We demonstrate effective control of spatial degrees of freedom for photon pairs generated in a multimode nonlinear waveguide by dispersive properties of the structure. This is confirmed by observation of Shih-Alley polarization entanglement.
The propagation of several spatial modes has a significant impact on the structure of the emission from parametric down-conversion in a nonlinear waveguide. This manifests itself not only in the spatial correlations of the photon pairs but also, due to new phase-matching conditions, in the output spectrum, radically altering the degree of entanglement within each pair. Here we investigate both theoretically and experimentally the results of higher-order spatial-mode propagation in nonlinear waveguides. We derive conditions for the creation of pairs in these modes and present observations of higher-order mode propagation in both the spatial and spectral domains. Furthermore, we observe correlations between the different degrees of freedom and finally we discuss strategies for mitigating any detrimental effects and optimizing pair production in the fundamental mode.
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).