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arXiv:quant-ph/0510218 · Physical Review A

Theory and experiment of entanglement in a quasi-phase-matched two-crystal source

Daniel Ljunggren, Maria Tengner, Philip A. Marsden, Matthew A. Pelton

Published Mar 20, 2006• 30 citations
arXivHTMLPDF

Abstract

We report results regarding a source of polarization entangled photon pairs created by the process of spontaneous parametric downconversion in two orthogonally oriented, periodically poled, bulk ${\mathrm{KTiOPO}}_{4}$ crystals. The source emits light colinearly at the nondegenerate wavelengths of 810 and $1550\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and is optimized for a single-mode optical fiber collection and long-distance quantum communication. The configuration favors long crystals, which promote a high photon-pair production rate at a narrow bandwidth, together with a high pair probability in fibers. The quality of entanglement is limited by chromatic dispersion, which we analyze by determining the output state. We find that such a decoherence effect is strongly material dependent, providing for long crystals an upper bound on the visibility of the coincidence fringes of 41% for ${\mathrm{KTiOPO}}_{4}$, and zero for ${\mathrm{LiNbO}}_{3}$. The best obtained raw visibility, when canceling decoherence with an extra piece of crystal, was $91\ifmmode\pm\else\textpm\fi{}0.2%$, including background counts. We confirm by a violation of the CHSH-inequality ($S=2.679\ifmmode\pm\else\textpm\fi{}0.004$ at $55\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1∕2}$ standard deviations) and by complete quantum state tomography that the fibers carry high-quality entangled pairs at a maximum rate of $55\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{THz}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{mW}}^{\ensuremath{-}1}$.

DOI
10.1103/physreva.73.032326

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We extend our earlier results of a bright source of non‐degenerate polarization entangled photon‐pairs by making a thorough theoretical and experimental investigation of its single‐mode emission and state‐decoherence. Using two perpendicular bulk crystals of periodically poled KTP, the source directly creates the polarization‐entangled state (|HH〉 + |VV〉)/√ with signal and idler wavelengths of 810 nm and 1550 nm, respectively. In order to optimize the coupling into single‐mode fiber we have developed a numerical algorithm which determines the emission mode and the fiber coupling efficiency for a given crystal length and focussing of the pump. For a 4.5 mm long crystal the optimal focussing of the pump is to a beam waist radius of 14 μm. With these focussing conditions the computer calculations give the lowest M2 value for the emission mode, M2 ≈ 3, and the best possible fiber coupling efficiency, γ ≈ 75%. Using the theoretical results to optimize our experimental setup we obtained photon count rates of 1.4 MHz singles and 12 kHz coincidences, and visibilities H, V: 99.6% and 45°: 94.2%.
Entangled photon pairs play a crucial role in emerging quantum technologies, acting as tamper-proof padlocks in secure quantum communication, ultra-precise probes in quantum metrology and high-fidelity information carriers in photonic quantum computing. Amongst the many technological possibilities for generating photon pairs, sources based on spontaneous parametric down-conversion (SPDC) in second-order nonlinear crystals are still the workhorse tool in quantum optics laboratories, and more recently even in long-distance quantum communication with satellites. SPDC is a widely used method to create entangled photon pairs. The number of photon pairs that can be detected in a particular choice of collection modes, typically being optical single-mode fibers, depends critically on the spatial characteristics of the multi-mode SPDC emission as well as the particular beam waist of the collection modes. While several studies have already addressed the issue of optimal fiber coupling of SPDC photons in theory and experiment, the results of these studies arrive at different conclusions. Here, we present the results of a comprehensive experimental study on the optimal collection of photon pairs into single-mode optical fibers. Our approach is based on quasi-phase-matched type II SPDC from a periodically poled KTiOPO4 (ppKTP) crystal. We discuss the influence of pump and collection focal parameters on the spectral brightness and heralding efficiency, as well as practical issues of alignment tolerances into an optical single mode fiber. Further, Using two-photon interference (Hong-Ou-Mandel interference), we assess the spectral bandwidth of the photon pairs for variable crystal lengths. The results are in good agreement with our theoretical model, thus providing the recipe of building ultra bright and stable entangled photon sources.
We demonstrate a broadband entangled photon source based on a single-pass, type-0 phase-matched, non-collinear spontaneous parametric down-conversion (SPDC) process. By spatially multiplexing the intrinsically random transverse momentum states of biphotons emitted in an annular spatial distribution from a single-frequency-pumped, 2-mm-long periodically poled KTP crystal, we generate polarization-entangled pair photons with a spectral bandwidth of ∼130 nm centered at 810 nm. The negligible group-velocity mismatch of the co-polarized near-degenerate photons in single-pass and low birefringence of standard optical components preserves indistinguishability across the broadband emission without phase compensation, enabling high-quality polarization entanglement over the entire emission bandwidth. The source achieves a brightness of 0.57 Mpairs/s/mW and a two-photon coherence length of 6.97 μm, while exhibiting an interference visibility exceeding 95%, a Bell–CHSH parameter of 2.526 ± 0.005 that remains stable over 12 h of continuous operation and violates the Bell inequality by more than 100 standard deviations, and a state fidelity of 96.3%. The generic scheme providing the broadest bandwidth entangled biphotons at 810 nm, to our knowledge, can readily be used for other wavelengths as required for multiparty quantum networks and quantum sensing applications.
We demonstrate a broadband entangled photon source based on a single-pass, type-0 phase-matched, non-collinear spontaneous parametric down-conversion (SPDC) process. By spatially multiplexing the intrinsically random transverse momentum states of biphotons emitted in an annular spatial distribution from a single-frequency-pumped, 2-mm-long periodically poled KTP crystal, we generate polarization-entangled pair photons with a spectral bandwidth of ∼130 nm centered at 810 nm. The negligible group-velocity mismatch of the co-polarized near-degenerate photons in single-pass and low birefringence of standard optical components preserves indistinguishability across the broadband emission without phase compensation, enabling high-quality polarization entanglement over the entire emission bandwidth. The source achieves a brightness of 0.57 Mpairs/s/mW and a two-photon coherence length of 6.97 μm, while exhibiting an interference visibility exceeding 95%, a Bell–CHSH parameter of 2.526 ± 0.005 that remains stable over 12 h of continuous operation and violates the Bell inequality by more than 100 standard deviations, and a state fidelity of 96.3%. The generic scheme providing the broadest bandwidth entangled biphotons at 810 nm, to our knowledge, can readily be used for other wavelengths as required for multiparty quantum networks and quantum sensing applications.
We propose a scheme for the generation of counterpropagating polarization-entangled photon pairs from a dual-periodically-poled crystal. Compared with the usual forward-wave-type source, this source, in the backward-wave way, has a much narrower bandwidth. With a 2-cm-long bulk crystal, the bandwidths of the example sources are estimated to be 3.63.63.6 GHz, and the spectral brightnesses are more than 100 pairs///(s GHz mW). Two concurrent quasi-phase-matched spontaneous parametric down-conversion processes in a single crystal enable our source to be compact and stable. This scheme does not rely on any state projection and applies to both degenerate and nondegenerate cases, facilitating applications of the entangled photons.