Calibration of cryogenic amplification chains using normal-metal–insulator–superconductor junctions

Abstract

Various applications of quantum devices call for an accurate calibration of cryogenic amplification chains. To this end, we present a convenient calibration scheme and use it to accurately measure the total gain and noise temperature of an amplification chain by employing normal-metal-insulator-superconductor (NIS) junctions. Our method is based on the radiation emitted by inelastic electron tunneling across voltage-biased NIS junctions. We derive an analytical equation that relates the generated power to the applied bias voltage which is the only control parameter of the device. After the setup has been characterized using a standard voltage reflection measurement, the total gain and the noise temperature are extracted by fitting the analytical equation to the microwave power measured at the output of the amplification chain. The 1σ uncertainty of the total gain of 51.84 dB appears to be of the order of 0.1 dB.Superconducting circuits provide a promising approach to implement a variety of quantum devices and to explore fundamental physical phenomena, such as the lightmatter interaction 1 in the ultrastrong coupling regime 2 . In addition, superconducting circuits are potential candidates for building a large-scale quantum computer 3,4 : superconducting qubits can be coupled in a scalable way 5-12 , and both the gate and the measurement fidelity of qubits exceed the threshold required for quantum error correction 10,13-15 .Since superconducting quantum circuits typically operate in the single-photon regime, signals are amplified substantially for readout 3,16-21 using a chain of amplifiers, which is distributed over several temperature stages 16,17 . In the first stage, a near-quantumlimited amplifier 22 , such as a Josephson parametric amplifier 23-26 , is often used to lower the noise temperature of the amplification chain 27 . As a result of cascading several amplifiers, the uncertainty in the total gain of the amplification chain becomes significant and may complicate, for example, the estimation of the photon number in the superconducting circuit. Therefore, accurate, fast, and simple methods for measuring the total gain of an amplification chain are desirable in the investigation of quantum electric devices.The gain and the noise temperature of cryogenic amplifiers can be measured, for example, using superconducting qubits 22,28 , Planck spectroscopy of a sub-kelvin thermal noise source 29 , and the Y -factor method 30,31 which utilizes the Johnson-Nyquist noise emitted at different temperatures. In addition to these methods, shot noise 32,33 sources, such as normal-metal-insulatornormal-metal junctions, can be used to determine the gain and noise temperature of cryogenic amplifiers 34,35 . However, this method typically requires a calibration measurement of the setup due to impedance mismatch 34 .In this paper, we present an accurate alternative calibration scheme for the total gain and noise temperature of an amplification chain by utilizing photonassisted electron tunneling in normal-metal-insulatorsuper...

Tunable refrigerator for nonlinear quantum electric circuits

“…1 is of the order of a few hundred microseconds [16,45,46] for state-of-the-art transmons, and we find an upper limit for the Dynes parameter in this case to be γ D < 10 −5 /α 2 . For α = 1, this value is smaller than those already obtained in experiments with a QCR [40,42,48,50], but in general, values down to 10 −7 have been demonstrated [51]. If it appears challenging to reduce the Dynes parameter to such a low value in practice, it is straightforward to reduce α by reducing the coupling capacitance between the qubit and the QCR in fabrication.…”

“…Finite temperature corrections to Eq. (A1) can be found using a Sommerfeld expansion [41,50]. For energies below the gap, E < , we can distinguish two cases.…”

Fast control of dissipation in a superconducting resonator

“…It has been used to cool down a photon mode of the resonator 27 , and to observe a Lamb shift in a cQED system 31 . Furthermore, QCR can be used as a cryogenic photon source 29 , which makes it applicable for a calibration of cryogenic amplification chains 30 . Details of the QCR operation and theory are described in Ref.…”

Recent Developments in Quantum-Circuit Refrigeration

“…The voltage-enabled control of the microwave power renders it feasible to use such a system for characterizing the total gain and noise temperature of an amplification chain connected to the QCR-resonator system. This was experimentally studied in Hyyppä et al in 2019 [55] using a sample illustrated schematically in Figure 9a. The sample incorporates a superconducting CPW resonator that is capacitively coupled to a dc-biased QCR and a transmission line.…”

“…The characterization protocol relies on the known relation between the input power of the transmission line P tr and the bias voltage of the QCR. In the high voltage regime eV QCR /(2∆) 1, an accurate ap-proximation for the the input power P tr is obtained as [55] P tr ≈ γ tr γT…”