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We report the achievement of single-qubit gates with sub-part-per-million error rates, in a trapped-ion $^{43}$Ca$^{+}$ hyperfine clock qubit. We explore the speed/fidelity trade-off for gate times $4.4\leq t_{g}\leq35~\mu$s, and benchmark a minimum error of $1.5(4) \times 10^{-7}$. Gate calibration errors are suppressed to $< 10^{-8}$, leaving qubit decoherence ($T_{2}\approx 70$ s), leakage and measurement as the dominant error contributions. The ion is held above a microfabricated surface-electrode trap which incorporates a chip-integrated microwave resonator for electronic qubit control; the trap is operated at room temperature without magnetic shielding.

We present an optomechanical method for locally measuring the rheological properties of complex fluids in the ultra-high frequency range (UHF). A mechanical disk of microscale volume is used as a small-amplitude oscillating probe that monitors the fluid at rest in thermal equilibrium, while the oscillation is detected by optomechanical transduction within a sub-millisecond measurement time, thanks to an optimized signal collection. An original analytical model for fluid-structure interactions is used to extract from these measurements the rheological properties of liquids over the frequency range 100 MHz - 1 GHz. This new micro-rheology method is calibrated by measurements on liquid water, in which we observe pronounced compressibility effects above 500 MHz, but which we show remains Newtonian all over the explored range. In contrast, measurements reveal that liquid 1-decanol exhibits a non-Newtonian behavior, with a frequency-dependent viscosity associated to several relaxation frequencies in the UHF. Our data agree well with an extended Maxwell model for the viscosity of this alcohol, involving two relaxation times of 797 and 151 picoseconds, which are respectively analyzed as supramolecular and intramolecular relaxation processes. A shear elastic response of the liquid appears at the highest frequencies, compatible with the entropic elasticity of molecules as they attempt to uncurl, and whose value enables estimating the volume of a single molecule of liquid. UHF optomechanical micro-rheology demonstrates here a direct mechanical access to the fast molecular dynamics at play in a liquid, in a quantitative manner and in a short time.

Quantum state preparation for trapped-ion qubits often relies on high-quality circularly-polarised light, which may be difficult to achieve with chip-based integrated optics technology. We propose and implement a hybrid optical/microwave scheme for intermediate-field hyperfine qubits which instead relies on frequency selectivity. Experimentally, we achieve $99.94\%$ fidelity for linearly-polarised ($\sigma^+$/$\sigma^-$) light, using $^{43}$Ca$^+$ at 28.8 mT. We find that the fidelity remains above $99.8\%$ for a mixture of all polarisations ($\sigma^+$/$\sigma^-$/$\pi$). We calculate that the method is capable of $99.99\%$ fidelity in $^{43}$Ca$^+$, and even higher fidelities in heavier ions such as $^\text{137}$Ba$^\text{+}$.

Microwave-driven logic is a promising alternative to laser control in scaling trapped-ion based quantum processors. However, such electronic gates have yet to match the speed offered by their laser-driven counterparts. Here, we implement M{\o}lmer-S{\o}rensen two-qubit gates on $^{43}\text{Ca}^+$ hyperfine clock qubits in a cryogenic ($\approx25~\text{K}$) surface trap, driven by near-field microwaves. We achieve gate durations of $154~\mu\text{s}$ (with $1.0(2)\%$ error) and $331~\mu\text{s}$ ($0.5(1)\%$ error), which approaches the performance of typical laser-driven gates. In the $331~\mu\text{s}$ gate, we demonstrate a new Walsh-modulated dynamical decoupling scheme which suppresses errors due to fluctuations in the qubit frequency as well as imperfections in the decoupling drive itself.

Reducing errors in quantum gates is critical to the development of quantum computers. To do so, any distortions in the control signals should be identified, however, conventional tools are not always applicable when part of the system is under high vacuum, cryogenic, or microscopic. Here, we demonstrate a method to detect and compensate for amplitude-dependent phase changes, using the qubit itself as a probe. The technique is implemented using a microwave-driven trapped ion qubit, where correcting phase distortions leads to a three-fold improvement in single-qubit gate error, to attain state-of-the-art performance benchmarked at $1.6(4)\times 10^{-6}$ error per Clifford gate.

A leading approach to implementing small-scale quantum computers has been to use laser beams, focused to micron spot sizes, to address and entangle trapped ions in a linear crystal. Here we propose a method to implement individually-addressed entangling gate interactions, but driven by microwave fields, with a spatial-resolution of a few microns, corresponding to $10^{-5}$ microwave wavelengths. We experimentally demonstrate the ability to suppress the effect of the state-dependent force using a single ion, and find the required interaction introduces $3.7(4)\times 10^{-4}$ error per emulated gate in a single-qubit benchmarking sequence. We model the scheme for a 17-qubit ion crystal, and find that any pair of ions should be addressable with an average crosstalk error of $\sim 10^{-5}$.

We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for $^{43}\text{Ca}^{+}$ hyperfine "atomic clock" qubits in a cryogenic (100K) surface trap. For a single qubit, we benchmark an error of $1.5$ $\times$ $10^{-6}$ per Clifford gate (implemented using $600~\text{ns}$ $\pi/2$-pulses). For two qubits in the same trap zone (ion separation $5~\mu\text{m}$), we use a spatial microwave field gradient, combined with an efficient 4-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error $3.4$ $\times$ $10^{-5}$ per addressed $\pi/2$-gate. The scheme scales theoretically to larger numbers of qubits in a single register.

We report the design, fabrication, and characterization of a cryogenic ion trap system for the implementation of quantum logic driven by near-field microwaves. The trap incorporates an on-chip microwave resonator with an electrode geometry designed to null the microwave field component that couples directly to the qubit, while giving a large field gradient for driving entangling logic gates. We map the microwave field using a single $^{43}$Ca$^+$ ion, and measure the ion trapping lifetime and motional mode heating rates for one and two ions., Comment: 18 pages, 13 figures

Atomic force microscopy (AFM) has been constantly supporting nanosciences and nanotechnologies for over 30 years, being present in many fields from condensed matter physics to biology. It enables measuring very weak forces at the nanoscale, thus elucidating interactions at play in fundamental processes. Here we leverage the combined benefits of micro/nanoelectromechanical systems and cavity optomechanics to fabricate a sensor for dynamic mode AFM at a frequency above 100 MHz. This is two decades above the fastest commercial AFM probes, suggesting opportunity for measuring forces at timescales unexplored so far. The fabrication is achieved using very-large scale integration technologies inherited from photonic silicon circuits. The probe's ring optomechanical cavity is coupled to a 1.55 um laser light and features a 130 MHz mechanical resonance mode with a quality factor of 900 in air. A limit of detection in displacement of 3.10-16 m/sqrt(Hz) is obtained, enabling the detection of the Brownian motion of the probe and paving the way for force sensing experiments in the dynamic mode with a working vibration amplitude in the picometer range. Inserted in a custom AFM instrument embodiment, this optomechanical sensor demonstrates the capacity to perform force-distance measurements and to maintain a constant interaction strength between tip and sample, an essential requirement for AFM applications. Experiments show indeed a stable closed-loop operation with a setpoint of 4 nN/nm for an unprecedented sub-picometer vibration amplitude, where the tip-sample interaction is mediated by a stretched water meniscus.

Multimode optomechanical systems are an emerging platform for studying fundamental aspects of matter near the quantum ground state and are useful in sensitive sensing and measurement applications. We study optomechanical cooling in a system where two nearly degenerate mechanical oscillators are coupled to a single microwave cavity. Due to an optically mediated coupling the two oscillators hybridize into a bright mode with strong optomechanical cooling rate and a dark mode nearly decoupled from the system. We find that at high coupling, sideband cooling of the dark mode is strongly suppressed. Our results are relevant to novel optomechanical systems where multiple closely-spaced modes are intrinsically present., Comment: 6 pages, 4 figures

We experimentally investigate dissipation in mechanical resonators made of a disordered superconducting thin film of Molybdenum-Rhenium(MoRe) alloy. By electrostatically driving the drum with a resonant AC voltage, we detect its motion using a superconducting microwave cavity. From the temperature dependence of mechanical resonance frequencies and quality factors, we find evidence for non-resonant, mechanically active two-level systems (TLSs) limiting its quality factor at low temperature. In addition, we observe a strong suppression of mechanical dissipation at large mechanical driving amplitudes, suggesting an unconventional saturation of the non-resonant TLSs. These new observations shed light on the mechanism of mechanical damping in superconducting drums and routes towards understanding dissipation in such mechanical systems.