Monotonic quantum-to-classical transition enabled by positively correlated biphotons

Multiparticle interference is a fundamental phenomenon in the study of quantum mechanics. It was discovered in a recent experiment [Y.-S. Ra et al., Proc. Natl. Acad. Sci. USA 110, 1227 (2013)] that spectrally uncorrelated biphotons exhibited a nonmonotonic quantum-to-classical transition in a four-photon Hong-Ou-Mandel (HOM) interference. In this work, we consider the same scheme with spectrally correlated photons. By theoretical calculation and numerical simulation, we found the transition not only can be nonmonotonic with negatively correlated or uncorrelated biphotons, but also can be monotonic with positively correlated biphotons. The fundamental reason for this difference is that the HOM-type multiphoton interference is a differential-frequency interference. Our study may shed new light on understanding the role of frequency entanglement in multiphoton behavior.

Figure 1

The 2/2, 3/1, and 4/0 detection schemes for the HOM-type interference. All the beam splitters (BS) are 50:50 beam splitters. $D_n$ ($n=1,2,3,4$) is the single photon detector. $\tau$ is the time delay in the signal arm.

Figure 2

Three different JSAs $f({\omega }_s,{\omega }_i)$: (a1) uncorrelated, (b1) negatively correlated, and (c1) positively correlated. The corresponding HOM-type interference patterns are shown in (a2)–(c4): (a2)–(c2) 2/2 detection scheme, (a3)–(c3) 3/1 detection scheme, and (a4)–(c4) 4/0 detection scheme. All the $y$ axes in (a2)–(c4) are normalized.