Amplitude Noise Cancellation of Microwave Tones

TL;DR

This paper addresses the problem of amplitude noise in microwave generator tones, which can limit sensitivity and cause heating in microwave optomechanics. It introduces an FPGA-based amplitude-noise cancellation technique with tunable gain and time delay to destructively interfere with the carrier’s noise, achieving up to 13 dB total-noise reduction at a 2 MHz offset from a 4 GHz tone. The method is validated in a microwave optomechanics setup with a silicon nitride membrane, where cancellation reduces externally induced cavity heating by a factor of 3.5 and lowers the minimum oscillator occupation by a factor of 2, outperforming room-temperature filtering in this regime. The approach offers tunable bandwidth and offset, broadening noise-cancellation strategies for high-power microwave experiments and enabling better control in low-noise measurements and sideband cooling.

Abstract

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. The FPGA additionally 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.

Figures (4)

• Figure 1: (a) Comparison of the measured total noise and phase noise of a microwave tone: At low offsets the phase noise is the dominant contributor to the total noise. Cancellation is done at an offset of 2 MHz, where the difference between the two noise powers is significant. (b) Schematic of the circuit used for amplitude noise cancellation.
• Figure 2: Noise cancellation of a 4 GHz tone. The dark gray line depicts the uncanceled total noise and the shaded light gray region shows the phase noise: (a) With optimized parameters we measure amplitude noise cancellation reaching the phase noise level for filter bandwidths [0.1; 0.2; 1; 2] MHz from narrowest to widest, where $f_\mathrm{offset}$ is the frequency offset from the carrier tone. Black lines are fits to the data based on Eq. (\ref{["Eq:S'"]}). (b) Canceling with smaller filter bandwidths [0.1; 1; 10] kHz from left to right. The effect of an unoptimized phase is presented here with asymmetric noise profiles and a shift in the frequency of minimum power to be off-center from the filter. Here, $f_\mathrm{filter}$ is the central frequency of the band-pass filter. The resulting FWHM of each profile are labeled in the plot.
• Figure 3: Optomechanical system: (a) Schematic of the equivalent circuit for the optomechanical system. The temperatures of relevant baths are shown in units of quanta with colored regions. Couplings between baths and their strengths are shown with labeled two-way arrows. (b) Photographs of a representative membrane and antenna device mounted to a 3D copper cavity.
• Figure 4: Extracting occupation numbers from the measured mechanical sidebands in the output spectrum: (a) Three example mechanical noise spectra for the filtered noise scenario with theoretical fits. From bottom to top the cooperativities are [18; 180; 1800]. Data are offset for clarity. (b) Fit parameters give the cavity bath occupations $n_\mathrm{c}^T$ and (c) oscillator occupations $n_\mathrm{m}$ as a function of cooperativity for the three noise scenarios. Missing data points occur when $n_\mathrm{c}^T = 0$, adjacent points to these are connected with dashed lines.