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

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.