Integrated Optical Addressing Of An Ion Qubit

[Billie Kjergaard]

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The long coherence times and strong Coulomb interactions afforded by trapped ion qubits have enabled realizations of the necessary primitives for quantum information processing and the highest-fidelity quantum operations in any qubit to date. Although light delivery to each individual ion in a system is essential for general quantum manipulations and readout, experiments so far have employed optical systems that are cumbersome to scale to even a few tens of qubits. Here we demonstrate lithographically defined nanophotonic waveguide devices for light routing and ion addressing that are fully integrated within a surface-electrode ion trap chip. Ion qubits are addressed at multiple locations via focusing grating couplers emitting through openings in the trap electrodes to ions trapped 50 μm above the chip; using this light, we perform quantum coherent operations on the optical qubit transition in individual 88Sr+ ions. The grating focuses the beam to a diffraction-limited spot near the ion position with 2 μm 1/e2 radius along the trap axis, and we measure crosstalk errors between 10-2 and 4 10-4 at distances 7.5-15 μm from the beam centre. Owing to the scalability of the planar fabrication technique employed, together with the tight focusing and stable alignment afforded by the integration of the optics within the trap chip, this approach presents a path to creating the optical systems required for large-scale trapped-ion quantum information processing.

Grating couplers are fabricated for the optical addressing of trapped ion qubits, where their respective feasibility is evaluated. From the obtained results, optical addressing of 1 to 2 ions is possible along various axes.

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Log in to access Optica Member Subscription or free downloadsMore Like ThisEO Integration of Planar Ion Trap and Silicon Photonics for Optical Addressing in Quantum ComputingYu Dian Lim, Jing Tao, Peng Zhao, Hong Yu Li, Anak Agung Alit Apriyana, Luca Guidoni, and Chuan Seng Tan

ATh1I.3 CLEO: Applications and Technology (CLEO:A&T) 2020

Large-scale trapped-ion quantum computers hold great promise to outperform classical computers and are crucially desirable for finance, pharmaceutical industry, fundamental chemistry and other fields. Currently, a big challenge for trapped-ion quantum computers is the poor scalability mainly brought by the optical elements that are used for optical addressing. Metasurfaces provide a promising solution due to their excellent flexibility and integration ability. Here, we propose and numerically demonstrate a scalable off-axis metalens array for optical addressing working at the wavelength of 350 nm. Metalens arrays designed for x linearly polarized and left circularly polarized light respectively can focus the collimated addressing beam array into a compact focused spot array with spot spacing of 5 μm, featuring crosstalk below 0.82%.

Quantum computers employ qubits that are the quantum superposition of traditional bits 0 and 1, and are expected to outperform classical computers. Trapped-ion quantum computers arouse much research interest due to their advantages over other types of practical quantum computers. However, it is challenging to scale up the number of the trapped-ion qubits while maintaining the ability to control them individually with high operation fidelities [1]. The primary restrictions of current trapped-ion quantum computers result from the free-space optical elements used in the optical addressing system [2]. Optical addressing, a technology to focus and align individual addressing beams onto quantum particles, needs integrated, miniatured, and flexible focusing optical elements to realize precise manipulation over quantum states of individual trapped ion and neutral atom [3]. Previously, many related pioneering works have been reported, such as refractive lens group [4, 5], micromirrors based on micro-electromechanical systems (MEMS) [6, 7], microfabricated Fresnel lens arrays [8] and diffractive mirrors interfaced with reconfigurable planar waveguide circuits [9, 10], and focusing grating couplers [2, 11,12,13]. Existing technologies are limited by the lack of scalability and face challenges in obtaining good focusing properties, such as diffraction-limited focusing spot size, small focusing spot spacing, low crosstalk, and high efficiency.

Metasurfaces, composed of planar subwavelength-scale meta-antenna arrays, have shown versatile capabilities in manipulating amplitude, phase, polarization, and frequency of light at the subwavelength resolution [16]. Also, metasurfaces can be integrated with various functional materials, e.g., dyes, nonlinear materials, liquid crystals, etc., to realize dynamic manipulation [17,18,19]. Recently, metasurfaces have become an unprecedented platform for realizing numerous compact devices [20,21,22,23,24,25], such as polarization converters, meta-holograms, and metalenses. Especially, metalenses have boosted a wide range of applications including optical trapping, full-color achromatic imaging, polarization imaging, and microscopic imaging due to their compact size, planar structure, and compatibility with CMOS processing [26,27,28,29,30].

Previously, intensive studies focused on on-axis metalens working in the visible and the near-infrared band. Yet few works studied the ultraviolet UV off-axis metalenses and melalens array. Compact metalenses working at the UV band are crucially important for lithography, imaging, spectroscopy, and quantum computing [31]. Metalens array can generate focused spot array with a compact configuration and has found applications in a wide range of fields from full-color light field imaging [32], optical multiparameter detection [33,34,35], to the generation of a multiphoton quantum source [36]. On the other hand, the off-axis metalens can modify the position of the focus, thus adding a design freedom compared to the on-axis metalens. Notably, existing designs of metalens array can only generate a spot array with spacing equal to the distance of two neighboring metalenses, while metalens array composed of both on-axis metalenses and off-axis metalenses can achieve an arbitrarily arranged spot array.

If the nanopillar is rotated with an angle of \(0^ \circ \) and normally illuminated by the x-LP light which can be described by a Jones vector \(\left[ 1 \,\space 0 \right]^\text T\), the Jones vector of output light can be written as

If the nanopillar is illuminated by circularly polarization (CP) light under normal incidence, as the Jones vector of CP light is \(\left[ 1 \space \pm\texti \right]^\textT\), the Jones vector of output light can be written as

\(f^(i)\) and \(d_z^(i)\) are the focal length and working distance of ith metalens; \((d_x^(i) ,d_y^(i) ,d_z^(i) )\) is the location of the ith focused spot relative to the center of the ith metalens; λ is the working wavelength, and \(\varphi_\textc\) is the reference phase of the center of the ith metalens. The optical performance of the focused spot can be flexibly manipulated by optimizing \((d_x^(i) ,d_y^(i) ,d_z^(i) )\).

In the simulation, the near-field distribution was obtained by the FDTD method. While the far-field calculation was performed using plane wave expansion and chirped Z-transform to reduce the simulation time [40]. Table 1 summarizes some metrics used in this paper.

Metalenses 2, 3, and 5 in one metalens molecule designed for the x-LP light are characterized in Figs. 4. The normalized intensity distributions at the focal plane of metalenses 2, 3, and 5 (illuminated by the x-LP light) are respectively shown in Figs. 4a, e, and i. These results verify that the metalenses can focus the collimated x-LP light into tightly optical spots. Under the y-LP incidence, the normalized intensity distributions at the focal plane of metalenses 2, 3, and 5 are respectively shown in Figs. 4b, f, and j. And these results demonstrate that metalenses 2, 3, and 5 can well scatter the incoming y-LP light. For visualization, Figs. 4c, g, and k, respectively show the intensity distributions along the x-axis at the focal plane. The relative encircled power of metalenses 2, 3, and 5 are shown respectively in Figs. 4d, h, and l. These results demonstrate that the designed metalenses for x-LP incident light have functionalities of a polarizer and a focusing lens at the same time, which is preferred in controlling the trapped \(^43\text Ca^ + \) ion qubits for optical addressing applications. Taking metalens 2 as an example, the polarization extinction ratio is 13.97 dB calculated from the results shown in Figs. 4a and b. The spot radius is 0.64 μm calculated from the results of Fig. 4c, which is smaller than the reported results of other optical focusing elements for optical addressing applications, to the best of our knowledge. Since there are discrepancies in the utilization of focusing efficiency to characterize a metalens, we would rather use the relative encircled power instead [41]. Figure 4d indicates that more than 80% of the power is confined within a circle with a radius of seven times FWHM of intensity distribution at the focal plane. Here we note that the encircled power can be improved by using materials (\(\textSi_3\text N_4\), \(\textHfO_2\), etc.) of less optical loss and optimizing the nanopillars for higher transmittance. Results for metalenses 3 and 5 are similar.

Figure 6 shows simulated results of metalenses 2, 3, and 5 designed for the LCP plane wave. The normalized intensity distributions at the focal plane of metalenses 2, 3, and 5 are respectively shown in Figs. 6a, e, and i, when these metalenses are illuminated by LCP incidence. While Figs. 6b, f, and j, respectively show the normalized intensity distributions at the focal plane of metalenses 2, 3, and 5, which are illuminated by the RCP light. Then the polarization extinction ratios of the metalenses 2, 3, and 5 are 27.42 (calculated from the results of Figs. 6a and b), 15.86 (calculated from the results of Figs. 6e and f), and 25.63 dB (calculated from the results of Figs. 6i and j), respectively. These results demonstrate that the metalenses designed for the LCP incident light have good polarization sensitivity, which is preferred in controlling the trapped \(^171\text Yb^ + \) ion qubits for optical addressing applications. That means the designed metalenses can generate tightly focused spots when the collimated LCP plane wave illuminates the metalenses, while the incident RCP light will be diverged by the metalenses. Figures 6c, g, and k, respectively show the normalized intensity distributions along the x-axis at the focal plane of metalenses 2, 3, and 5 under LCP and RCP incidence, where the spot radiuses are calculated to be 0.61, 0.71, and 0.75 m, respectively. Figures 6d, h, and l indicate that nearly 70% of the powers are confined within a circle with radiuses of seven times FWHM of intensity distribution at the focal plane. These results demonstrate that the metalenses designed for LCP light have good focusing performance.

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