Current distribution and transition width in superconducting transition-edge sensors

Present models of the superconducting-to-normal transition in transition-edge sensors (TESs) do not describe the current distribution within a biased TES. This distribution is complicated by normal-metal features that are integral to TES design. We present a model with one free parameter that describes the evolution of the current distribution with bias. To probe the current distribution experimentally, we fabricated TES devices with different current return geometries. Devices where the current return geometry mirrors current flow within the device have sharper transitions, thus allowing for a direct test of the current-flow model. Measurements from these devices show that current meanders through a TES low in the resistive transition but flows across the normal-metal features by 40% of the normal-state resistance. Comparison of transition sharpness between device designs reveals that self-induced magnetic fields play an important role in determining the width of the superconducting transition. [http://dx.doi.org/10.1063/1.4771984]Comment: 5 pages, 4 figure

The Practice of Pulse Processing

The analysis of data from x-ray microcalorimeters requires great care; their excellent intrinsic energy resolution cannot usually be achieved in practice without a statistically near-optimal pulse analysis and corrections for important systematic errors. We describe the essential parts of a pulse-analysis pipeline for data from x-ray microcalorimeters, including steps taken to reduce systematic gain variation and the unwelcome dependence of filtered pulse heights on the exact pulse-arrival time. We find these steps collectively to be essential tools for getting the best results from a microcalorimeter-based x-ray spectrometer.Comment: Accepted for publication in J. Low Temperature Physics, special issue for the proceedings of the Low Temperature Detectors 16 conferenc

Approaches to the Optimal Nonlinear Analysis of Microcalorimeter Pulses

We consider how to analyze microcalorimeter pulses for quantities that are nonlinear in the data, while preserving the signal-to-noise advantages of lin- ear optimal filtering. We successfully apply our chosen approach to compute the electrothermal feedback energy deficit (the "Joule energy") of a pulse, which has been proposed as a linear estimator of the deposited photon energy.Comment: Accepted by Journal of Low Temperature Physics. Contribution to the proceedings of Low Temperature Detectors 17, (Kurume Japan, 2017

Filters for High Rate Pulse Processing

We introduce a filter-construction method for pulse processing that differs in two respects from that in standard optimal filtering, in which the average pulse shape and noise-power spectral density are combined to create a convolution filter for estimating pulse heights. First, the proposed filters are computed in the time domain, to avoid periodicity artifacts of the discrete Fourier transform, and second, orthogonality constraints are imposed on the filters, to reduce the filtering procedure's sensitivity to unknown baseline height and pulse tails. We analyze the proposed filters, predicting energy resolution under several scenarios, and apply the filters to high-rate pulse data from gamma-rays measured by a transition-edge-sensor microcalorimeter.Comment: 5 pages, 6 figures, 1 tabl

Insensitivity of sub-Kelvin electron-phonon coupling to substrate properties

We have examined the role of the substrate on electron-phonon coupling in normal metal films of Mn-doped Al at temperatures below 1 K. Normal metal-insulator-superconductor junctions were used to measure the electron temperature in the films as a function of Joule heating power and phonon temperature. Theory suggests that the distribution of phonons available for interaction with electrons in metal films may depend on the acoustic properties of the substrate, namely, that the electron-phonon coupling constant Sigma would be larger on the substrate with smaller sound speed. In contrast, our results indicate that within experimental error (typically +/- 10%), Sigma is unchanged among the two acoustically distinct substrates used in our investigation.Comment: 4 pages, 2 figures. Version 2 contains changes reflected in the final published articl

A three-wave mixing kinetic inductance traveling-wave amplifier with near-quantum-limited noise performance

We present a theoretical model and experimental characterization of a microwave kinetic inductance traveling-wave amplifier (KIT), whose noise performance, measured by a shot-noise tunnel junction (SNTJ), approaches the quantum limit. Biased with a dc current, the KIT operates in a three-wave mixing fashion, thereby reducing by several orders of magnitude the power of the microwave pump tone and associated parasitic heating compared to conventional four-wave mixing KIT devices. It consists of a 50 Ohms artificial transmission line whose dispersion allows for a controlled amplification bandwidth. We measure $16.5^{+1}_{-1.3}$ dB of gain across a 2 GHz bandwidth with an input 1 dB compression power of -63 dBm, in qualitative agreement with theory. Using a theoretical framework that accounts for the SNTJ-generated noise entering both the signal and idler ports of the KIT, we measure the system-added noise of an amplification chain that integrates the KIT as the first amplifier. This system-added noise, $3.1\pm0.6$ quanta (equivalent to $0.66\pm0.15$ K) between 3.5 and 5.5 GHz, is the one that a device replacing the SNTJ in that chain would see. This KIT is therefore suitable to read large arrays of microwave kinetic inductance detectors and promising for multiplexed superconducting qubit readout

Energy calibration of nonlinear microcalorimeters with uncertainty estimates from Gaussian process regression

The nonlinear energy response of cryogenic microcalorimeters is usually corrected through an empirical calibration. X-ray or gamma-ray emission lines of known shape and energy anchor a smooth function that generalizes the calibration data and converts detector measurements to energies. We argue that this function should be an approximating spline. The theory of Gaussian process regression makes a case for this functional form. It also provides an important benefit previously absent from our calibration method: a quantitative uncertainty estimate for the calibrated energies, with lower uncertainty near the best-constrained calibration points.Comment: Submitted to J. Low Temperature Physics for the Proceedings of the 19th International Workshop on Low-Temperature Detectors (2021

Optimization and analysis of code-division multiplexed TES microcalorimeters

We are developing code-division multiplexing (CDM) systems for transition-edge sensor arrays with the goal of reaching multiplexing factors in the hundreds. We report on x-ray measurements made with a four-channel prototype CDM system that employs a flux-summing architecture, emphasizing data-analysis issues. We describe an empirical method to determine the demodulation matrix that minimizes cross-talk. This CDM system achieves energy resolutions of between 2.3 eV and 3.0 eV FWHM at 5.9 keV.Comment: 7 pages, 5 figures. Presented at the 14th International Workshop on Low Temperature Detectors, Heidelberg University, August 1-5, 2011, proceedings to be published in the Journal of Low Temperature Physic

Superconducting micro-resonator arrays with ideal frequency spacing and extremely low frequency collision rate

We present a wafer trimming technique for producing superconducting micro-resonator arrays with highly uniform frequency spacing. With the light-emitting diode (LED) mapper technique demonstrated previously, we first map the measured resonance frequencies to the physical resonators. Then, we fine-tune each resonator's frequency by lithographically trimming a small length, calculated from the deviation of the measured frequency from its design value, from the interdigitated capacitor. We demonstrate this technique on a 127-resonator array made of titanium-nitride (TiN) and show that the uniformity of frequency spacing is greatly improved. The array yield in terms of frequency collisions improves from 84% to 97%, while the quality factors and noise properties are unaffected. The wafer trimming technique provides an easy-to-implement tool to improve the yield and multiplexing density of large resonator arrays, which is important for various applications in photon detection and quantum computing.Comment: 5 pages,4 figure

A Highly Linear Calibration Metric for TES X-ray Microcalorimeters

Transition-edge sensor X-ray microcalorimeters are usually calibrated empirically, as the most widely-used calibration metric, optimal filtered pulse height (OFPH), in general has an unknown dependance on photon energy, $E_{\gamma}$. Because the calibration function can only be measured at specific points where photons of a known energy can be produced, this unknown dependence of OFPH on $E_{\gamma}$ leads to calibration errors and the need for time-intensive calibration measurements and analysis. A calibration metric that is nearly linear as a function of $E_{\gamma}$ could help alleviate these problems. In this work, we assess the linearity of a physically motivated calibration metric, $E_{Joule}$. We measure calibration pulses in the range 4.5 keV$<$$E_{\gamma}$$<$9.6 keV with detectors optimized for 6 keV photons to compare the linearity properties of $E_{Joule}$ to OFPH. In these test data sets, we find that $E_{Joule}$ fits a linear function an order of magnitude better than OFPH. Furthermore, calibration functions using $E_{J}$, an optimized version of $E_{Joule}$, are linear within the 2-3 eV noise of the data