Several quantum physics experiments have been conducted in a low-temperature environment inside a dilution refrigerator to observe low energy scale phenomena such as superfluidity and superconductivity. Herein, we report an approach to generate a precise quantized voltage in a cryogenic environment cooled with a dilution refrigerator using Josephson voltage standard (JVS) devices. Our aim is to realize quantum metrology triangle (QMT) measurements in a configuration, which is constructed of three independent quantum devices, that is, single-electron pump (SEP), quantized Hall resistance (QHR), and JVS devices, are connected in one dilution refrigerator [1]-[3]. The operation of JVS devices with 10^–8 order accuracy in a dilution refrigerator is challenging owing to the limited cooling power of the cryostat, electrical noise from long wiring cables, strong magnetic field necessary for the QHR operation, etc., when compared with the operation in ordinary refrigerator dedicated to JVS-device cooling with liquid helium or 4 K mechanical coolers.
In our experiment, a NbN-based programmable Josephson voltage standard (PJVS) device capable of generating arbitrary voltages up to 2 V was used [4]. The PJVS device was driven with a DC bias current and a 16 GHz microwave and operated at temperatures around 10 K.
First, the thermal stability of the module for the PJVS device assembled on the 4 K stage of a dilution refrigerator was designed and evaluated considering the heat balance between the cooling power of the 4 K stage and the heat inflow to the PJVS system setup [5]. The cooling power of the 4 K stage is 1.3 W. Out of 1.3 W, 0.9 W will be used for the other setups for SEP, QHR and dilution systems, resulting in a residual cooling power of 0.4 W. To keep heat inflow from bias and microwave cables to the 4 K stage within 0.4 W, the thermal conductivity of them must be kept sufficiently low. However, materials with low thermal conductivity also have low electrical conductivity and generate high Joule heating when electrical current flows. As a result of optimizing the heat balance of wiring and their implementation, we succeeded in stabilizing the temperature of the PJVS module within ±5 mK.
Next, we attempted to optimize the bias-current and microwave for the proper operation of the PJVS device. We investigated the bias margin by changing the microwave frequency and the microwave power and found the best operating condition. Then, we measured the generated voltage and accumulated the data for 16 h to reduce the measurement uncertainty due to random noise. As a result, we confirmed that the PJVS device appropriately outputs a quantized voltage of 1 mV within a 10 nV/V order uncertainty.