Microwave Modeling and Characterization of Superconductive Circuits for Quantum Voltage Standard Applications at 4 K

On-Wafer Vector-Network-Analyzer Measurements at mK Temperatures

“…We also repeated any movements for which the difference between the target and final measured position exceeded 30 µm. 4 We also developed a calibration procedure to relate the positions measured by the resistive sensors to actual positions on the circuit board. We included nine 500 µm by 500 µm positioning squares etched in the top-level metal in our design for this purpose.…”

“…4 shows the 36 edge positions we detected as red crosses during one of the room-temperature positioning calibrations we performed. 4 The figure also shows the positions of the nine calibration squares in blue. If the resistive position sensors were completely accurate, the detected edge positions would all lie on the edges of the nine calibration squares.…”

“…The energy required to move the positioners and probes at mK temperatures quickly heats the mixing-chamber plate and can easily exceed the capacity of the dilution refrigerator to maintain normal helium circulation by boiling off the helium mix too quickly, thereby requiring the user to recollect and recondense the helium to return to normal helium circulation. To address this, we developed an approach for positioning the probes at mK temperatures by limiting motions to smaller 4 increments than we used a 4.4 K and allowing the dilution refrigerator to cool between these steps. However, this approach required roughly 8 hours on average to move the probes between devices, potentially increasing measurement error due to drift in the system.…”

“…10(b) shows the corresponding 101-tone modulated signal in the frequency domain, which had a 10 MHz tone spacing and a 3) performed with the direct-mK strategy. 4 repetition rate of 100 ns. This modulation is typical of those used to control transmon qubits at the cooled on-wafer reference plane [18], [19], [24].…”

“…Microwave scattering-parameter measurements performed at mK temperatures have proved extremely useful in the design of microwave components utilized for qubit control and readout. While we and others have been performing on-wafer microwave measurements at 4 K for some time [1], [2], [3], [4], [5], microwave measurements at mK temperatures are more challenging: signals input into the dilution refrigerators used to reach mK temperatures must be greatly attenuated to reduce noise and control thermal loading, signals exciting nonlinear superconducting circuits must be weak, cooling power is limited, cabling is long and obtaining repeatable measurements is difficult. The first system for performing calibrated two-port vector scattering parameters at mK temperatures was reported by Ranzani,et al,in [6].…”