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arXiv:1109.2268 · Physical Review A

Efficient collection of single photons emitted from a trapped ion into a single-mode fiber for scalable quantum-information processing

Taehyun Kim, Peter Maunz, Jungsang Kim

Published Dec 27, 2011• 44 citations
arXivHTMLPDF

Abstract

Interference and coincidence detection of two photons emitted by two remote ions can lead to an entangled state, which is a critical resource for scalable quantum-information processing. Currently the success probabilities of experimental realizations of this protocol are mainly limited by low coupling efficiency of a photon emitted by an ion into a single-mode fiber. Here we consider two strategies to enhance the collection probability of a photon emitted from a trapped Yb${}^{+}$ ion, using analytic methods that can be easily applied to other types of ions or neutral atoms. Our analysis shows that we can achieve fiber coupling efficiency of over 30$%$ with an optical cavity made of a flat fiber tip and a spherical mirror. We also investigate ways to increase the fiber coupling efficiency using high-numerical-aperture optics, and show that collection probability of over 15$%$ is possible with proper control of aberration.

DOI
10.1103/physreva.84.063423

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Interference and coincidence detection of two photons emitted by two remote ions can lead to an entangled state, which is a critical resource for scalable quantum-information processing. Currently the success probabilities of experimental realizations of this protocol are mainly limited by low coupling efficiency of a photon emitted by an ion into a single-mode fiber. Here we consider two strategies to enhance the collection probability of a photon emitted from a trapped Yb+{}^{+}+ ion, using analytic methods that can be easily applied to other types of ions or neutral atoms. Our analysis shows that we can achieve fiber coupling efficiency of over 30% with an optical cavity made of a flat fiber tip and a spherical mirror. We also investigate ways to increase the fiber coupling efficiency using high-numerical-aperture optics, and show that collection probability of over 15% is possible with proper control of aberration.
Trapped atomic ions are natural candidates for quantum information processing and have the potential to realize or improve quantum computing, sensing, and networking. These applications often require the collection of individual photons emitted from ions into guided optical modes, in some cases for the production of entanglement between separated ions. Proof-of-principle demonstrations of such photon collection from trapped ions have been performed using high-numerical-aperture lenses or cavities and single-mode fibers, but integrated photonic elements in ion-trap structures offer advantages in scalability and manufacturability over traditional optics. In this paper we analyze structures monolithically fabricated with an ion trap for collecting ion-emitted photons, coupling them into waveguides, and manipulating them via interference. We calculate geometric limitations on collection efficiency for this scheme, simulate a single-layer grating that shows performance comparable to demonstrated free-space optics, and discuss practical fabrication and fidelity considerations. Based on this analysis, we conclude that integrated photonics can support scalable systems of trapped ions that can distribute quantum information via photon-mediated entanglement.
Long-range transport of quantum information across a network is most readily achieved through the use of photons as the information carriers. The nodes of such a quantum network are most naturally a quantum memory or information processor, which typically do not rely upon photonic qubits. Realizing a large-scale distributed quantum network therefore requires an efficient interface between the two physical manifestations of the quantum information. The most promising platform for realizing a quantum computer is the manipulation of trapped atomic ions, as this system has demonstrated all the fundamental requirements to realize a quantum computer. Additionally, trapped ions posses long coherence times necessary for quantum memories. The interface between atomic and photonic qubits relies on a high photon emission rate into the collected solid angle. Most methods of photon collection for quantum networks use a high numerical aperture microscope objective, which only collects on the order of 1% of all the emitted photons. This results in a small probability of successfully linking two quantum nodes. In this work, I present the design, simulation, and implementation of a trapped ion cavity QED system capable of improving the photon collection efficiency. A single ytterbium ion is coupled to a high-finesse optical cavity. The photon scatter rate into the cavity mode is enhanced by a factor of 130 over the free-space scatter rate into the cavity solid angle. This represents the first step towards realizing a protocol to entangle the polarization of an emitted photon to the Zeeman sublevels of the ion with high photon collection efficiency. Simulations of the experimental system indicate that with an optical cavity up to 4% of the light emitted by the ion can be collected.
We have realized a compact system to efficiently couple the fluorescent light emitted by a single trapped ion to two opposing optical fibers. The fibers are tightly integrated in the center electrodes of a miniature endcap trap. They capture light from the ion with a numerical aperture of 0.34 each, corresponding to 6% of the solid angle in total. The high collection efficiency and high signal-to-background ratio make the setup an ideal quantum light source. We have observed strong antibunching of the photons emitted from the two fibers. The system has a range of applications from single-ion state detection in quantum information processing to strong coupling cavity-QED with ions.
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}).
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.
Scalable quantum information processing requires efficient coupling between stationary qubits (trapped atoms, ions, NV centres, etc.) via “flying” single-photon qubits. Here we investigate the optimisation and integration of fibre-tip microcavities into radiofrequency ion traps to achieve (i) high-fidelity transfer of ion qubits onto single photons, (ii) low-loss coupling of cavity photons into single-mode optical fibre, and (iii) achieving conditions (i) and (ii) without disturbing the ion trap. Our cavities are fabricated by laser micro-machining the ends of optical fibres and subsequent coating with a thin dielectric mirror, giving rise to cavity mirrors with a Gaussian profile. These cavities allow for small mode volume and thus large ion-photon coupling fulfilling requirement (i), while simultaneously providing intrinsic coupling to optical fibres, requirement (ii), as long as mode matching between the cavity mode and the fibre mode can be achieved at the cavity mirror. Using a semi-analytical numerical method, we show that Gaussian-shaped mirrors can in fact be used to enhance ion-photon coupling beyond what is possible with more common spherical cavity mirrors. Ion traps are notoriously sensitive to the presence of dielectric materials such as cavity mirrors near the trap centre, preventing requirement (iii) from being achieved. We performed an extensive numerical study of five different common ion traps to find the optimum configurations for integrating fibre-tip cavities with minimised effects on the trapping potentials. We discuss these results and present simple and effective design rules for realising optimum ion-cavity based quantum networks.