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arXiv:0811.3135 · Physical Review A

Monitoring the quantum-classical transition in thermally seeded parametric down-conversion by intensity measurements

Ivo Pietro Degiovanni, Marco Genovese, Valentina Schettini, Maria Bondani, Alessandra Andreoni, Matteo G. A. Paris

Published Jun 24, 2009• 22 citations
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Abstract

We address the pair of conjugated field modes obtained from parametric down-conversion as a convenient system to analyze the quantum-classical transition in the continuous variable regime. We explicitly evaluate intensity correlations, two-mode antibunching, and entanglement for the system initially in a thermal state and show that a hierarchy of nonclassicality thresholds naturally emerges in terms of thermal and down-conversion photon number. We show that the transition from quantum to classical regime may be tuned by controlling the intensities of the seeds and detected by intensity measurements, even in the case of the transition between separability and entanglement. Besides, we show that the thresholds are not affected by losses, which only modify the amount of nonclassicality. The multimode case is also analyzed in some detail.

DOI
10.1103/physreva.79.063836

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We address the pair of conjugated field modes obtained from parametric down-conversion as a convenient system to analyze the quantum-classical transition in the continuous variable regime. We explicitly evaluate intensity correlations, two-mode antibunching, and entanglement for the system initially in a thermal state and show that a hierarchy of nonclassicality thresholds naturally emerges in terms of thermal and down-conversion photon number. We show that the transition from quantum to classical regime may be tuned by controlling the intensities of the seeds and detected by intensity measurements, even in the case of the transition between separability and entanglement. Besides, we show that the thresholds are not affected by losses, which only modify the amount of nonclassicality. The multimode case is also analyzed in some detail.
We address parametric down-conversion seeded by multimode pseudothermal fields. We show that this process may be used to generate multimode pairwise correlated states with entanglement properties that can be tuned by controlling the seed intensities. Parametric down-conversion seeded by multimode pseudothermal fields represents a source of correlated states, which allows one to explore the classical-quantum transition in pairwise correlations and to realize ghost imaging and ghost diffraction in regimes not yet explored by experiments.
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the elementary physical mechanism of stimulation by individual photons has remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by an ultra-weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we access the regime in which the single-photon component of the seed can stimulate the emission of a photon pair, giving rise to a temporally correlated three-photon event. We observe a clear enhancement that cannot be explained by spontaneous processes or accidental coincidences alone, providing time-domain evidence of the fundamental stimulation mechanism at the single-photon level. Beyond its fundamental significance, these results suggest new ways to characterize seed–PDC mode overlap, phase matching, and weak nonlinear coupling in regimes where bright stimulated-emission measurements are not appropriate. Multimode and interferometric extensions could enable correlation-based imaging and phase-sensitive spectroscopy.
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Using stimulated emission, a photon pair source can be characterized by seeding the signal mode with a bright classical beam and measuring the stimulated idler field, thus replacing two-photon coincidence counting with classical intensity detection. We apply this approach to the continuous transverse spatial degrees of freedom of a down conversion source and show that it is possible to certify spatial entanglement with only intensity measurements. We demonstrate this capability through variance-based entanglement and steering witnesses, as well as the Fedorov ratio. This method is useful for studying entanglement properties of photon pair sources in conditions where alignment and photon counting measurements are difficult and time-consuming.
We consider a two-mode stabilized squeezed coherent state (SSCS) of light and introduce the ΠNΠ_{\rm N}ΠN​ indicator, a novel measure for characterizing nonclassicality in the resulting EPR-entangled state. Unlike existing methods based on Cauchy-Schwarz or Murihead inequalities, ΠNΠ_{\rm N}ΠN​ leverages analytical solutions to the quantum Langevin equations to directly analyze nonclassicality arising from key processes like bichromatic injection, frequency conversion, and parametric down-conversion (both spontaneous and stimulated). This approach not only identifies the optimal phase for maximum nonclassicality but also reveals two new phenomena: first, both intra-cavity and extra-cavity fields exhibit the same degree of nonclassicality, and second, balanced seeding in phase-mismatched configurations induces nonclassicality across a broad range of squeezing and seeding parameters. Our work deepens the understanding of the intricate dependence of nonclassicality on system parameters in the context of SSCS, paving the way for investigations into the quantum-to-classical transition in entangled systems. The potential of ΠNΠ_{\rm N}ΠN​ holds significant promise for advancements in quantum optics and information science.