A SQUID-Based Picovoltmeter for Quantum Resistors
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A SQUID‑Based Picovoltmeter for Quantum Resistors Vidhi Shingla1 · Ethan Kleinbaum1 · Gábor A. Csáthy1,2,3 Received: 21 August 2019 / Accepted: 2 February 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We present a sensitive voltage amplifier suited for measurements of source impedances in the k Ω range at dilution refrigerator temperatures. The circuit is based on a commercial dc SQUID, an impedance matching transformer, and it works on the principle of √ negative feedback. At 10 mK, the amplifier contribution to the noise is only 17 pV/ Hz , which is negligible in comparison with the fluctuations of the thermal voltage of a 3.25 kΩ metallic source resistor. Various circuit parameters of the amplifier are discussed. Keywords Low-noise amplifier · dc SQUID · Quantum resistor
1 Introduction In many applications, SQUIDs (Superconducting QUantum Interference Devices) are used as low-noise current amplifiers [1–3]. In such setups, the current to be measured is passed through an input coil and the magnetic field generated by this coil is efficiently coupled to the SQUID loop. Modern dc SQUIDs with the largest √ input coils achieve noise levels as low as 0.5 pA/ Hz [2]. If in addition an impedance matching device is used, such as a transformer [4–15] or a cryogenic current √ comparator [16–23], noise levels of a few fA/ Hz are accessible. Such sensitive current amplifiers are often used in high precision resistance bridges [16–23] and in noise thermometry [24–29]. SQUIDs can also be configured for voltage measurement [1]. Sensitive voltage amplifiers based on the principle of negative feedback were built first using early Vidhi Shingla and Ethan Kleinbaum have contributed equally. * Gábor A. Csáthy [email protected] 1
Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
2
Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA
3
Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
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Journal of Low Temperature Physics
SQUID-like devices [30], rf SQUIDs [31–37], dc SQUIDs [38–40], and high Tc SQUIDs [41, 42]. In contrast to current amplifiers, voltage amplifiers have an input impedance greatly exceeding the resistance of the source to be measured. Most SQUID-based voltmeters offer low-noise performance and sufficiently high input impedance for source resistors RS in the m Ω–Ω range [31–35, 38–42]. However, numerous phenomena of interest occur in sources of resistance well into the k Ω range. Examples are the integer and fractional quantum Hall effect [43, 44], conduction phenomena in quantum point contacts [45], in topological insulators [46, 47], and the quantum anomalous Hall effect [48, 49], for which resistances are of the order of the quantum resistance h∕e2 ≃ 25.8 kΩ . The use of impedance matching transformers extended the use of SQUID-based voltage√amplifiers for source resistances in the k Ω range, achieving noise levels of 0.8 nV/ Hz [36]
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