In situ calibration of microwave attenuation and gain using a cryogenic on-chip attenuator

Abstract

Accurate in situ calibration of microwave attenuation and amplification-chain noise is essential for superconducting quantum circuits. We demonstrate a compact, self-calibrating cryogenic noise source based on an on-chip chromium attenuator that can be resistively heated with nanowatt-level power and directly integrated into a coaxial microwave line at the mixing-chamber stage. By comparing Johnson-Nyquist noise generated by Joule and microwave heating, measured through the amplification chain, the attenuation of the input line, and hence the gain of the chain, is determined without requiring knowledge of the attenuator temperature. The device exhibits millisecond-scale response times and negligible heating of the cryostat base plate. Using this approach, we determine the gain and added noise of a cryogenic amplification chain over the 4-8 GHz band. Our results provide a simple and accurate method to characterize near-quantum-limited parametric amplifiers used in superconducting-qubit readout.

Figures (5)

• Figure 1: a) On-chip attenuator design with R$_{1} = 26$$\Omega$ and R$_{2} = 70$$\Omega$. b) Experimental setup showing the placement of the on-chip attenuator and the fixed-frequency radiation-field thermometer at the base plate of the dilution refrigerator, and their connection to microwave lines (black) and DC lines (orange). The input and output band-pass filters were chosen depending on the experiment. More details can be found in the main text. (BP: band-pass, LP: low-pass, HP: high-pass, $A_{\rm line}$: attenuation of the input line at the reference plane of the on-chip attenuator, $A_{\rm att}$: attenuation of the on-chip attenuator) c) The temperature of the 5.5 GHz microwave field measured with the thermometer as a function of the Joule power applied to the on-chip attenuator. The experimental data (blue) is fitted by the power law as shown in eq. \ref{['eq:PowerLaw']} (orange). d) Thermalization times of the on-chip attenuator after applying a microwave heating pulse (green). The heating and cooling responses are fitted (orange) by single exponential to estimate the time constants.
• Figure 2: a) Sketch showing the frequency overlap between the thermal noise, the transmission band of the amplification chain, and the three output band-pass filters (1: 6.8-7.8 GHz, 2: 4.9-6.2 GHz; 3: 3.5-4.5 GHz) used to restrict the analog bandwidth in different power spectral density (PSD) measurements. For each filter, the signal tone to be calibrated, $\omega_{\rm sig}$, is swept in the rejection band of the filter (gray region), whereas noise is detected at $\omega_{\rm det}$ (black dot) in the transmission band (colored region). b) Power spectral densities measured at $\omega_{\rm det}=7$ GHz by Joule heating (purple) and a RF heating (blue) at $\omega_{\rm sig}=4$ GHz of the on-chip attenuator. The tone applied was rejected at room temperature with the output band-pass filter 1. The Joule and RF heating traces are separated by the attenuation $A$ of the input line. The tone heating was also acquired via the reference line without the on-chip attenuator (orange) to show the onset of heating of the bulkhead attenuators (diamond marker). Since their contribution is negligible (see main text), the best overlap (red) of the RF heating with the Joule heating giving the attenuation $A$ was fitted from $P_{\rm sig}=-22.5$ dBm (above the noise floor, dot marker) until an arbitrary power $P_{\rm sig}=-5$ dBm (cross marker). c) Attenuation profile obtained by comparing Joule and RF heating at different $\omega_{\rm sig}$. Three detection frequencies were considered and implemented with the set of output band-passes depicted in a). The red band in the background highlights the bandwidth of the amplification chain.
• Figure 3: a) Scattering in the $I-Q$ plane of a weak coherent tone transmitted through the amplification chain. The projections onto the $I$ and $Q$ axes are fitted with Gaussian distributions, from which the mean $\mu$ and standard deviation $\sigma$ are extracted. b) Added noise (top) and gain (bottom) of the amplification chain, referenced to the input plane of the noise source as mounted in Fig. \ref{['fig:Fig1']}(b). The error bars are obtained by propagating the uncertainty in the attenuation, taken to be $\pm 0.5$ dB.
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