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Comparative numerical studies of ion traps with integrated optical cavities

Nina Podoliak, Hiroki Takahashi, Matthias Keller, Péter Horák

Published Oct 17, 2016• 11 citations
OpenAlex

Abstract

We study a range of radio-frequency ion trap geometries and investigate the effect of integrating dielectric cavity mirrors on their trapping potential using numerical modelling. We compare five different ion trap geometries with the aim to identify ion trap and cavity configurations that are best suited for achieving small cavity volumes and thus large ion-photon coupling as required for scalable quantum information networks. In particular, we investigate the trapping potential distortions caused by the dielectric material of the cavity mirrors in all 3 dimensions for different mirror orientations with respect to the trapping electrodes. We also analyze the effect of the mirror material properties such as dielectric constants and surface conductivity, and study the effect of surface charges on the mirrors. As well as perfectly symmetric systems, we also consider traps with optical cavities that are not centrally aligned where we find a spatial displacement of the trap centre and asymmetry of the resulting trap only at certain cavity orientations. The best trapcavity configurations with the smallest trapping potential distortions are those where the cavities are aligned along the major symmetry axis of the electrode geometries. These cavity configurations also appear to be the most stable with respect to any mirror misalignment. Although we consider particular trap sizes in our study, the presented results can be easily generalized and scaled to different trap dimensions.

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Comparative Numerical Studies of Ion Traps with Integrated Optical Cavities

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Integrating an optical cavity into a radio-frequency ion trap yields an ideal building block for quantum information networks or quantum computers. Unfortunately, it also jeopardizes the trap's stability. The authors compare the advantages and disadvantages of known ion-trap geometries and cavity configurations, and identify general features of the geometries best suited to developing a scalable network. This comprehensive study is an essential step in the development of tomorrow's secure quantum networks.

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Fibre-tip microcavities for enhanced ion-photon coupling in scalable quantum information networks

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We study a range of radio-frequency ion trap geometries and investigate the effect of integrating dielectric cavity mirrors on their trapping potential using numerical modelling. We compare five different ion trap geometries with the aim to identify ion trap and cavity configurations that are best suited for achieving small cavity volumes and thus large ion-photon coupling as required for scalable quantum information networks. In particular, we investigate the trapping potential distortions caused by the dielectric material of the cavity mirrors in all 3 dimensions for different mirror orientations with respect to the trapping electrodes. We also analyze the effect of the mirror material properties such as dielectric constants and surface conductivity, and study the effect of surface charges on the mirrors. As well as perfectly symmetric systems, we also consider traps with optical cavities that are not centrally aligned where we find a spatial displacement of the trap centre and asymmetry of the resulting trap only at certain cavity orientations. The best trapcavity configurations with the smallest trapping potential distortions are those where the cavities are aligned along the major symmetry axis of the electrode geometries. These cavity configurations also appear to be the most stable with respect to any mirror misalignment. Although we consider particular trap sizes in our study, the presented results can be easily generalized and scaled to different trap dimensions.
Integrating an optical cavity into a radio-frequency ion trap yields an ideal building block for quantum information networks or quantum computers. Unfortunately, it also jeopardizes the trap's stability. The authors compare the advantages and disadvantages of known ion-trap geometries and cavity configurations, and identify general features of the geometries best suited to developing a scalable network. This comprehensive study is an essential step in the development of tomorrow's secure quantum networks.
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.
In recent years there has been rapid progress into realising a working universal quantum computer, in particular with the development of chip-based radio frequency ion traps. The next significant leap will come with successfully integrating optical cavities into these ion traps to allow for interaction between remote ions via photons as required for more efficient and scalable quantum networking schemes. Fibre-tip cavities are especially interesting for such applications as they enable highly efficient coupling of photons from the cavity into optical fibres for onward transmission. Here we analyse theoretically and numerically the effects of parallel off-axial misalignment in millimetre scale optical Fabry-Perot cavities. While near-concentric cavity configurations produce the smallest mode waist and thus strongest coupling to a trapped ion, their mode is extremely sensitive to misalignment. Shorter cavities exhibit more robust modes, but at the cost of larger mode waists. For example, for typical experimental parameters (mirror radius of curvature 0.7 mm, mirror diameter 0.140 mm, operation wavelength 850 nm) we find that the cavity lifetime is reduced by a factor 1/e for a misalignment of 0.95 nm for a beam waist of 2.91 um (cavity length of 1.397 mm), which increases to 11.0 nm for a waist of 4.33 um (length of 1.386 mm), and 3.12 um for a waist of 7.38 um (length of 1.273 mm). In the parameter regimes of interest, we derive a simple relation between cavity length, mirror radius, and misalignment sensitivity. Finally, we also consider the effect of mode matching of the misaligned cavity mode with the optical mode of the fibre for efficient cavity to fibre coupling. In conclusion, our model allows us to optimise photon-ion coupling in fibre-tip resonators for quantum information processing in the presence of finite fabrication and alignment tolerances.
Abstract Trapped ions in micro-cavities constitute a key platform for advancing quantum information processing and quantum networking. By providing an efficient light–matter interface within a compact architecture, they serve as highly efficient quantum nodes with strong potential for a scalable quantum network. However, in such systems, ion trapping stability is often compromised by surface charging effects, and nearby dielectric materials are known to cause a dramatic increase in the ion heating rate by several orders of magnitude. These challenges significantly hinder the practical implementation of ion trap systems integrated with micro-cavities. To overcome these limitations, we present the design and fabrication of metal-shielded fiber-cavity mirrors, enabling the stable realization of ion trap systems integrated with fiber cavities. Using this method, we constructed a needle ion trap integrated with a fiber Fabry–Pérot cavity and successfully achieved stable trapping of a single ion within the cavity. The measured ion heating rate was reduced by more than an order of magnitude compared with unshielded configurations. This work establishes a key technique toward fully integrated ion–photon interfaces for scalable quantum networks.
The integration of photonic components into surface ion traps provides a scalable approach for trapped-ion quantum computing, sensing, and metrology, enabling compact systems with enhanced stability and precision. However, the introduction of optical apertures in the trap electrodes can distort the trapping electric field. This can lead to excess micromotion and ion displacement, which degrade the performance of quantum logic operations and optical clocks. In this work, we systematically investigate the electric field distortion in a surface ion trap with integrated waveguides and grating couplers that require apertures in the surface electrode using finite element method simulations. We analyze methods to reduce these distortions by exploiting symmetries and transparent conductive oxide materials.