Near-100% two-photon-like coincidence-visibility dip with classical light and the role of complementarity Simanraj Sadana, 1 Debadrita Ghosh, 1 Kaushik Joarder, 1 A. Naga Lakshmi, 1 Barry C. Sanders, 1, 2, 3 and Urbasi Sinha 1, ∗ 1 Raman Research Institute, Sadashivanagar, Bangalore 560 080, India 2 Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada T2N 1N4 3 Program in Quantum Information Science, Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8 The Hong-Ou-Mandel effect is considered a signature of the quantumness of light, as the dip in coincidence probability using semiclassical theories has an upper bound of 50%. Here we show, theoretically and experimentally, that, with proper phase control of the signals, classical pulses can mimic a Hong-Ou-Mandel-like dip. We demonstrate a dip of (99.635 ± 0.002)% with classical microwave fields. Quantumness manifests in wave-particle complementarity of the two-photon state. We construct quantum and classical interferometers for the complementarity test and show that while the two-photon state shows wave-particle complementarity the classical pulses do not. I. INTRODUCTION The Hong-Ou-Mandel (HOM) two-photon coincidence- visibility dip (TPCVD) [1, 2], is a salient fourth-order interference effect [3], and one of the most important ef- fects and tools in quantum optics. Myriad applications include measuring photon purity [4] and distinguishabil- ity [5], heralding in optical quantum computing gates [6], conceptually underpinning the complexity of the boson sampling problem [7], and realizing a NOON state for quantum metrology [8]. TPCVD is manifested by injecting a single photon into each input port of a balanced beam splitter and observing anticorrelated output in the form of bunching. Mathe- matically, the input is the pure product state |11〉 and the output is the symmetric or antisymmetric superposition of |20〉 and |02〉, resulting in a coincidence probability of zero. Given some delay τ between photon arrivals at the two input ports, the coincidence probability C (τ ) drops as τ approaches zero. The TPCVD, V := C (∞) − C (0) C (∞) =1 − C (0) C (∞) , (1) is unity in the ideal case [9, 10]. Despite the immense importance, applicability, and suc- cess of HOM TPCVD, a widespread misconception is that exceeding a 50% TPCVD falsifies classical electromag- netic field theory. Example quotations include “fourth- order interference of classical fields cannot yield visibil- ity larger than 50%” [11], “as long as the visibility of the coincidence dip is greater than 50%, no semiclassi- cal field theory can account for the observed interference” [9], “visibility, being greater than 50%, is clear evidence of non-classical interference” [12], and “classical theory of the coherent superposition of electromagnetic waves, how- ever, can only explain a HOM dip with V≤0.5” [13]. This myth matters as the 50% dip threshold is widely accepted as proving that two-photon interferometry has entered the quantum domain. The 50% TPCVD is believed to be the threshold be- tween classical and quantum behavior of light, because independent classical pulses with uniformly randomized relative phase yield V =1/2[13, 14]. The argument against the classical description is that it fails to predict the observed 100% visibility and, instead, puts an upper bound of 50% on it. In this paper, we perform two precision experiments and show that if the phase between the input signals is randomized over a preselected set, 100% visibility can be achieved even with classical pulses. Therefore, the afore- mentioned reason for the failure of the classical descrip- tion of light is invalid. The real quantum signature lies in completing the interferometer as a two-photon analog of the experimental proof of complementarity for a single photon [15]. Curiously, this subtle yet important point has no experimental demonstration in the literature. II. THEORY In the semiclassical theory of photodetection [16, 17], the coincidence probability at the two detectors is propor- tional to the cross correlation of the integrated intensities at the detectors. The normalized correlation function is C (τ ) :=  dϕP (ϕ)  T off Ton dt |E + (t; ω,τ,ϕ)| 2  T off Ton dt ′ |E − (t ′ ; ω,τ,ϕ)| 2   dϕP (ϕ)  T off Ton dt |E + (t; ω,τ,ϕ)| 2   dϕ ′ P (ϕ ′ )  T off Ton dt |E − (t; ω,τ,ϕ ′ )| 2  , (2) * usinha@rri.res.in arXiv:1810.01297v3 [quant-ph] 18 Jul 2019