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arXiv:2304.06296

Multi-Tone Microwave Locking via Real-Time Feedback

Jean-Paul van Soest, C. A. Potts, Sarwan Peiter, Adrián Sanz Mora, Gary Alexander Steele

Published Apr 13, 2023• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2304.06296

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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 400400400 Hz, with a reduction of cavity fluctuations by 84%84\%84% integrating up to a bandwidth of 222 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by 73%73\%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.
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High-gain amplifiers of electromagnetic signals operating near the quantum limit are crucial for quantum information systems and ultrasensitive quantum measurements.However, the existing techniques have a limited gain-bandwidth product and only operate with weak input signals.Here, we demonstrate a two-port optomechanical scheme for amplification and routing of microwave signals, a system that simultaneously performs high-gain amplification and frequency conversion in the quantum regime.Our amplifier, implemented in a two-cavity microwave optomechanical device, shows 41 dB of gain and has a high dynamic range, handling input signals up to 10 13 photons per second, 3 orders of magnitude more than corresponding Josephson parametric amplifiers.We show that although the active medium, the mechanical resonator, is at a high temperature far from the quantum limit, only 4.6 quanta of noise is added to the input signal.Our method can be readily applied to a wide variety of optomechanical systems, including hybrid optical-microwave systems, creating a universal hub for signals at the quantum level.
Carrier noise in coherent tones limits sensitivity and causes heating in many experimental systems, such as force sensors, time-keeping, and studies of macroscopic quantum phenomena. Much progress has been made to reduce carrier noise using phase noise cancellation techniques; however, in systems where amplitude noise dominates, these methods are ineffective. Here, we present a technique to reduce amplitude noise from microwave generators using feedback cancellation. The method uses a field-programmable gate array (FPGA) to reproduce noise with a tunable gain and time delay, resulting in destructive interference when combined with the original tone. In addition, the FPGA allows for tuning of the frequency offset and bandwidth in which the noise is canceled. By employing the cancellation, we observe 13 dB of noise power reduction at a 2 MHz offset from a 4 GHz microwave tone, lowering the total noise to the phase noise level. To verify its applicability, we utilize the setup in a microwave optomechanics experiment to investigate the effect of generator noise on the sideband cooling of a 0.5 mm silicon nitride membrane resonator. We observe that with our technique, the rate of externally induced cavity heating is reduced by a factor of 3.5 and the minimum oscillator occupation is lowered by a factor of 2. This method broadens the field of noise cancellation techniques, where amplitude noise is becoming an increasingly important consideration in microwave systems as phase noise performances improve over time.
We successfully demonstrate low-frequency noise suppression in the resonant-frequency fluctuations of a cavity-embedded Cooper-pair transistor (cCPT) driven at single-photon occupancy. In particular, we report a reduction in the resonant-frequency fluctuations caused by the internal charge noise over a bandwidth of approximately 1.4kHz1.4\phantom{\rule{0.2em}{0ex}}\text{kHz}1.4kHz when the cavity is driven at an average photon number n=10n=10n=10 and a bandwidth of 11 Hz for an average n=1n=1n=1. The gate-dependent tunability of the cCPT allows us to implement a feedback scheme derived from the Pound-Drever-Hall locking technique. This reduces fluctuations due to intrinsic charge noise, which otherwise interfere with the operation of the cCPT as a near quantum-limited electrometer. Our technique can be generalized to achieve frequency stabilization in tunable microwave resonators that play a vital role in today's quantum computing architectures, thereby moderating the limitations in detection caused by the intrinsic 1/f1/f1/f noise on such circuit devices. The work discusses the various aspects relating to the operation of a fully functional feedback loop down to the single-photon level.
We successfully demonstrate low-frequency noise suppression in the resonant frequency fluctuations of a cavity-embedded Cooper pair transistor (cCPT) driven at single-photon occupancy. In particular, we report a reduction in the resonant frequency fluctuations caused by the internal charge noise over a bandwidth of $\sim$1.4 kHz when the cavity is driven at an average photon number n=10n=10n=10, and a bandwidth of 11 Hz for average n=1n=1n=1. The gate-dependent tunability of the cCPT allows us to implement a feedback-scheme, derived from the Pound-Drever-Hall locking technique. This reduces fluctuations due to intrinsic charge-noise, which otherwise interferes with the cCPT's operation as a near quantum-limited electrometer. We believe our technique can be generalized to achieve frequency stabilization in tunable microwave resonators that play a vital role in today's quantum computing architecture, thereby moderating the limitations in detection caused by the intrinsic 1/f1/f1/f-noise on such circuit devices. The work discusses the various aspects relating to the operation of a fully functional feedback loop down to the single-photon level.