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Applied Physics Letters

Observation of quantum Talbot effect from a domain-engineered nonlinear photonic crystal

Hongming Jin, Ping Xu, J. S. Zhao, H. Y. Leng, M. L. Zhong, Shining N. Zhu

Published Nov 19, 2012• 11 citations
Publisher

Abstract

The quantum Talbot effect is observed from a domain-engineered nonlinear photonic crystal dispensing with a real grating. We deduce and experimentally verify the quantum self-imaging formula which is related to the crystal's structure parameter and working wavelengths. A two-photon Talbot carpet is captured to characterize the Fresnel diffraction dynamics of entangled photons wherein the quantum fractional Talbot effect is specified. The compact and stable quantum Talbot effect can be considered as the contactless diagnosis of domain's homogeneity and developed for new types of entangled photon source and quantum technologies such as quantum lithography with improved performance.

DOI
10.1063/1.4766728

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The quantum Talbot effect is observed from a domain-engineered nonlinear photonic crystal dispensing with a real grating. We deduce and experimentally verify the quantum self-imaging formula which is related to the crystal's structure parameter and working wavelengths. A two-photon Talbot carpet is captured to characterize the Fresnel diffraction dynamics of entangled photons wherein the quantum fractional Talbot effect is specified. The compact and stable quantum Talbot effect can be considered as the contactless diagnosis of domain's homogeneity and developed for new types of entangled photon source and quantum technologies such as quantum lithography with improved performance.
We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first- and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.
Lenses play a key role in quantum imaging but inevitably constrain the spatial resolution and working wavelength. In this work we develop and demonstrate a lensless quantum ghost imaging by engineering quadratic nonlinear photonic crystals. With a transverse parabolic domain modulation introduced into the lithium tantalate crystal, the entangled photon pairs generated from parametric down-conversion will self-focus. Therefore we can dispense with additional lenses to construct imaging in a nonlocal way. The lensless imaging is found to follow a specific imaging formula where the effective focal length is determined by the domain modulation and pump wavelength. Additionally, two nonlocal images can be retrieved when the entangled photon pair is generated under two concurrent noncollinear phase-matching geometries. Our work provides a principle and method to realize lensless ghost imaging, which may be extended to other wavelengths and stimulate new types of practical quantum technologies.
The second-order Talbot effect is analyzed for a periodic object illuminated by entangled photon pairs in both the quantum imaging and quantum lithography configurations. The Klyshko picture is applied to describe the quantum imaging scheme, in which self-images of the object that may or may not be magnified can be observed nonlocally in the photon coincidences but not in the singles count rate. In the quantum lithography setup, we find that the second-order Talbot length is half that of the classical first-order case, thus the resolution may be improved by a factor of 2.
Wave propagation on the surface of cylinders exhibits interferometric self-imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a higher-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-core fiber, our findings open the door to applications in optical telecommunications as a compact beam multiplexer as well as in quantum information processing tasks as a scalable realization of a linear optical network.
We demonstrate the quantum Talbot effect using a beam of single photons produced by parametric down conversion. In contrast to the previous works, we use a programmable spatial light modulator to behave as a diffraction grating. Thus, the investigation of the Talbot diffraction patterns under the variation of grating structure can be easily performed. The influence of spectral bandwidth of the down-converted photons on the diffraction pattern is also investigated. A theoretical model based on the wave nature of photons is presented to explain the Talbot diffraction patterns under varying conditions. The measured diffraction patterns are in good agreement with the theoretical prediction. We are convinced that our study improves the understanding of the quantum Talbot effect.
The electromagnetically induced Talbot effect (EITE) resulting from the repeated self-reconstruction of a spatially intensity-modulated probe field is experimentally demonstrated in a three-level atomic configuration. The probe beam is launched into an optically induced lattice (established by the interference of two coupling fields) inside a rubidium vapor cell and is diffracted by the electromagnetically induced grating that was formed. The diffraction pattern repeats itself at the planes of integer multiple Talbot lengths. In addition, a fractional EITE is also investigated. The experimental observations agree well with the theoretical predictions. This investigation may potentially pave the way for studying the nonlinear and quantum dynamical features that have been predicted for established periodic optical systems.