Noise Thermometry for Ultralow Temperatures
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Noise Thermometry for Ultralow Temperatures A. Fleischmann1 · A. Reiser1 · C. Enss1 Received: 22 December 2019 / Accepted: 18 August 2020 © The Author(s) 2020
Abstract In recent years, current-sensing dc-SQUIDs have enabled the application of noise thermometry at ultralow temperatures. A major advantage of noise thermometry is the fact that no driving current is needed to operate the device and thus the heat dissipation within the thermometer can be reduced to a minimum. Such devices can be used either in primary or relative primary mode and cover typically several orders of magnitude in temperature extending into the low microkelvin regime. Here we will review recent advances of noise thermometry for ultralow temperatures. Keywords Thermometry · Thermal noise · Ultralow temperatures
1 Introduction Measuring the temperature at low temperatures is a particular challenge, as only very small power can be used. While for moderately low temperatures down to about 20 mK many suitable choices for thermometry exist, measuring even lower temperatures still remains a difficult task and the number of applicable methods is rather limited. Overviews on the different methods available for thermometry at low temperatures can be found for example in [1, 2]. In recent years noise thermometry has emerged as a new way of determining low temperatures with the potential to be used over a wide range of cryogenic temperatures and in particular going down to ultralow temperatures. It is based on the Brownian motion of electrons in conductors, a phenomenon that was already considered by Einstein in his second paper on the theory of Brownian motion in * C. Enss [email protected]‑heidelberg.de A. Fleischmann [email protected]‑heidelberg.de A. Reiser [email protected]‑heidelberg.de 1
Kirchhoff‑Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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Journal of Low Temperature Physics
1906 [3]. The existence of this effect was discovered experimentally more than two decades later by Johnson, who showed that any resistor exhibits thermally driven voltage fluctuations that depend only on two parameters, the resistance R itself and the equilibrium temperature T [4, 5]. The theoretical description was worked out by Nyquist, who calculated the resulting power spectral density [6]: ⟨ 2⟩ ] [ U 1 1 (1) , SU = = 4hfR + hf ∕k T 𝛥f 2 e B −1 with f denoting the frequency and 𝛥f the bandwidth over which the fluctuations are measured. For temperatures and frequencies fulfilling the condition hf ∕kB T ≪ 1 this expression can be expanded, with the two leading terms given by ⟨ 2⟩ ] [ U 1 hf SU = ≈ 4kB TR 1 + . (2) 𝛥f 12 kB T The first term SU = 4kB TR is often referred to as classical approximation of the Nyquist noise. For the typical conditions relevant to practical noise thermometers the classical expression is fully sufficient. Even for temperatures as low as 10 μK the corresponding frequency is 200 kHz, and thus exceeding the bandwidth of a typical noise measurem
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