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Europhysics Letters (EPL)

Optimal ion shuttling for a noisy trap

Xiao-Jing Lu, Juan Gonzalo Muga

Published Dec 20, 2024• 0 citations
Publisher

Abstract

Abstract We find continuous optimal trap trajectories to shuttle one ion with minimal excitation, when the trap spring constant is affected by white noise. The Euler-Lagrange method gives a lower bound for the dynamical (trajectory-dependent) energy sensitivity to the noise. Using a trigonometric ansatz for the state trajectories, the optimal trap trajectories are found for a given shuttling time and a fixed number of terms in the ansatz. The corresponding dynamical sensitivity tends to the lower bound as the number of terms increases. While the dynamical sensitivity increases by shortening the shuttling times, the static (trajectory-independent) one decreases, so we also find optimal shuttling times that minimize the global (static plus dynamical) sensitivity.

DOI
10.1209/0295-5075/ada1f2

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Abstract We find continuous optimal trap trajectories to shuttle one ion with minimal excitation, when the trap spring constant is affected by white noise. The Euler-Lagrange method gives a lower bound for the dynamical (trajectory-dependent) energy sensitivity to the noise. Using a trigonometric ansatz for the state trajectories, the optimal trap trajectories are found for a given shuttling time and a fixed number of terms in the ansatz. The corresponding dynamical sensitivity tends to the lower bound as the number of terms increases. While the dynamical sensitivity increases by shortening the shuttling times, the static (trajectory-independent) one decreases, so we also find optimal shuttling times that minimize the global (static plus dynamical) sensitivity.
We investigate the excitation of a quantum particle shuttled in a harmonic trap with weak spring-constant colored noise. The Ornstein-Uhlenbeck model for the noise correlation function describes a wide range of possible noises, in particular for short correlation times the white-noise limit examined by Lu et al. [Phys. Rev. A 89, 063414 (2014)] and, by averaging over correlation times, ``1/f1/f1/f flicker noise.'' We find expressions for the excitation energy in terms of static (independent of trap motion) and dynamical sensitivities, with opposite behavior with respect to shuttling time, and demonstrate that the excitation can be reduced by proper process timing and design of the trap trajectory.
Abstract Shuttling ions at high speed and with low motional excitation is essential for realizing fast and high-fidelity algorithms in many trapped-ion-based quantum computing architectures. Achieving such performance is challenging due to the sensitivity of an ion to electric fields and the unknown and imperfect environmental and control variables that create them. Here we implement a closed-loop optimization of the voltage waveforms that control the trajectory and axial frequency of an ion during transport in order to minimize the final motional excitation. The resulting waveforms realize fast round-trip transport of a trapped ion across multiple electrodes at speeds of 0.5 electrodes per microsecond (35 m·s −1 for a one-way transport of 210 μm in 6 μs) with a maximum of 0.36 ± 0.08 mean quanta gain. This sub-quanta gain is independent of the phase of the secular motion at the distal location, obviating the need for an electric field impulse or time delay to eliminate the coherent motion.
The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.
We investigate optimized vertical ion-shuttling protocols for trapped-ion applications across a range of ion-trap experiments, including three-dimensional gradient-measurement sensors, on-chip ion fluorescence collection and imaging, improved laser accessibility, and quantum information processing. In this work, we focus on minimizing motional energy gain during ion transport. Our findings indicate that anomalous heating becomes the dominant limiting factor only for shuttling durations exceeding \SI{500}{\micro\second}, whereas the final motional excitation is strongly dependent on the selected shuttling protocol. Using a recently measured heating rate of (3.1±0.35)(3.1 \pm 0.35)(3.1±0.35) quanta\,ms−1^{-1}−1 at an ion--surface separation of $134 \pm 1.5\,\si{\micro\meter}$, we demonstrate that the motional excitation can be restricted to fewer than eight quanta when the ion is vertically displaced to \SI{86}{\micro\meter} from its initial position at \SI{134}{\micro\meter} within \SI{500}{\micro\second}. These results establish the feasibility of near-adiabatic vertical ion shuttling compatible with the operational requirements of high-fidelity quantum sensing and scalable quantum information processing applications.