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Asia Communications and Photonics Conference

Spiral Holographic Imaging through Quantum Interference

Jie Ying Tang, Yang Ming, Wei Hu, Yanqing Lu

Published Jan 1, 2017• 0 citations
Publisher

Abstract

Spiral holographic imaging based on the Hong-Ou–Mandel (HOM) interference scheme is introduced. The first-order interference of light beams in standard holographic imaging is replaced by the quantum interference of two-photon probability amplitudes. The full information of the object can be recorded in the joint orbital angular momentum spectrum.

DOI
10.1364/acpc.2017.s3j.7

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Spiral holographic imaging based on the Hong-Ou–Mandel (HOM) interference scheme is introduced. The first-order interference of light beams in standard holographic imaging is replaced by the quantum interference of two-photon probability amplitudes. The full information of the object can be recorded in the joint orbital angular momentum spectrum.
Spiral holographic imaging in the Hong-Ou–Mandel interference scheme is introduced. Using spontaneous parametric down-conversion as a source of photon pairs, we analyze the joint orbital angular momentum spectrum of a reference photon and the photon encoding information of the object. The first-order interference of light beams in standard holographic imaging is replaced by the quantum interference of two-photon probability amplitudes. The difficulty in retrieving the amplitude and phase structure of an unknown photon is thereby avoided as classical interferometric techniques such as optical holography do not apply. Our results show that the full information of the object's transmission function can be recorded in the spiral hologram, which originates directly from the joint orbital angular momentum spectrum. This presents a lateral demonstration of compressive imaging and can potentially be used for remote sensing.
The concept of correlated two-photon spiral imaging is introduced. We begin by analyzing the joint orbital angular momentum (OAM) spectrum of correlated photon pairs. The mutual information carried by the photon pairs is evaluated, and it is shown that when an object is placed in one of the beam paths the value of the mutual information is strongly dependent on object shape and is closely related to the degree of rotational symmetry present. After analyzing the effect of the object on the OAM correlations, the method of correlated spiral imaging is described. We first present a version using parametric down-conversion, in which entangled pairs of photons with opposite OAM values are produced, placing an object in the path of one beam. We then present a classical (correlated, but nonentangled) version. The relative problems and benefits of the classical versus entangled configurations are discussed. The prospect is raised of carrying out compressive imaging via two-photon OAM detection to reconstruct sparse objects with few measurements.
Two particle interference phenomena, such as the Hong–Ou–Mandel (HOM) effect, are a direct manifestation of the nature of the symmetry properties of indistinguishable particles as described by quantum mechanics. The HOM effect has recently been applied as a tool for pure state tomography of a single photon. In this article, we generalize the method to extract additional information for a pure state and extend this to the full tomography of mixed states as well. The formalism is kept general enough to apply to both boson and fermion based interferometry. Our theoretical discussion is accompanied by two proposals of interferometric setups that allow the measurement of a tomographically complete set of observables for single photon quantum states.
The Hong–Ou–Mandel (HOM) interference of two light beams having different longitudinal spatial coherence properties is investigated theoretically and experimentally. The normalized second-order correlation function ( g ( 2 ) ) is determined for the interfering photons from two sources of different angular widths using Feynman’s path integral theory. We find that the difference in angular width of the sources has an explicit impact on the HOM interference pattern, which can be quantified through the visibility and full width at half maxima of the HOM dip. The effect of distinguishability of the interfering longitudinally spatially coherent beams on the HOM dip is verified experimentally and is analogous to non-classical HOM interference. The magnitude of the angular width of beams manifested through the difference in angular width has a significant impact. Along with the difference of two sources, this HOM scheme is sensitive to the angular spectrum width of each source. The enhanced sensitivity can be useful in the remote sensing of objects and beams in metrological applications. This work can play a significant role in fundamental and applied physics.
We demonstrate that the combination of digital spiral imaging with high-dimensional orbital angular momentum (OAM) entanglement can be used for efficiently probing and identifying pure phase objects, where the probing light does not necessarily touch the object, via the experimental, non-local decomposition of non-integer pure phase vortices in OAM-entangled photon pairs. The entangled photons are generated by parametric downconversion and then measured with spatial light modulators and single-mode fibers. The fractional phase vortices are defined in the idler photons, while their corresponding spiral spectra are obtained non-locally by scanning the measured OAM states in the signal photons. We conceptually illustrate our results with the biphoton Klyshko picture and the effective dimensionality to demonstrate the high-dimensional nature of the associated quantum OAM channels. Our result is a proof of concept that quantum imaging techniques exploiting high-dimensional entanglement can potentially be used for remote sensing. Photon pairs entangled in their orbital angular momentum can reveal information about an object with a complex phase profile. Lixiang Chen and co-workers from China and Scotland used entangled photons to recover the spiral spectrum of an optical fractional phase vortex. First they used a beta barium borate crystal to generate a pair of signal and idler entangled photons through spontaneous parametric downconversion. They then split the beam into two arms, each containing a programmable spatial light modulator (SLM) that can imprint any desired phase profile onto an incident photon. By encoding a fractional phase vortex on the SLM of one arm, and scanning through different orbital angular momentum values on the SLM of the other arm, the team recovered the spiral spectra of the fractional phase vortex nonlocally.