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arXiv:1805.06592

Ghost Diffraction in Time Domain: Two-Photon Reciprocal Two-Slit Diffraction-Interference

Yoshiki O-oka, S. Fukatsu

Published May 17, 2018• 0 citations
arXivHTMLPDF

Abstract

Temporal ghost diffraction (TGD) is observed by taking two-photon cross-correlation in the configuration of reciprocal two-slit diffraction (2SD) where interference fringes develop on the light source side as opposed to the detector side. To this end, a narrow-band chaotic light source and a gated detector are used in the frequency-time domain, which emulate a randomly pointing incoherent light source and a stationary pinhole detector in the momentum-space domain, respectively. Spectral fringes with visibility that closely follows a sinc function of spectral bandwidth are clear evidence that legitimate TGD fringes due to two-photon interference develop even with classical light.

DOI
10.48550/arxiv.1805.06592

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Temporal ghost diffraction (TGD) is observed by taking two-photon cross-correlation in the configuration of reciprocal two-slit diffraction (2SD) where interference fringes develop on the light source side as opposed to the detector side. To this end, a narrow-band chaotic light source and a gated detector are used in the frequency-time domain, which emulate a randomly pointing incoherent light source and a stationary pinhole detector in the momentum-space domain, respectively. Spectral fringes with visibility that closely follows a sinc function of spectral bandwidth are clear evidence that legitimate TGD fringes due to two-photon interference develop even with classical light.
Temporal ghost diffraction (TGD) is observed by taking two-photon cross-correlation in the configuration of reciprocal two-slit diffraction where interference fringes develop on the light source side as opposed to the detector side. To this end, a narrow-band chaotic light source and a gated detector are used in the frequency-time domain, which emulate a randomly pointing incoherent light source and a stationary pinhole detector in the momentum-space domain, respectively. Spectral fringes with a signed visibility that closely follows a sinc function of the spectral bandwidth are clear evidence that legitimate TGD fringes due to two-photon interference have developed. This compares with the previous attempt [M. Bellini et al., Phys. Rev. Lett. 90, 043602 (2003)] that is essentially ``ghost imaging of spectral fringes'' to be distinguished from TGD, which implies that the putative GD reports in the literature might demand a revision in terms of their physical insights.
The time domain is a one-dimensional space, and hence the diffraction–interference in three dimensions is absent. However, ghost diffraction–interference (GD) building on a two-particle-enabled Young's experiment is still relevant. This is because fixed-timing detection can emulate pinhole detection at the core of GD. Here is demonstrated a different class of GD free of pinhole detection in the time domain. The bucket detection in ghost imaging enables it, which is best paraphrased as “ghost diffraction–interference via ghost imaging.”
An attempt is made to implement acoustic ghost diffraction in the space-momentum domain using ultrasound. The Hanbury Brown—Twiss effect helps ghost diffraction—interference fringes hidden in a large backdrop of first-order fringes to materialize only after making the two emitters mutually incoherent in a post-selective manner, which is leveraged by programmed decoherence. Cross correlation of phononic coherent states is taken in a reciprocal two-slit diffraction geometry so that nontrivial fringes due to virtual one-phonon diffraction—interference fringes emulated by two phonons emerge on the side of the transmitter as opposed to the receiver.
Single-photon interference experiments are attempted in the time domain using true single-photon streams. Self-heterodyning beats are clearly observed by letting the field associated with a single photon interfere with itself on a field-quadratic detector, which is a time analogue of Young's two-slit interference experiment. The temporal first-order coherence of single-photon fields, i.e., transient interference fringes, develops as cumulative detection events are mapped point-by-point onto a virtual capture frame by properly correlating the time-series data. The ability to single out photon counts at a designated timing paves the way for digital heterodyning with faint light for such use as phase measurement and quantum information processing.
A double-slit ghost interference experiment performed on an entangled resource using type-II non-collinear degenerate spontaneous parametric down-conversion (SPDC) is demonstrated.The influence of the distance between the double-slit and the bucket detector preceded by a pinhole is studied.The experimental results show that the interference fringes become increasingly distinct with higher visibility when the pinhole-double-slit distance increases.A first-order classical theory based on the Klyshko's two-photon advanced-wave picture, and a second-order quantum-image theory are provided for explanations.The fitting results indicate that the divergence of the converted fluorescence significantly affects the ghost fringes.
The two-photon temporal coincidence detection amplitude obeys a pair of equations identical to those of classical partially coherent plane-wave pulses propagating in linearly dispersive media. These equations are also the same as the paraxial Wolf equations, for both the two-photon spatial probability amplitude and the cross-spectral density function. Therefore, a fourfold analogy between space and time, as well as between quantum entanglement and partial coherence, arises. In accordance to this, we predict nonlocal interference structures in a fourth-order interferometric configuration with classical partially coherent pulses under the assumption of Gaussian statistics. As an example, we present the classical temporal counterpart of the ghost diffraction phenomenon. Our work suggests that some time-domain entanglement phenomena that hitherto were considered as uniquely quantum can be mimicked by conventional partially coherent light pulses.