arXiv subjects

David J. Goldie

Publications and source records attributed to David J. Goldie.

At least 19 recordsLinked to original sources

arXiv2024

Superconducting Microwave Detector Technology for Ultra-Light Dark Matter Haloscopes and other Fundamental Physics Experiments: Background Theory (Part I)

We consider how superconducting microwave detector technology might be applied to the readout of cavity-axion haloscopes and similar fundamental physics experiments. Expressions for the sensitivity of two detection schemes are derived: 1) a dispersive spectrometer, and 2) a direct-conversion/homodyne receiver using detectors as mixing elements. In both cases the semi-classical/Poisson-mixture approach is used to account for quantum effects. Preliminary sensitivity calculations are performed to guide future development work. These suggest the homodyne scheme offers a near-term solution for realising near-quantum-noise limited receivers with improved usability compared with parametric amplifiers. Similarly, they show that the dispersive spectrometer offers a potential way to beat the quantum noise limit, but that significant technological development work is needed to do so.

physics.ins-det↗

arXiv2024

Superconducting Microwave Detector Technology for Ultra-Light Dark Matter Haloscopes and other Fundamental Physics Experiments: Device Physics (Part II)

We consider and compare candidate superconducting detector technologies that might be applied to the readout of cavity-axion haloscopes and similar fundamental physics experiments. We conclude that a transition edge sensor (TES) configured with ballistic-phonon thermal isolation operated with a superconducting transition temperature of order 30 mK would provide quantum-limited detection performance at frequencies above 5 GHz. This would permit the realisation of integrated homodyne detectors based on TESs that we believe would make a unique contribution to a variety of fundamental physics experiments, particularly those based on reading out microwave cavities in the quantum ground state.

physics.ins-det↗

arXiv2020

Characterising the optical response of ultra-low-noise far-infrared 60-110 $μ$m transition edge sensors

Far-infrared Transition Edge Sensors (TESs) are being developed for the SAFARI grating spectrometer on the cooled-aperture space telescope SPICA. In support of this work, we have devised a cryogenic (90 mK) test facility for carrying out precision optical measurements on ultra-low-noise TESs. Although our facility is suitable for the whole of the SAFARI wavelength range, 34-230 $μ$m, we focus on a representative set of measurements at 60-110 $μ$m using a device having a Noise Equivalent Power (NEP) of 0.32 $\mathrm{aW/\sqrt{Hz}}$. The system is able to perform a range of measurements: (i) Dark electrical characterisation. (ii) Optical efficiency with respect to a partially coherent beam having a modal composition identical to that of an ideal imaging telescope. (iii) Optical saturation and dynamic range. (iv) Fast optical transient response to a modulated thermal source. (v) Optical transient response in the presence of high-level background loading. We describe dark measurements to determine the operating characteristics of a TES, and then compare predicted optical behaviour with measured optical behaviour. By comparing electrical and optical transient response, we were able to observe thermalisation in the device. We comment on the challenge of eliminating stray light.

physics.ins-det↗

arXiv2020

Suppressed-gap millimetre wave kinetic inductance detectors using DC-bias current

In this study, we evaluate the suitability of using DC-biased aluminium resonators as low-frequency kinetic inductance detectors operating in the frequency range of 50 - 120 GHz. Our analysis routine for supercurrent-biased resonators is based on the Usadel equations and gives outputs including density of states, complex conductivities, transmission line properties, and quasiparticle lifetimes. Results from our analysis confirm previous experimental observations on resonant frequency tuneability and retention of high quality factor. Crucially, our analysis suggests that DC-biased resonators demonstrate significantly suppressed superconducting density of states gap. Consequently these resonators have lower frequency detection threshold and are suitable materials for low-frequency kinetic inductance detectors.

astro-ph.IM↗

arXiv2020

Nonlinear Effects in Superconducting Thin Film Microwave Resonators

We discuss how reactive and dissipative non-linearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of non-linear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative non-linearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.

cond-mat.mes-hall↗

arXiv2019

Nonlinear Properties of Supercurrent-Carrying Single and Multi-Layer Thin-Film Superconductors

Superconducting thin-films are central to the operation of many kinds of quantum sensors and quantum computing devices: Kinetic Inductance Detectors (KIDs), Travelling-Wave Parametric Amplifiers (TWPAs), Qubits, and Spin-based Quantum Memory elements. In all cases, the nonlinearity resulting from the supercurrent is a critical aspect of behaviour, either because it is central to the operation of the device (TWPA), or because it results in non-ideal second-order effects (KID). Here we present an analysis of supercurrent carrying superconducting thin-films that is based on the generalized Usadel equations. Our analysis framework is suitable for both homogeneous and multilayer thin-films, and can be used to calculate the resulting density of states, superconducting transition temperature, superconducting critical current, complex conductivities, complex surface impedances, transmission line propagation constants, and nonlinear kinetic inductances in the presence of supercurrent. Our analysis gives the scale of kinetic inductance nonlinearity (I*) for a given material combination and geometry, and is important in optimizing the design of detectors and amplifiers in terms of materials, geometries, and dimensions. To investigate the validity of our analysis across a wide range of supercurrent, we have measured the transition temperatures of superconducting thin-films as a function of DC supercurrent. These measurements show good agreement with our theoretical predictions in the experimentally relevant range of current values.

cond-mat.supr-con↗

arXiv2019

Loss and Saturation in Superconducting Travelling-Wave Parametric Amplifiers

We have developed a coupled-mode analysis framework for superconducting travelling-wave parametric amplifiers using the full Telegrapher's equations to incorporate loss-related behaviour. Our model provides an explanation of previous experimental observations regarding loss in amplifiers, advantages of concatenating amplifiers to achieve high gains, and signal gain saturation. This work can be used to guide the design of amplifiers in terms of the choice of material systems, transmission line geometry, operating conditions, and pump strength.

cond-mat.supr-con↗

arXiv2018

Calculation and measurement of critical temperature in thin superconducting multilayers

We have applied the Usadel equations to thin-film multilayer superconductors, and have calculated the critical temperature for general thin-film S-S' bilayer. We extended the bilayer calculation to general thin-film multilayers. The model demonstrates excellent fit with experimental data obtained from Ti-Al bilayers of varying thicknesses.

cond-mat.supr-con↗

arXiv2018

Electromagnetic models for multilayer superconducting transmission lines

Thin-film superconducting transmission lines play important roles in many signal transmission and detection systems, including qubit coupling and read-out schemes, electron spin resonance systems, parametric amplifiers, and various ultra high sensitivity detectors. Here we present a rigorous method for computing the electromagnetic behaviour of superconducting microstrip transmission lines and coplanar waveguides. Our method is based on conformal mapping, and is suitable for both homogeneous superconductors and proximity-coupled multilayers. We also present an effective conductivity approximation of multilayers, thereby allowing the multilayers to be analysed using existing electromagnetic design software. We compute the numerical results for Al-Ti bilayers and discuss the validity of our full computation and homogeneous approximation.

cond-mat.supr-con↗

arXiv2018

Superconducting transition edge sensors with phononic thermal isolation

The sensitivity of a low-noise superconducting transition edge sensor (TES) is determined by the thermal conductance of the support structure that connects the active elements of the device to the heat bath. Low-noise devices require conductances in the range 0.1 to 10 pWK$^{-1}$, and so have to rely on diffusive phonon scattering in long, narrow, amorphous SiN$_\text{x}$ legs. We show that it is possible to manufacture and operate TESs having short, ballistic low-dimensional legs (cross section 500$\times$200 nm) that contain multi-element phononic interferometers and ring resonators. These legs transport heat in effectively just 5 elastic modes at the TES's operating temperature (< 150 mK), which is close to the quantised limit of 4. The phononic filters then reduce the thermal flux further by frequency-domain filtering. For example, a micromachined 3-element ring resonator reduced the flux to 19 % of a straight-legged ballistic device operating at the quantised limit, and 38 % of a straight-legged diffusive reference device. This work opens the way to manufacturing TESs where performance is determined entirely by filtered, few-mode, ballistic thermal transport in short, low-heat capacity legs, free from the artifacts of two level systems.

cond-mat.mes-hall↗

arXiv2017

Exploring the performance of thin-film superconducting multilayers as Kinetic Inductance Detectors for low-frequency detection

We have solved numerically the diffusive Usadel equations that describe the spatially-varying superconducting proximity effect in Ti-Al thin-film bi- and trilayers with thickness values that are suitable for Kinetic Inductance Detectors (KIDs) to operate as photon detectors with detection thresholds in the frequency range of 50-90 GHz. Using Nam's extension of the Mattis-Bardeen calculation of the superconductor complex conductivity, we show how to calculate the surface impedance for the spatially varying case, and hence the surface impedance quality factor. In addition, we calculate energy-and spatially-averaged quasiparticle lifetimes at temperatures well-below the transition temperature and compare to calculation in Al. Our results for the pair-breaking threshold demonstrate differences between bilayers and trilayers with the same total film thicknesses. We also predict high quality factors and long multilayer-averaged quasiparticle recombination times compared to thin-film Al. Our calculations give a route for designing KIDs to operate in this scientifically-important frequency regime.

cond-mat.supr-con↗

arXiv2017

Thermal elastic-wave attenuation in low-dimensional SiN$_{x}$ bars at low temperatures

At low temperatures, < 200 mK, the thermal flux through low-dimensional amorphous dielectric bars, < 2 $μ$m wide and 200 nm thick, is transported by a small number of low-order elastic modes. For long bars, L > 400 $μ$m, it is known that the conductance scales as 1/L, where L is the length, but for short bars, 1 $μ$m < L < 400 $μ$m, the length dependence is poorly known. Although it is assumed that the transport must exhibit a diffusive to ballistic transition, the functional form of the transition and the scale size over which the transition occurs have not, to our knowledge, been measured. In this paper, we use ultra-low-noise superconducting Transition Edge Sensors (TESs) to measure the heat flux through a set of SiN$_{x}$ bars to establish the characteristic scale size of the ballistic to diffusive transition. For bars supporting 6 to 7 modes, we measure a thermal elastic-wave attenuation length of 20 $μ$m. The measurement is important because it sheds light on the scattering processes, which in turn are closely related to the generation of thermal fluctuation noise. Our own interest lies in creating patterned phononic filters for controlling heat flow and thermal noise in ultra-low-noise devices, but the work will be of interest to others trying to isolate devices from their environments, and studying loss mechanisms in micro-mechanical resonators.

cond-mat.mes-hall↗

arXiv2017

Modelling proximity effects in Transition Edge Sensors to investigate the influence of lateral metal structures

The bilayers of Transition Edge Sensors (TESs) are often modified with additional normal-metal features such as bars or dots. Previous device measurements suggest that these features improve performance, reducing electrical noise and altering response times. However, there is currently no numerical model to predict and quantify these effects. Here we extend existing techniques based on Usadel's equations to describe TESs with normal-metal features. We show their influence on the principal TES characteristics, such as the small-signal electrothermal parameters $α$ and $β$ and the superconducting transition temperature $T_{c}$. Additionally, we examine the effects of an applied magnetic field on the device performance. Our model predicts a decrease in $T_{c}$, $α$ and $β$ as the number of lateral metal structures is increased. We also obtain a relationship between the length $L$ of a TES and its critical temperature, $T_{c} \propto L^{-0.7}$ for a bilayer with normal-metal bars. We predict a periodic magnetic flux dependence of $α, β$ and $I_{c}$. Our results demonstrate good agreement with published experimental data, which also show the reduction of $α$, $β$ and $T_{c}$ with increasing number of bars. The observed Fraunhofer dependence of critical current on magnetic flux is also anticipated by our model. The success of this model in predicting the effects of additional structures suggests that in the future numerical methods can be used to better inform the design of TESs, prior to device processing.

astro-ph.IM↗

arXiv2016

Broadband illumination of superconducting pair breaking photon detectors

Understanding the detailed behaviour of superconducting pair breaking photon detectors such as Kinetic Inductance Detectors requires knowledge of the nonequilibrium quasiparticle energy distributions. We have previously calculated the steady state distributions resulting from uniform absorption of monochromatic sub gap and above gap frequency radiation by thin films. In this work, we use the same methods to calculate the effect of illumination by broadband sources, such as thermal radiation from astrophysical phenomena or from the readout system. Absorption of photons at multiple above gap frequencies is shown to not change the structure of the quasiparticle energy distribution close to the superconducting gap. Hence for typical absorbed powers, we find the effects of absorption of broadband pair breaking radiation can simply be considered as the sum of the effects of absorption of many monochromatic sources. Distribution averaged quantities, like quasiparticle generation effciency $η$, match exactly a weighted average over the bandwidth of the source of calculations assuming a monochromatic source. For sub gap frequencies, however, distributing the absorbed power across multiple frequencies does change the low energy quasiparticle distribution. For moderate and high absorbed powers, this results in a significantly larger $η$ - a higher number of excess quasiparticles for a broadband source compared to a monochromatic source of equal total absorbed power. Typically in KIDs the microwave power absorbed has a very narrow bandwidth, but in devices with broad resonance characteristics (low quality factors), this increase in $η$ may be measurable.

cond-mat.supr-con↗

arXiv2015

Quasiparticle effective temperature in superconducting thin films illuminated at THz frequencies

The response of superconducting pair-breaking detectors is dependent on the details of the quasiparticle distribution. In Kinetic Inductance Detectors (KIDs), where both pair breaking and non-pair breaking photons are absorbed simultaneously, calculating the detector response therefore requires knowledge of the often nonequilibrium distributions. The quasiparticle effective temperature provides a good approximation to these nonequilibrium distributions. We compare an analytical expression relating absorbed power and the quasiparticle effective temperature in superconducting thin films to full solutions for the nonequilibrium distributions, and find good agreement for a range of materials, absorbed powers, photon frequencies and temperatures typical of KIDs. This analytical expression allows inclusion of nonequilibrium effects in device models without solving for the detailed distributions. We also show our calculations of the frequency dependence of the detector response are in agreement with recent experimental measurements of the response of Ta KIDs at THz frequencies.

cond-mat.supr-con↗

arXiv2015

Elastic Interferometers as Phononic Filters for Thermal Isolation in Low-Noise Transition Edge Sensors

In order to achieve low Noise-Equivalent-Powers (NEP < 1 aW Hz$^{-1/2}$) Transition Edge Sensors (TES) require high levels of thermal isolation between the superconducting bilayer and the heat bath. We propose that short micro-machined acoustic interferometers can be used for low-noise thermal isolation, avoiding many of the difficulties inherent in conventional, long- legged TES designs. In this paper, we present a detailed elastic wave model of interferometric phononic legs, and demonstrate the successful fabrication of TESs that are thermally isolated by interferometric structures.

cond-mat.mes-hall↗

arXiv2015

Nonequilibrium superconducting thin films with sub-gap and pair-breaking photon illumination

We calculate nonequilibrium quasiparticle and phonon distributions for a number of widely-used low transition temperature thin-film superconductors under constant, uniform illumination by sub-gap probe and pair-breaking signal photons simultaneously. From these distributions we calculate material-characteristic parameters that allow rapid evaluation of an effective quasiparticle temperature using a simple analytical expression, for all materials studied (Mo, Al, Ta, Nb, and NbN) for all photon energies. We also explore the temperature and energy-dependence of the low-energy quasiparticle generation efficiency $η$ by pair-breaking signal photons finding $η\approx 0.6$ in the limit of thick films at low bath temperatures that is material-independent. Taking the energy distribution of excess quasiparticles into account, we find $η\to 1$ as the bath temperature approaches the transition temperature in agreement with the assumption of the two-temperature model of the nonequilibrium response that is appropriate in that regime. The behaviour of $η$ with signal frequency scaled by the superconducting energy gap is also shown to be material-independent, and is in qualitative agreement with recent experimental results. An enhancement of $η$ in the presence of sub-gap (probe) photons is shown to be most significant at signal frequencies near the superconducting gap frequency and arises due to multiple photon absorption events that increase the average energy of excess quasiparticles above that in the absence of the probe.

cond-mat.supr-con↗

arXiv2013

Partially Coherent Optical Modelling of the Ultra-Low-Noise Far-Infrared Imaging Arrays on the SPICA Mission

We have developed a range of theoretical and numerical techniques for modeling the multi-mode, 210-34 micron, ultra-low-noise Transition Edge Sensors that will be used on the SAFARI instrument on the ESA/JAXA cooled-aperture FIR space telescope SPICA. The models include a detailed analysis of the resistive and reactive properties of thin superconducting absorbing films, and a partially coherent mode-matching analysis of patterned films in multi-mode waveguide. The technique allows the natural optical modes, modal responsivities, and Stokes maps of complicated structures comprising patterned films in profiled waveguides and cavities to be determined.

astro-ph.IM↗