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arXiv:1606.01279 · Physical Review A

Generation of energy-entangled W states via parametric fluorescence in integrated devices

M. Menotti, Lorenzo Maccone, John E. Sipe, Marco Liscidini

Published Jul 26, 2016• 15 citations
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Abstract

Tripartite entangled states, such as Greenberger-Horne-Zeilinger and W states, are typically generated by manipulating two pairs of polarization-entangled photons in bulk optics. Here we propose a scheme to generate W states that are entangled in the energy degree of freedom in an integrated optical circuit. Our approach employs photon pairs generated by spontaneous four-wave mixing in a microring resonator. We also present a feasible procedure for demonstrating the generation of such a state, and we compare polarization-entangled and energy-entangled schemes for the preparation of W states.

DOI
10.1103/physreva.94.013845

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Tripartite entangled states, such as Greenberger-Horne-Zeilinger and W states, are typically generated by manipulating two pairs of polarization-entangled photons in bulk optics. Here we propose a scheme to generate W states that are entangled in the energy degree of freedom in an integrated optical circuit. Our approach employs photon pairs generated by spontaneous four-wave mixing in a microring resonator. We also present a feasible procedure for demonstrating the generation of such a state, and we compare polarization-entangled and energy-entangled schemes for the preparation of W states.
Tripartite entangled states, such as Greenberger-Horne-Zeilinger (GHZ) and W states, are appealing for tests of fundamental aspects of quantum mechanics, as well as for implementations of quantum communication protocols. While the information is typically encoded in the polarization or path of the photons, we propose a feasible scheme to generate W states that are entangled in the energy degree of freedom. This is achieved by propagating photon pairs generated by parametric fluorescence in a linear optical circuit and post-selecting on the output channels. Such source can be easily integrated, profiting from high stability and a compact footprint. We also present a simple protocol to characterize the generated tripartite state, which is based on the reduced density matrix approach. Unexpectedly, although we rely on the energy degree of freedom, the full state tomography does not require any frequency conversion.
We study the generation of Greenberger-Horne-Zeilinger (GHZ) states of three path-encoded photons. Inspired by the seminal work of Bouwmeester et al. [1] on polarization-entangled GHZ states, we find a corresponding path representation for the photon states of an optical circuit, identify the elements required for the state generation, and propose a possible implementation of our strategy. Besides the practical advantage of employing an integrated system that can be fabricated with proven lithographic techniques, our example suggests that it is possible to enhance the generation efficiency by using microring resonators.
We propose two interesting methods of generating the four-photon W state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon W state, the three-photon Greenberger–Horne–Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general n -photon W state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.
We propose two interesting methods of generating the four-photon WWW state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon WWW state, the three-photon Greenberger-Horne-Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general nnn-photon WWW state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.
Photonic integrated circuits (PICs) based on silicon-on-insulator (SOI) substrates provide a lightweight, compact platform for applications in quantum optics. We show the evaluation and characterization of an SOI-bascd PIC design for an entangled photon pair source, generating photon pairs by means of the nonlinear process of spontaneous four-wave mixing in microring resonators. Experimental results following from the chip fabrication fed back into the simulated parameter tuning effects, culminating in photon pair generation with measured correlations exceeding classically predicted limits.