Many physics experiments call on improved resolution to better define the experimental results, thus improving tests of theories. Modern microwave technology combined with high-Q resonators can achieve frequency readout and control with resolutions up to a part in 10(exp 18). When the physical quantity in question in the experiment can be converted to a frequency or a change in frequency, a high-stability microwave oscillator can be applied to obtain state-of-the-art precision. In this work we describe the overall physical concepts and the required experimental procedures for optimizing a high-resolution frequency measurement system that employs a high-Q superconducting microwave cavity and a low-noise frequency synthesizer. The basic approach is to resolve the resonant frequencies of a high-Q (Q > 10(exp 10)) cavity to extremely high precision (one part in 10(exp 17)- 10(exp 18)). Techniques for locking the synthesizer frequency to a resonant frequency of the superconducting cavity to form an ultra-stable oscillator are described. We have recently set up an ultra-high-vacuum high-temperature annealing system to process superconducting niobium cavities, and have been able to consistently achieve Q > 10(exp 9). We have integrated high-Q superconducting cavities with a low-noise microwave synthesizer in a phase-locked-loop to verify the frequency stability of the system. Effects that disturb the cavity resonant frequency (such as the temperature fluctuations and mechanical vibrations) and methods to mitigate those effects are also considered. Applicability of these techniques to experiments will be discussed, and our latest experimental progress in achieving high-resolution frequency measurements using the superconducting-cavity-stabilized-oscillator will be presented.
Many physics experiments call on improved resolution to better define the experimental results, thus improving tests of theories. Modern microwave technology combined with high-Q resonators can achieve frequency readout and control with resolutions up to a part in 10(exp 18). When the physical quantity in question in the experiment can be converted to a frequency or a change in frequency, a high-stability microwave oscillator can be applied to obtain state-of-the-art precision. In this work we describe the overall physical concepts and the required experimental procedures for optimizing a high-resolution frequency measurement system that employs a high-Q superconducting microwave cavity and a low-noise frequency synthesizer. The basic approach is to resolve the resonant frequencies of a high-Q (Q > 10(exp 10)) cavity to extremely high precision (one part in 10(exp 17)- 10(exp 18)). Techniques for locking the synthesizer frequency to a resonant frequency of the superconducting cavity to form an ultra-stable oscillator are described. We have recently set up an ultra-high-vacuum high-temperature annealing system to process superconducting niobium cavities, and have been able to consistently achieve Q > 10(exp 9). We have integrated high-Q superconducting cavities with a low-noise microwave synthesizer in a phase-locked-loop to verify the frequency stability of the system. Effects that disturb the cavity resonant frequency (such as the temperature fluctuations and mechanical vibrations) and methods to mitigate those effects are also considered. Applicability of these techniques to experiments will be discussed, and our latest experimental progress in achieving high-resolution frequency measurements using the superconducting-cavity-stabilized-oscillator will be presented.
Control electronics for superconducting quantum processors have strict requirements for accurate command of the sensitive quantum states of their qubits. Hinging on the purity of ultra-phase-stable oscillators to upconvert very-low-noise baseband pulses, conventional control systems can become prohibitively complex and expensive when scaling to larger quantum devices, especially as high sampling rates become desirable for fine-grained pulse shaping. Few-gigahertz radio-frequency (RF) digital-to-analog converters (DACs) present a more economical avenue for high-fidelity control while simultaneously providing greater command over the spectrum of the synthesized signal. Modern RF DACs with extra-wide bandwidths are able to directly synthesize tones above their sampling rates, thereby keeping the system clock rate at a level compatible with modern digital logic systems while still being able to generate high-frequency pulses with arbitrary profiles. We have incorporated custom superconducting qubit control logic into off-the-shelf hardware capable of low-noise pulse synthesis up to 7.5 GHz using an RF DAC clocked at 5 GHz. Our approach enables highly linear and stable microwave synthesis over a wide bandwidth, giving rise to high-resolution control and a reduced number of required signal sources per qubit. We characterize the performance of the hardware using a five-transmon superconducting device and demonstrate consistently reduced two-qubit gate error (as low as 1.8%), which we show results from superior control chain linearity compared to traditional configurations. The exceptional flexibility and stability further establish a foundation for scalable quantum control beyond intermediate-scale devices.
Resonance-frequency fluctuations can limit the sensitivity and stability of superconducting microwave cavities used for qubit readout, optomechanical displacement sensing, and magnetic flux detection. Here, we demonstrate the suppression of resonance-frequency fluctuations by locking a noisy nonlinear superconducting microwave cavity to a strong pump tone. The Kerr nonlinearity of this system, whereby the resonance frequency depends on the intracavity field amplitude, gives rise to an intrinsic feedback mechanism that enables passive stabilization without active external feedback. Using two-tone spectroscopy, we experimentally characterize the intrinsic nonlinear feedback mechanism and investigate its temporal stability through Allan deviation analysis. The frequency fluctuations of the locked cavity mode are reduced by nearly two orders of magnitude, reaching the 1/f noise floor, without continuous frequency tracking or active control. Kerr locking provides a general approach for self-stabilizing nonlinear microwave resonators by suppressing low-frequency cavity noise while preserving sensitivity to signals outside the locking bandwidth. This approach may benefit a broad range of systems, including SQUID-based resonators, optomechanical devices, and parametric amplifiers.
Measurements on the superconducting cavity maser (SCM) oscillator that show frequency stability of parts in 10/sup 5/ for times from 1 s to 10000 s are reported. A phase noise of approximately -80 dB/f/sup 3/ was measured. This short- and midterm performance is believed to be better than that of any known microwave oscillator. In particular, stability at a measuring time of 1 s is ten times better than that of a hydrogen maser, and phase noise is more than 20 dB below that of the best multiplied quartz crystal oscillators.>
The International Space Station provides an ideal platform for high precision frequency measurements, both as applied to scientific experiments and as regards basic time metrology. Consequently, a variety of clocks are being developed for flight on the Space Station, a majority of which are atomic clocks with very good stability for time periods in excess of 1,000 seconds. We plan to significantly augment the scope and capability of the ensemble of space clocks by adding to it SUperconducting Microwave Oscillator, SUMO. SUMO is a space version of the superconducting cavity stabilized oscillator, SCSO; the most precise clock developed to date for the interval range of around 100seconds. Short descriptions are given of the SUMO project and the SCSO technology and the principal disturbances causing frequency fluctuations are outlined. The planned improvements to the SCSO and preliminary results of the development work for SUMO are also highlighted.
Environmental noise coupling to mechanical experiments often introduces low-frequency fluctuations to the resonators, adding noise to measurements and reducing signal to noise. To counter these fluctuations, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency-modulating (FM) the microwave generator. The feedback has a bandwidth of 400 Hz, with a reduction of cavity fluctuations by 84% integrating up to a bandwidth of 2 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by 73%. This scheme can be scaled to enable multi-tone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked, multi-tone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multi-tone microwave locking technique presented here is expected to be relevant for a wide range of fields of research.
Microwave cavities are commonly used in many experiments, including optomechanics, magnetic field sensing, magnomechanics, and circuit quantum electrodynamics. Noise, such as variations in the magnetic field or mechanical vibrations, can cause fluctuations of the natural frequency of the cavity, creating challenges in operating them in experiments. To overcome these challenges, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne-interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency modulating the microwave generator. The feedback has a bandwidth of 400 Hz, with a reduction of cavity fluctuations by $85\mathrm{%}$ integrating up to a bandwidth of 2 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by $73\mathrm{%}$. This scheme can be scaled to enable multitone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked multitone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multitone microwave locking technique presented here is expected to be relevant for a wide range of microwave-cavity experiments.