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arXiv:1701.05769 · Physical Review A

Generation and characterization of discrete spatial entanglement in multimode nonlinear waveguides

Michał Jachura, Michał Karpiński, Konrad Banaszek, Divya Bharadwaj, Jasleen Lugani, Krishnan Thyagarajan

Published Mar 20, 2017• 4 citations
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Abstract

We analyze theoretically spontaneous parametric down-conversion in a multimode nonlinear waveguide as a source of entangled pairs of spatial qubits, realized as superpositions of a photon in two orthogonal transverse modes of the waveguide. It is shown that, by exploiting intermodal dispersion, down-conversion into the relevant pairs of spatial modes can be selected by spectral filtering, which also provides means to fine tune the properties of the generated entangled state. We also discuss an inverting interferometer detecting the spatial parity of the input beam as a versatile tool to characterize properties of the generated state. A single-photon Wigner function obtained by a scan of the displaced parity can be used to identify the basis modes of a spatial qubit, whereas correlations between displaced parity measurements on two photons can directly verify quantum entanglement through a violation of Bell's inequalities.

DOI
10.1103/physreva.95.032322

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We analyze theoretically spontaneous parametric down-conversion in a multimode nonlinear waveguide as a source of entangled pairs of spatial qubits, realized as superpositions of a photon in two orthogonal transverse modes of the waveguide. It is shown that, by exploiting intermodal dispersion, down-conversion into the relevant pairs of spatial modes can be selected by spectral filtering, which also provides means to fine tune the properties of the generated entangled state. We also discuss an inverting interferometer detecting the spatial parity of the input beam as a versatile tool to characterize properties of the generated state. A single-photon Wigner function obtained by a scan of the displaced parity can be used to identify the basis modes of a spatial qubit, whereas correlations between displaced parity measurements on two photons can directly verify quantum entanglement through a violation of Bell's inequalities.
We present a scheme for generation and characterization of entangled spatial qubits based on type-II spontaneous parametric down-conversion (SPDC) in a periodically poled titanyl phosphate (PPKTP) multimode nonlinear waveguide [1]. Our scheme exploits intermodal dispersion which has been hitherto successfully employed to produce spatially pure SPDC photon pairs from a multimode waveguide without spatial filtering [2]. Production of discrete entanglement relies on driving simultaneously two SPDC processes that involve different combinations of transverse spatial modes for which phase matching bandwidths significantly overlap. We propose a procedure for experimental identification of the spatial qubit subspace based on a scan of the spatial Wigner function via the displaced parity measurement using an inverting Sagnac interferometer and photon counting. We numerically verified the robustness of the mode reconstruction procedure against experimental imperfections. We also propose an experimental method for detecting spatial entanglement in the position-wave vector phase space. Numerical simulations indicate that waveguide parameters required for experimental demonstrations are compatible with current manufacturing capabilities. Using simulated mode profiles we calculate the maximum attainable Clauser-Horne- Shimony-Holt combination value reaching 2.12, which clearly violates the classical limit and confirms the feasibility of observing non-classical features of the generated state. [1] M. Jachura et al. Physical Review A, 95, 032322 (2017). [2] M. Jachura, M. Karpiński, C. Radzewicz, K. Banaszek, Optics Express, 22, 8624-8632 (2014).
We present experimental realization of type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide. We demonstrate that by careful exploitation of intermodal dispersion in the waveguide it is feasible to produce photon pairs in well defined transverse modes without any additional spatial filtering at the output. Spatial characteristics is verified by measurements of the M2 beam quality factors. We also prepared a postselected polarization-entangled two-photon state shown to violate Bell’s inequality. Similar techniques based on intermodal dispersion can be used to generate spatial entanglement and hyperentanglement.
We present a study of the propagation of higher-order spatial modes in a waveguided parametric down-conversion photon-pair source. Observing the multimode photon-pair spectrum from a periodically poled KTiOPO(4) waveguide allowed us to isolate individual spatial modes through their distinctive spectral properties. We have measured directly the spatial distribution of each mode of the photon pairs, confirming the findings of our waveguide model, and demonstrated by coincidence measurements that the total parity of the modes is conserved in the nonlinear interaction. Furthermore, we show that we can combine the advantages of a waveguide source with the potential to generate spatially entangled photon pairs as in bulk-crystal down-converters.
We predict that all-optically-reconfigurable generation of photon pairs with tailored spatial entanglement can be realized via spontaneous parametric down conversion in integrated nonlinear coupled waveguides. The required elements of the output quantum wave function are directly mapped from the amplitudes and phases of the classical laser pump inputs in each waveguide. This is achieved through special nonuniform domain poling, which locally inverts the sign of quadratic nonlinear susceptibility and accordingly shapes the interference of biphoton quantum states generated along the waveguides. We demonstrate a device configuration for the generation of any linear combination of two-photon Bell states.
Summary form only given. Correlated photons are a key ingredient of many experiments testing the foundations of quantum mechanics and in quantum information processing. Many of these experiments harness entanglement by means of the nonclassical interference of photon pairs. A critical issue for such experiments is the mode matching of the photonic wave packets. Spontaneous parametric down-conversion is a well-established and practical method for generating pairs of correlated photons. High visibility interference of photon pairs generated by down-conversion in bulk crystals, a standard source for this type of experiments, can be achieved only by significant spatial filtering, which dramatically reduces the useful fraction of photon pairs. It also reduces the correlations between the presence of photons, thus opening for example the efficiency loophole in tests of Bell's inequalities. Nonlinear waveguides, compared to bulk crystals, offer several advantages as a source of correlated photon pairs. Most importantly, the waveguide structure provides a means to control precisely the spatial characteristics of generated photons, because of the well-defined transverse modes of the guide. in addition, nonlinear waveguides offer both higher pair production rates by utilizing the technique of quasiphase matching, and possibilities for spectral mode engineering.