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arXiv:1702.07391 · Physical Review A

Free-space entangled quantum carpets

Mariana R. Barros, Andreas Ketterer, O. Jiménez Farías, Stephen Patrick Walborn

Published Apr 10, 2017• 15 citations
arXivHTMLPDF

Abstract

The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as ``quantum carpets,'' corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a $D$-level qudit in such a way that the Talbot effect can be used to process the $D$-dimensional quantum information [Far\'{\i}as et al., Phys. Rev. A 91, 062328 (2015)]. Here we introduce a scheme to produce free-propagating ``entangled quantum carpets'' with pairs of photons produced by spontaneous parametric down-conversion. First we introduce an optical device that can be used to synthesize arbitrary superposition states of Talbot qudits. Sending spatially entangled photon pairs through a pair of these devices produces an entangled pair of qudits. As an application, we show how the Talbot effect can be used to test a $D$-dimensional Bell inequality. Numerical simulations show that violation of the Bell inequality depends strongly on the amount of spatial correlation in the initial two-photon state. We briefly discuss how our optical scheme might be adapted to matter wave experiments.

DOI
10.1103/physreva.95.042311

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The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as quantum carpets,'' corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a $D$-level qudit in such a way that the Talbot effect can be used to process the $D$-dimensional quantum information [Far\'{\i}as et al., Phys. Rev. A 91, 062328 (2015)]. Here we introduce a scheme to produce free-propagating entangled quantum carpets'' with pairs of photons produced by spontaneous parametric down-conversion. First we introduce an optical device that can be used to synthesize arbitrary superposition states of Talbot qudits. Sending spatially entangled photon pairs through a pair of these devices produces an entangled pair of qudits. As an application, we show how the Talbot effect can be used to test a DDD-dimensional Bell inequality. Numerical simulations show that violation of the Bell inequality depends strongly on the amount of spatial correlation in the initial two-photon state. We briefly discuss how our optical scheme might be adapted to matter wave experiments.
Single-photon interference due to passage through a periodic grating is considered in a novel proposal for processing DDD-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free-space propagation naturally implements basic single-quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near-field diffraction regime. By adding a diagonal phase gate, we show that a complete set of single-quDit gates can be implemented. We then introduce a spatially dependent beam splitter that allows for projective measurements in the computational basis and can be used for the implementation of controlled operations between two quDits. Universal quantum information processing can then be implemented with linear optics and ancilla photons via postselection and feed-forward following the original proposal of Knill-Laflamme and Milburn. Although we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.
Abstract We report a proof of concept experiment illustrating the implementation of several simple quantum logic gates on D -level quantum systems (quDits) using the Talbot effect. A number of QuDit states are encoded into the transverse profile of a paraxial laser beam using a spatial light modulator. These states are transformed through a diagonal phase element and then free-propagation via the fractional Talbot effect, demonstrating the realization of some well-known single quDit gates in quantum computation. Our classical optics experiment allows us to identify several important technical details, and serves as a first experimental step in performing D -dimensional quantum operations with single photons or other quantum systems using this scheme.
We report an experiment to generate and propagate two entangled spatial qudits, [Formula: see text]-dimensional quantum systems, using spontaneous parametric down-conversion. The manipulation, via pump beam, of the transverse spatial correlation between the photon pairs is explored. Inserting apertures with [Formula: see text]-slits in the arms of the down-converted photons, we associate the qudit space with the [Formula: see text] possible paths followed by each photon. Experimental results for qudits with [Formula: see text] and 8 are shown. We demonstrate that the generated states cannot be classically correlated. We also show the propagation of entangled states of spatial qudits. Their free-space distribution is performed at the laboratory scale and the propagated states maintain a high fidelity with their original form.
We show the propagation of entangled states of high-dimensional quantum systems. The qudits states were generated using the transverse correlation of the twin photons produced by spontaneous parametric down-conversion. Their free-space distribution was performed at the laboratory scale and the propagated states maintained a high fidelity with their original form. The use of entangled qudits allow an increase in the quantity of information that can be transmitted and may also guarantee more privacy for communicating parties. Therefore, studies about propagating entangled states of qudits are important for the effort of building quantum communication networks.
The Talbot effect, a wave-optical self-imaging phenomenon originally observed in real-space, has developed into a powerful framework for programmable modal transformations across diverse physical platforms. Here, we report the experimental demonstration of nonlocal Talbot transformations within a high-dimensional, orbital angular momentum (OAM) entangled two-photon system. By exploiting the intrinsic nonlocal correlations generated through spontaneous parametric down-conversion, we show that applying an azimuthal Talbot phase on one photon of an entangled pair is sufficient to coherently reshape the OAM modal distribution of its spatially separated partner, without any direct local operation on the latter. As a proof of principle, we further demonstrate the inverse Talbot transformation within the same platform by incorporating the required quadratic phase during the state-preparation stage. These results extend Talbot physics from local mode manipulation to entanglement-assisted nonlocal transformations in a high-dimensional discrete basis. The demonstrated platform opens versatile routes toward conditional remote OAM-mode conversion, structured entangled-state engineering, and high-dimensional quantum information processing.
Nonlinear holography shapes the amplitude and phase of generated new harmonics using nonlinear processes. Classical nonlinear holography influenced many fields in optics, from information storage, demultiplexing of spatial information, and all-optical control of accelerating beams. Here, we extend the concept of nonlinear holography to the quantum regime. We directly shape the spatial quantum correlations of entangled photon pairs in two-dimensional patterned nonlinear photonic crystals using spontaneous parametric down conversion, without any pump shaping. The generated signal-idler pair obeys a parity conservation law that is governed by the nonlinear crystal. Furthermore, the quantum states exhibit quantum correlations and violate the Clauser-Horne-Shimony-Holt inequality, thus enabling entanglement-based quantum key distribution. Our demonstration paves the way for controllable on-chip quantum optics schemes using the high-dimensional spatial degree of freedom.