Classical Imaging with Undetected Photons

Abstract

Barreto Lemos et al. [Nature 512, 409-412 (2014)] reported an experiment in which a non-degenerate parametric downconverter and a non-degenerate optical parametric amplifier-used as a wavelengthconverting phase conjugator-were employed to image object transparencies in a manner akin to ghost imaging. Their experiment, however, relied on single-photon detection, rather than the photon-coincidence measurements employed in ghost imaging with a parametric downconverter source. More importantly, their system formed images despite the photons that passed through the object never being detected. Barreto Lemos et al. interpreted their experiment as a quantum imager, as assuredly it is, owing to its downconverter's emitting entangled signal and idler beams. We show, however, that virtually all the features of their setup can be realized in a quantum-mimetic fashion using classical-state light, specifically a pair of bright pseudothermal beams possessing a phasesensitive cross correlation. Owing to its much higher signal-to-noise ratio, our bright-source classical imager could greatly reduce image-acquisition time compared to that of Barreto Lemos et al.'s quantum system, while retaining the latter's ability to image with undetected photons.Light is intrinsically quantum mechanical, and photodetection is a quantum measurement. Consequently, all imaging is really quantum mechanical. It has long been known, however, that the semiclassical theory of photodetection-in which light is a classical field and the discreteness of the electron charge results in photodetection shot noise-predicts measurement statistics identical to those obtained from quantum theory when the illumination is in a classical state, namely a Glauber coherent state or a classically-random mixture of such states. (See Ref. 1 for a review of quantum versus semiclassical photodetection.) Thus, because experiments whose quantitative behavior is correctly predicted by two disparate theories cannot distinguish between those two theories, it is entirely appropriate that the term quantum imaging be reserved for imagers whose quantitative understanding requires the use of quantum theory. (See Refs. 2-4 for how a debate on this point has been settled with regards to pseudothermal ghost imaging.)Three-wave mixing in a second-order nonlinear material is the workhorse of nonclassical light-beam generation, with spontaneous parametric downconverters producing entangled signal and idler beams 5 , optical parametric amplifiers producing squeezed-vacuum states 6 , and optical parametric oscillators producing photon-twin beams 7 . It follows that imagers using any such sources will be quantum imagers, according to the criterion described in the preceding paragraph. Two such examples are the initial ghost-imaging experiment 8 , and quantum optical coherence tomography (Q-OCT) 9,10 . Both used continuous-wave (cw) spontaneous parametric downconversion (SPDC) sources, whose signal and idler outputs were taken to comprise streams of biphotons detectable by photon-coincidence c...

Optical sectioning in induced coherence tomography with frequency-entangled photons

“…We have demonstrated it using frequency-entangled photons generated in SPDC processes embedded in a nonlinear interferometer. Notwithstanding, Shapiro et al [32] have shown that similar results can also be obtained using a pair of bright pseudo-thermal beams possessing a phase-sensitive cross correlation.…”

Three-dimensional classical imaging of a pattern localized in a phase space

“…The imaging laser beam is not interacting with actual objects used to produce the localized phase space pattern. Imaging of objects localized in a position space has been realized with quantum & classical methods with undetected photons [8,9]. Quantum imaging with undetected photons, and unlike the ghost imaging [10][11][12][13][14][15][16], does not rely on coincidence detection of photons.…”