A classical model of spontaneous parametric down-conversion

TL;DR

This paper presents a classical model for spontaneous parametric down-conversion (SPDC) that replicates quantum correlations and interference effects, providing a new perspective on the classical-quantum boundary in quantum optics.

Contribution

The authors develop a classical difference frequency generation model that accurately reproduces quantum SPDC correlations and interference phenomena across different gain regimes.

Findings

Model replicates quantum second-order correlations

Accurately predicts interference and coherence effects

Matches experimental measurements at high gain

Abstract

We model spontaneous parametric down-conversion (SPDC) as classical difference frequency generation (DFG) of the pump field and a hypothetical stochastic "vacuum" seed field. We analytically show that the second-order spatiotemporal correlations of the field generated from the DFG process replicate those of the signal field from SPDC. Specifically, for low gain, the model is consistent with the quantum calculation of the signal photon's reduced density matrix; and for high gain, the model's predictions are in good agreement with our experimental measurements of the far-field intensity profile, orbital angular momentum spectrum, and wavelength spectrum of the SPDC field for increasing pump strengths. We further theoretically show that the model successfully captures second-order SU(1,1) interference and induced coherence effects in both gain regimes. Intriguingly, the model also correctly predicts the linear scaling of the interference visibility with object transmittance in the low-gain regime -- a feature that is often regarded as a quintessential signature of the nonclassicality of induced coherence. Our model may not only lead to novel fundamental insights into the classical-quantum divide in the context of SPDC and induced coherence, but can also be a useful theoretical tool for numerous experiments and applications based on SPDC.