Breaking the Entangling Gate Speed Limit for Trapped-Ion Qubits Using a Phase-Stable Standing Wave

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Breaking the Entangling Gate Speed Limit for Trapped-Ion Qubits Using a Phase-Stable Standing Wave

S. Saner, O. Băzăvan, M. Minder, P. Drmota, D. J. Webb, G. Araneda, R. Srinivas, D. M. Lucas, and C. J. Ballance

Phys. Rev. Lett. 131, 220601 – Published 1 December 2023

Abstract

All laser-driven entangling operations for trapped-ion qubits have hitherto been performed without control of the optical phase of the light field, which precludes independent tuning of the carrier and motional coupling. By placing ${}^{88}{Sr}^{+}$ ions in a $λ = 674 nm$ standing wave, whose relative position is controlled to $\approx λ / 100$ , we suppress the carrier coupling by a factor of 18, while coherently enhancing the spin-motion coupling. We experimentally demonstrate that the off-resonant carrier coupling imposes a speed limit for conventional traveling-wave Mølmer-Sørensen gates; we use the standing wave to surpass this limit and achieve a gate duration of $15 μ s$ , restricted by the available laser power.

Received 31 May 2023
Accepted 16 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.220601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Coherent control Quantum description of light-matter interaction Quantum entanglement Quantum gates Quantum information with trapped ions Quantum metrology Quantum optics

Trapped ions

Adiabatic approximation Jaynes-Cummings model Optical lattices & traps

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

S. Saner ^*,†, O. Băzăvan ^†,‡, M. Minder , P. Drmota , D. J. Webb , G. Araneda , R. Srinivas , D. M. Lucas, and C. J. Ballance

Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom

^*sebastian.saner@physics.ox.ac.uk
^†oana.bazavan@physics.ox.ac.uk
^‡These authors contributed equally to this work.

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Issue

Vol. 131, Iss. 22 — 1 December 2023

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Images

Figure 1
(a) Schematic of the experimental apparatus. The incoming 674-nm beam is split into two beams ( $b_{1}$ , $b_{2}$ ). The acousto-optic modulators (AOMs) are used to control the frequencies ( $f_{1}$ , $f_{2}$ ) and phases ( $ϕ_{1}$ , $ϕ_{2}$ ) of the two counterpropagating beams, which have polarization parallel to $B_{0}$ and equal intensities at the ions. We close the resulting interferometer with a pick-off window $(PW) \approx 30 cm$ away from the ion(s). For fast feedback (see text) we stabilize the interference fringe intensity on a photodiode (PD) by adjusting $ϕ_{1}$ . (b) Monochromatic resonant SW for single-qubit rotations. (c) Bichromatic off-resonant SW for two-qubit gates.
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Figure 2
Monochromatic SW interacting with a single ion. (a) Qubit state transfer probability as a function of the SW phase at the ion position, while the SW is resonant with the carrier. We indicate the ion positions in the SW that maximize ( $Δ ϕ = π$ ) or minimize ( $Δ ϕ = 0$ ) the carrier coupling for a quadrupole transition. The SW pulse duration $t_{p}$ is set such that complete population transfer is achieved at maximal carrier coupling. (b) Detuning scans over carrier (circles) and motional sideband (triangles) resonance while placing the ion at a field node (left column) or field antinode (right column). For each resonance, $t_{p}$ is chosen such that full population transfer is reached in the case of maximal coupling to the SW.
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Figure 3
Spin-dependent force magnitude $Ω_{SDF}$ (normalized by $η Ω$ in the inset) versus $2 Ω / δ$ , as measured for a single ion with $η = 0.051$ . We extract $Ω_{SDF}$ by applying a conventional bichromatic TW field (squares), or a bichromatic SW field (triangles), for variable durations. The solid lines show the analytical dependence; as predicted by the theory and shown explicitly in the inset, the TW coupling follows the Bessel functions ( $| J_{0} + J_{2} |$ ), while the SW coupling remains constant [35].
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Figure 4
Characterization of SW (triangles) and TW (squares) Mølmer-Sørensen gates as a function of the effective two-qubit gate duration $(2 π / δ_{g})$ . (a) Using the SW, we achieve gate fidelities that are consistent with $\approx 0.95$ (solid line) for all gate durations. Using the TW the fidelity decreases rapidly for durations $\leq 25 μ s$ . As a guide to the eye, we show TW-MS simulations (dotted and dashed lines), with the maximum fidelity normalized to 0.95. (b) Total laser power required at the ions to generate the gate interaction. The constructive interference of the SW reduces the required power at the ions by a factor of 2. The solid curve shows an inverse-square fit to the SW data. We scale this curve by a factor of 2 (dotted line) for comparison with the TW data. At fast gate durations $(≲ 40 μ s)$ , the required power for TW gates exceeds this prediction as a result of the saturation of the SDF (Fig. 3). We scale this prediction by the expected Bessel function dependence (dashed line) and find good agreement with the measurements.
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