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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Toward remote ion-ion entanglement with barium

Thomas W. Noel, Carolyn Auchter, Chen-Kuan Chou, B. B. Blinov

Published Mar 4, 2015• 0 citations
Publisher

Abstract

We present work toward remote entanglement of barium ions in traps separated by a few meters. A new version of an ion trap specialized for remote entanglement is introduced. The new trap allows for highly efficient collection of ion fluorescence while simultaneously minimizing ion micromotion and aligning the trap position precisely to the focus of an in-vacuum parabolic mirror by using a set of bias electrodes and a piezoelectric micro-positioning system. The success rate of the remote entanglement procedure depends strongly on the efficiency with which ion fluorescence can be coupled into an optical fiber. Characterization of our system in terms of ion fluorescence collection and fiber coupling efficiency is presented. Results demonstrating entanglement between a single barium ion and single spontaneously emitted photons are shown. The entanglement fidelity of the ion-photon state is measured to be 0.84(1) and a CHSH Bell signal of 2.303(36) finds violation of the CHSH version of the Bell inequality by over eight standard deviations. Barium’s relatively long wavelength transitions make it an ideal candidate for our longer term goal of remote entanglement of ions separated by a kilometer or more. Such long distance remote entanglement should allow for a loophole-free verification of the violation of the Bell inequality.

DOI
10.1117/12.2183522

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We present work toward remote entanglement of barium ions in traps separated by a few meters. A new version of an ion trap specialized for remote entanglement is introduced. The new trap allows for highly efficient collection of ion fluorescence while simultaneously minimizing ion micromotion and aligning the trap position precisely to the focus of an in-vacuum parabolic mirror by using a set of bias electrodes and a piezoelectric micro-positioning system. The success rate of the remote entanglement procedure depends strongly on the efficiency with which ion fluorescence can be coupled into an optical fiber. Characterization of our system in terms of ion fluorescence collection and fiber coupling efficiency is presented. Results demonstrating entanglement between a single barium ion and single spontaneously emitted photons are shown. The entanglement fidelity of the ion-photon state is measured to be 0.84(1) and a CHSH Bell signal of 2.303(36) finds violation of the CHSH version of the Bell inequality by over eight standard deviations. Barium’s relatively long wavelength transitions make it an ideal candidate for our longer term goal of remote entanglement of ions separated by a kilometer or more. Such long distance remote entanglement should allow for a loophole-free verification of the violation of the Bell inequality.
We report on the demonstration of ion–photon entanglement and Bell inequality violation in a system of trapped Ba138+ ions. Entanglement between the Zeeman sublevels of the ground state of a single Ba138+ ion and the polarization state of a single 493 nm photon emitted by the ion with a fidelity of 0.84±0.01 was achieved, along with a Bell signal of 2.3, exceeding the classical limit of 2 by more than eight standard deviations. This system is a promising candidate for a loophole-free Bell inequality violation test using long-range ion–ion entanglement as the wavelengths of the transitions of Ba138+ are in the visible region and thus suitable for long-range transmission over fiber optic cable.
Abstract Quantum networking links quantum processors through remote entanglement for distributed quantum information processing and secure long-range communication. Trapped ions are a leading quantum information processing platform, having demonstrated universal small-scale processors and roadmaps for large-scale implementation. Overall rates of ion–photon entanglement generation, essential for remote trapped ion entanglement, are limited by coupling efficiency into single mode fibers and scaling to many ions. Here, we show a microfabricated trap with integrated diffractive mirrors that couples 4.1(6)% of the fluorescence from a174Yb+ion into a single mode fiber, nearly triple the demonstrated bulk optics efficiency. The integrated optic collects 5.8(8)% of theπtransition fluorescence, images the ion with sub-wavelength resolution, and couples 71(5)% of the collected light into the fiber. Our technology is suitable for entangling multiple ions in parallel and overcomes mode quality limitations of existing integrated optical interconnects.
Efficient ion-photon interface is critical for ion-photon and ion-ion entanglement generation, which are the fundamental building blocks for loophole-free Bell inequality violation tests based on ion qubits, and for the quantum computer architecture based on ion-photon networks. As one approach to address the problem, the feasibility of integrating reflective optics into ion trap to increase free-space photon interception is studied. The development and operation of two novel ion traps are demonstrated: one integrates a spherical mirror with a linear quadrapole trap, and the other combines the optical surface with the RF electrode. The possibility of using aspherical optics to improve ion images is studied and partially implemented. A continuously excited single photon source based on 138Ba+ ion is demonstrated and calibrated. Methods of scaling up current design are also discussed.
We demonstrate remote entanglement of trapped-ion qubits via a quantum-optical fiber link with fidelity and rate approaching those of local operations. Two ^{88}Sr^{+} qubits are entangled via the polarization degree of freedom of two spontaneously emitted 422 nm photons which are coupled by high-numerical-aperture lenses into single-mode optical fibers and interfere on a beam splitter. A novel geometry allows high-efficiency photon collection while maintaining unit fidelity for ion-photon entanglement. We generate heralded Bell pairs with fidelity 94% at an average rate 182 s^{-1} (success probability 2.18×10^{-4}).
Efficient fluorescence collection is the most challenging part in remote entangled ion qubit state generation. To address this issue, we developed an ion trap consisting of a reflective parabolic surface and a needle electrode. This parabolic trap design covers a solid angle of 2π steradians and allows precise ion placement at the focal point of the parabola. We measured (39 ± 3)% fluorescence collection from a single ion with this trap and analyzed the mirror optical performance. We observed single ion image spot size of 3.4 times diffraction limit, improved to 2.8 times diffraction limit with the help of an external deformable mirror. The micromotion of the ion is determined to be the limiting factor, and the result is consistent with theoretical calculation.
Quantum devices are rapidly gaining momentum as a technology that will induce a paradigm shift in computing, communication and cryptography. Trapped ion qubits are one of the leading candidates for implementing a quantum computer, having previously demonstrated all of the required criteria. Local gate fidelities between ions exceed those for all other platforms, but the total number of ions in a trap is limited by unavoidable issues – one possibility for scaling the ion trap quantum processor is to create entanglement between ions in separate traps via single photons. The work in this thesis demonstrates the generation of remote entanglement between ions at high fidelity and rate, paving the way towards protocols using multiple entangled pairs for computations. We describe the construction from scratch of a twin-trap apparatus designed to entangle separated ions. We demonstrate the entanglement of strontium ions in traps separated by ∼ 2 m by swapping entanglement from single photons emitted by the 88Sr+ ions. A novel photon collection geometry is used, maximising the entanglement between the ion and photon without impeding optical access for standard ion trap laser beam geometries. The Bell state fidelity of the ion-photon state, which is itself a valuable entanglement resource for blind computation, is at least 97.70(12) % in either trap, with entangled pairs detected at a rate of at least 3.98 × 103 s−1. The remote ion-ion Bell state fidelity is 94.0(5) %, and is generated at a rate of 182 s−1, representing the highest fidelity remote entanglement reported in ions by a large margin, at a rate more than an order of magnitude faster than previous experiments. The two identical trap systems are designed with capabilities beyond those demonstrated here. We can co-trap 88Sr+ and 43Ca+ in a microfabricated trap suitable for local ion transport operations, opening up the possibility of performing distillation of remote entanglement in the same apparatus. Entanglement distillation can be used to make remote entanglement with similar fidelity to local operations, and would represent a significant step towards a fully scalable ion trap quantum computer architecture.