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arXiv:0906.2642 · Applied Physics Letters

Polarization entanglement with graded-index lenses

Giuseppe Vallone, Gaia Donati, F. De Martini, Paolo Mataloni

Published Nov 2, 2009• 4 citations
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Abstract

By using an optical device based on the integration of a graded-index (GRIN) rod lens and a single-mode optical fiber we efficiently collected photon pairs generated by spontaneous parametric down-conversion. We show that this system preserves the polarization entanglement of the two-photon states. Hence this device, characterized by a remarkable easiness of alignment and allowing for high coupling efficiency of single-mode radiation, can be used with photons entangled in various degrees of freedom, such as polarization and spatial momentum and to interconnect different sides of complex optical circuits.

DOI
10.1063/1.3257376

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By using an optical device based on the integration of a graded-index (GRIN) rod lens and a single-mode optical fiber we efficiently collected photon pairs generated by spontaneous parametric down-conversion. We show that this system preserves the polarization entanglement of the two-photon states. Hence this device, characterized by a remarkable easiness of alignment and allowing for high coupling efficiency of single-mode radiation, can be used with photons entangled in various degrees of freedom, such as polarization and spatial momentum and to interconnect different sides of complex optical circuits.
We present a novel optical device based on an integrated system of microlenses and single-mode optical fibers. It allows us to collect and direct into many modes two photons generated by spontaneous parametric down-conversion. By this device multiqubit entangled states and/or multilevel qudit states of two photons, encoded in the longitudinal momentum degree of freedom, are created. The multipath photon entanglement realized by this device is expected to find important applications in modern quantum information technology.
The transverse momentum correlation of photon pairs generated by noncollinear spontaneous parametric down-conversion with type-I phase matching is transformed into polarization entanglement. A robust wavefront-splitting interferometer scheme is used, due to which the phase of the entangled state does not require active stabilization. Frequency-degenerate signal and idler photons are separated and coupled into single-mode optical fibers. The concept is demonstrated in a compact and modular setup. A straightforward alignment process for producing any of the Bell states is presented. The entangled source has an output photon flux of $8.33\ifmmode\pm\else\textpm\fi{}1.27$ kcps/mW normalized to pump power (150 mW), and $17\ifmmode\pm\else\textpm\fi{}3%$ heralding ratio. The measured state fidelity with respect to the negative anticorrelated Bell state is $0.951\ifmmode\pm\else\textpm\fi{}0.004$.
We present a study of spontaneously arisen spatially entangled photon pairs via intermodal four-wave mixing in a graded-index multimode optical fiber. Unique dispersive features of the fiber allow spectral indistinguishability of two different phase-matched processes, producing entangled pairs of spatial qubits. The bases are realized as superpositions of orthogonal transverse fiber modes having opposite parities. In particular, we take into consideration the spectral properties of the processes by examining their joint spectral amplitudes. It is shown that illuminating graded-index optical fiber with different pump wavelengths has an impact upon efficiency parameters accordingly the degree of spatial entanglement and gives rise to photon pairs with various spectral purities. Photons with higher spectral purity enable desired single-photon based interactions to take place, whereas photons with lower spectral purity exhibit hybrid entanglement in frequency and transverse mode. We also discuss Wigner function formalism and parity-displacement-based realization to characterize spatial properties of the states, as well as to verify quantum entanglement through a violation of Clauser-Horne-Shimony-Holt inequality.
It is known that photons produced by spontaneous parametric down-conversion can be coupled into optical fibers more efficiently by focusing the pump field. We find that focusing the pump in type-II down-conversion causes photons of ordinary and extraordinary polarization to acquire very different angular spreads, which amounts to spatial information that distinguishes between the polarization states. Numerical studies predict that the photons collected by a detector or quantum channel will be of predominantly one polarization and that the degree of polarization entanglement will be lessened in some cases.
Two-photon states generated from spontaneous parametric down-conversion (SPDC) can display entanglement in all degrees of freedom (DoFs) of light, including spatial, temporal, and polarization. The coupling between different DoFs of a two-photon state has been shown to display rich structures that enable novel and robust information processing schemes. While existing literature has studied these couplings by post-selecting the SPDC field, a comprehensive understanding of the inherent spatial-polarization coupling produced in the SPDC process is still lacking. This work produces a full spatial map of the polarization entanglement generated across the entire SPDC field, which contains an entire class of near-maximally polarization-entangled states with an average concurrence of 0.8303 +/- 0.0004. The spatial-polarization coupling manifests as radially or linearly varying polarization-entangled states, whose wavefunctions are dependent on the transverse momenta of the down-converted photons and the pump beam, respectively. Our study lays important groundwork for further exploiting the coupling between entanglement in different DoFs for future quantum technologies
We present two experiments geared toward the realization of a robust and intense source of polarization-entangled photons. First, we describe a novel source of polarization-entangled pairs that uses periodically-poled potassium titanyl phosphate (PPKTP) and an interferometer based on polarization beam displacers. The source emits an intense flux of high-quality single-mode entangled photons and is stable, robust, and easy to align. Second, we report on sources of correlated photons generated in PPKTP waveguides. Waveguide sources of correlated pairs have been shown to generate high fluxes of pairs: we theoretically and experimentally investigate spontaneous parametric down-conversion generation of photon pairs in waveguides at different wavelengths.