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arXiv:2210.06869 · Physical Review Letters

Voltage Fluctuations in ac Biased Superconducting Transition-Edge Sensors

Luciano G. Gottardi, M. de Wit, E. Taralli, Kenichiro Nagayashi, Alexander G. Kozorezov

Published May 26, 2021• 21 citations
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Abstract

We present a detailed analysis of the fundamental noise sources in superconducting transition-edge sensors (TESs), ac voltage biased at MHz frequencies and treated as superconducting weak links. We have studied the noise in the resistive transition as a function of bath temperature of several detectors with different normal resistances and geometries. We show that the "excess" noise, typically observed in the TES electrical bandwidth, can be explained by the equilibrium Johnson noise of the quasiparticles generated within the weak link. The fluctuations at the Josephson frequency and higher harmonics contribute significantly to the measured voltage noise at the detector bandwidth through the nonlinear response of the weak link with a sinusoidal current-phase relation.

DOI
10.1103/physrevlett.126.217001

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Applied Physics Letters•May 7, 2004•124 citations
We present a detailed analysis of the fundamental noise sources in superconducting transition-edge sensors (TESs), ac voltage biased at MHz frequencies and treated as superconducting weak links. We have studied the noise in the resistive transition as a function of bath temperature of several detectors with different normal resistances and geometries. We show that the "excess" noise, typically observed in the TES electrical bandwidth, can be explained by the equilibrium Johnson noise of the quasiparticles generated within the weak link. The fluctuations at the Josephson frequency and higher harmonics contribute significantly to the measured voltage noise at the detector bandwidth through the nonlinear response of the weak link with a sinusoidal current-phase relation.
Transition-edge sensors (TESs) are two-dimensional superconducting films utilized as highly sensitive detectors of energy or power. These detectors are voltage biased in the superconducting-normal transition where the film resistance is both finite and a strong function of temperature. Unfortunately, the amount of electrical noise observed in TESs exceeds the predictions of existing noise theories. We describe a possible mechanism for the unexplained excess noise, which we term "mixed-down noise." The source is Johnson noise, which is mixed down to low frequencies by Josephson oscillations in devices with a nonlinear current-voltage relationship. We derive an expression for the power spectral density of this noise and show that its predictions agree with measured data.
We report the experimental evidence of the ac Josephson effect in a transition edge sensor (TES) operating in a frequency domain multiplexer and biased by ac voltage at MHz frequencies. The effect is observed by measuring the non-linear impedance of the sensor. The TES is treated as a weakly linked superconducting system and within the resistively shunted junction model framework. We provide a full theoretical explanation of the results by finding the analytic solution of the non-inertial Langevian equation of the system and calculating the non-linear response of the detector to a large ac bias current in the presence of noise.
The current noise at the output of a microcalorimeter with a voltage biased superconducting transition edge thermometer is studied in detail. In addition to the two well-known noise sources: thermal fluctuation noise from the heat link to the bath and Johnson noise from the resistive thermometer, a third noise source strongly correlated with the steepness of the thermometer is required to fit the measured noise spectra. Thermal fluctuation noise, originating in the thermometer itself, fully explains the additional noise. A simple model provides quantitative agreement between the observed and calculated noise spectra for all bias points in the superconducting transition.
It has been recently demonstrated that superconducting transition edge-sensors behave as weak-links due to longitudinally induced superconductivity from the leads with higher Tc. In this work we study the implication of this behaviour for transition-edge sensors (TES)-based bolometers and microcalorimeter under ac bias. The TESs are read-out at frequencies between 1 and 5 MHz by a frequency domain multiplexer based on a linearised two-stage SQUID amplifier and high-Q lithographically made superconducting LC resonators. In particular, we focus on SRON TiAu TES bolometers with a measured dark noise equivalent power of 3.2 \\times 10 -19 W/\\sqrt{Hz} developed for the short wavelength band for the instrument SAFARI on the SPICA telescope.
It has long been recognized that weak-link effects play an important role in transition edge sensors (Sadleir et al., 2010 and Sadleir et al., 2011), especially when the intrinsic transition temperature of the leads is much higher than that of the device itself. The weak-link physics has also been identified as an important complication if the TES is read-out under MHz-range AC bias for multiplexing purposes (Gottardi et al., 2014). More recently, it has been proposed that the commonly observed “excess” Johnson noise could also be explained as a white Johnson noise component that is mixed down into the signal band from higher frequencies via Josephson oscillations on a non-linear I-V relation (Gottardi et al., 2021 and Wessels et al., 2021). In recent experiments with small scale Mo/Au (50μ\muμm length, 15μ\muμm wide) TES devices with Nb leads (fabricated at GSFC) with a small DC bias applied, we have been able to directly observe Josephson oscillations over a kHz to MHz frequency range. The spectrum of the oscillations is well described by a simple damped oscillator model, with its center frequency scaling in direct proportion to the voltage across the TES. The second harmonic is also observed at small bias. If nothing else, we show that the Josephson oscillations provide a straightforward way to determine the value of the shunt-resistor with accuracy of10−4\mathbf {10^{-4}}10−4or better, as well as the offset voltage of the bias circuit. This is complementary to our previous work demonstrating that Shapiro steps in the IV curve induced by AC magnetic fields can be used for shunt resistor calibration (Zhou et al., 2018). Further work will be needed to determine if this effect can be observed in larger TES or those with relatively low-Tc\mathbf {T_{c}}Tc​contacts, where Shapiro steps are too weak to observe. It remains to be seen whether additional insights on the mixed-down Johnson noise can be obtained from a physics-based model of the weak-link.
The noise in superconducting transition-edge sensors (TESs) commonly exceeds simple theoretical predictions. The reason for this discrepancy is presently unexplained. We have measured the amplitude and frequency dependence of the noise in TES sensors with eight different geometries. In addition, we have measured the dependence of the noise on operating resistance, perpendicular magnetic field, and bath temperature. We find that the unexplained noise contribution is inversely correlated with the temperature width of the superconducting-to-normal transition and is reduced by a perpendicular field and in certain geometries. These results suggest paths to improved sensor performance.