homodyne tomography (QHT) has been used for characterizing the output of a degenerate below-threshold type-I OPO. The recovered photon number distributions deviated from those relative to Gaussian thermal states. The Kurtosis of the homodyne data confirmed these deviations, thus proving the power of QHT to highlight unexpected features of quantum states.
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.
In a recent paper by D'Auria et al (2009 Phys. Rev. Lett. 102 020502) we reported the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator (OPO) below threshold using a single homodyne detector. Here we investigate more deeply the Gaussian character of the OPO output addressing the homodyne traces. More precisely, we apply a suitable normality test to check the actual Gaussian distribution of the homodyne data and then we perform the full reconstruction of the signal.
Quantum images, that is inhomogeneous field distributions purely generated by quantum fluctuations, persist when passing from the degenerate to the non-degenerate case of optical parametric oscillators (OPO). Below the threshold for parametric oscillation where the near-field distributions are homogeneous both in intensity and phase, appropriate spatial correlation functions anticipate the transverse spatial pattern that appears above threshold. In particular, the angular dependence of the far field spatial correlation function is able to reveal the travelling-wave nature of the phase pattern above threshold typical of nondegenerate OPOs. Cross-correlation functions between signal and idler intensities show clear evidence of the non-classical nature of the output light.
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.