The Superconducting Low-inductance Undulatory Galvanometer (SLUG) is a linear, phase-sensitive, quantum-limited amplifier that can amplify ultra-weak microwave signals at frequencies up to 10 GHz or potentially higher, such as the output from cavity-based searches for the axion, a dark matter candidate. The SLUG amplifier differs from the closely related Superconducting Quantum Interference Device (SQUID) amplifier in that the input signal is directly injected into the SLUG rather than being inductively coupled through a multiturn input coil. The direct injection greatly simplifies the SLUG's microwave circuit integration and modeling, whilst enabling potentially higher frequency operation. Here we present the design and modeling of a SLUG amplifier that can be realised from a single-layer of Nb, with nanobridge weak-links fabricated using either electron-beam (EBL) or focussed ion beam (FIB) lithography as the Josephson elements. We discuss the input and output impedance, the forward transimpedance, and the potential power gain assuming a matched source and load. We also discuss the necessary impedance matching of the SLUG to the characteristic 50 Omega on-chip microwave environment.

Superconducting circuits play a crucial role in the advancement of quantum computing and quantum sensing. Typically such circuits require the presence of a non-linear element, where the engineered anharmonicity (Kerr factor) and resonant linewidth determine the potential applications of the circuit. In this work we have fabricated Nb-based CPW resonators embedded with a DC SQUID incorporating Nb nanobridges as the weak links. We use two-tone spectroscopy to study the non-linear behaviour of the device at 15 mK up to a field of 2.48 mT. Under the application of a blue-detuned pump, the device shows a decrease in the resonant frequency which is used to estimate the Kerr factor. We further apply a red-detuned pump to go beyond the bifurcation threshold and observe the appearance of an additional idler mode with net gain. The gain of the device was maximized by further decreasing the pump frequency, showing a maximum amplification of 15 dB. Finally, we show agreement between the Kerr non-linear oscillator model and the measured transmission spectrum, and highlight further design modifications to improve the gain and bandwidth of such devices.

Recently the exploration of nonlinear microwave response in superconducting circuits has been extended to Nb nanobridges that can operate at higher magnetic fields, frequencies, and temperatures than their conventional Al counterparts. Nb nanobridge-based Superconducting Quantum Interference Devices (SQUIDs) have shown potential applications in quantum information processing, weak signal detection, and single spin detection. Combining such non-linear elements with circuit Quantum Electrodynamic (QED) elements like coplanar waveguide (CPW) resonators allows the study of the nonlinearity of such systems. In this work we report on the design, fabrication and dispersive microwave readout of a Nb DC nanoSQUID embedded in a superconducting quarter-wavelength resonator. The measured flux-tuneability of the resonance shows a modulation of a few MHz and fits simulations, giving a critical current of 330 mu A and a screening parameter beta(L) of 4.07. Following this we present results showing Kerr-type detuning with a pump tone applied to the device.

Niobium nanobridge SQUIDs have shown exceptional noise performance with potential applications in quantum information processing, weak signal detection and single spin detection where the nanobridge geometry should enable efficient electromagnetic coupling to implanted spins. Combining such devices with dispersive microwave readout circuitry allows the spin sensitivity to be further improved by overcoming the standard thermal limit. Here we report on the fabrication and dispersive microwave readout of an array of niobium nanobridge rf SQUIDs incorporated into a superconducting resonator, including the optimization of the nanobridge fabrication process by electron beam lithography. We show the measured flux-tuneability of the resonance is in good agreement with theory, and we also discuss how the nonlinearity of the weak-link in the resonator structure allows for the mediation of parametric effects to enhance performance.

In 2021 the Quantum Sensors for the Hidden Sector (QSHS) collaboration was founded in the UK and received funding to develop and demonstrate quantum devices with the potential to detect hidden sector particles in the \muμeV to 100 \muμeV mass window. The collaboration has been developing a range of devices. It is building a high-field, low-temperature facility at the University of Sheffield to characterise and test the devices in a haloscope geometry. This paper introduces the collaboration’s motivation, aims, and progress.

In 2021 the Quantum Sensors for the Hidden Sector (QSHS) collaboration was founded in the UK. We received funding as part of the Quantum Technologies for Fundamental Physics programme to develop and demonstrate quantum devices with the potential to detect hidden-sector particles such as axions and dark photons in the ~1μeV/c^2 to ~100μeV/c^2 mass window. Our collaboration is formed from a diverse community of condensed matter physicists, quantum technologists, theorists and (astro) particle physics experimentalists. We are designing and fabricating a range of “quantum devices” and constructing a high-field, low-temperature facility at the University of Sheffield to characterise and test the devices in an axion haloscope geometry, initially using an rf cavity. This poster was presented at the 17th Patras workshop on axions, WIMPs and WISPs on the 8th August 2022 in Mainz, Germany.

SQUIDs (Superconducting Quantum Interference Devices) are macroscopic quantum devices capable of detecting and measuring a wide variety of physical parameters with unprecedented sensitivity. SQUIDs based on nanobridge weak links have shown increasing promise for quantum information and quantum sensing applications such as single spin detection. Focussed ion beam etched nanobridges have properties which can enhance nanoSQUID device performance but are often limited in terms of their non-hysteretic operating temperature range. Here we describe measurements of FIB-milled nanobridges, as single weak links or in nanoSQUIDs, made using either Ga, Xe or Ne ion beam sources. Their properties as a function of temperature, bias current, magnetic field and microwave power are measured and modelled according to a range of superconductivity models, as a means for improved understanding of the associated nanobridge parameters. We further propose techniques to extend the non-hysteretic operating temperature range of the devices.

Niobium-based nanobridge superconducting quantum interference devices (SQUIDs) have shown very low noise performance and high-frequency operation. We describe how we are bringing together these two aspects of nanobridge SQUIDs with the aim of realizing single spin-flip detection using microwave inductive readout techniques, where the nanobridge SQUID is integrated into a superconducting coplanar waveguide resonator. Using electron beam lithography (EBL) is ideal for fabricating nanobridge junctions and has the advantage of being easily scalable compared to using a focused ion beam. In this article, we demonstrate that EBL is suitable for fabricating nanobridge junction SQUIDs, and they exhibit very comparable performance to previous focused ion beam milled SQUIDs. Our integrated devices show potential to be used for flux-tunable sensors.

Josephson junctions and SQUIDs with graphene or other 2D materials as the weak link between superconductors have become a hot topic of research in recent years, with respect to both fundamental physics and potential applications. We have previously reported ultra-wide Josephson junctions (up to 80 {\mu}m wide) based on CVD graphene where the critical current was found to be uniformly distributed in the direction perpendicular to the current. In this paper, we demonstrate that the unusually large Josephson penetration depth {\lambda}_J that this corresponds to is enabled by the unique geometric structure of Josephson junctions based on 2D materials. We derive a new expression for the Josephson penetration depth of such junctions and verify our assumptions by numerical simulations.

Superconducting QUantum Interference Devices (SQUIDs) based on nanobridge junctions have shown increasing promise for single particle detection. This paper describes the development of the fabrication of improved and reproducible nanobridge junctions fabricated by focused ion beam (FIB) milling from niobium thin films. Although the very low noise properties of nanobridge SQUIDs are well known, the nature of the milling process is little understood at the level of local superconducting properties. In this paper, we report the results for nanobridge Josephson devices and SQUIDs, which we believe are the first to be made by Xenon (Xe) FIB milling. Temperature-dependent current-voltage behavior, microwave-induced Shapiro steps, and SQUID response to magnetic fields have been measured. We make preliminary comparisons with nominally identical devices milled from Nb thin films using either Xe or Ga ions.

Josephson junctions with graphene as the weak link between superconductors have been intensely studied in recent years, with respect to both fundamental physics and potential applications. However, most of the previous work was based on mechanically exfoliated graphene, which is not compatible with wafer-scale production. To overcome this limitation, we have used graphene grown by chemical vapour deposition (CVD) as the weak link of Josephson junctions. We demonstrate that very short, wide CVD-graphene-based Josephson junctions with Nb electrodes can work without any undesirable hysteresis in their electrical characteristics from 1.5 K down to a base temperature of 320 mK, and their gate-tuneable critical current shows an ideal Fraunhofer-like interference pattern in a perpendicular magnetic field. Furthermore, for our shortest junctions (50 nm in length), we find that the normal state resistance oscillates with the gate voltage, consistent with the junctions being in the ballistic regime, a feature not previously observed in CVD-graphene-based Josephson junctions.

We discuss steps toward the readout of the position of a nanoelectromagnetic system (NEMS) beam resonator using a Nb nanosuperconducting quantum interference device (nanoSQUID). We describe our fabrication procedure for coupling the nanoSQUID and a suspended Al-coated Si3N4 NEMS resonator together by a combination of focused ion beam lithography and nanomanipulation. We discuss typical electrical characteristics of the integrated devices, and independent postfabrication atomic force microscope nanoindentation measurements of the elastic properties of the integrated resonator to estimate its natural frequencies of vibration. We compare and discuss the response of a nanoSQUID with current-carrying and superconducting screening (noncurrent carrying) modes of operation of the resonator.

We present a two-signal single flux quantum (SFQ) detection scheme for the purpose of reading out two pixels of a superconducting nanowire single photon detector (SNSPD). The circuit is based on a coincidence buffer element which is able to output a signal when both of its input lines are triggered. The circuit model for the SNSPD element is simulated in SPICE and optimized to match the experimental SNSPD response data. The two-signal detection scheme is simulated using JSIM which allows for the simulation of Josephson junction elements in a circuit. We demonstrate a model of the two-signal circuit operating with two simulated SNSPD pixel inputs and investigate the response of the scheme when a phase shift is applied to one of the inputs. The scheme shows potential as a useful coincidence detector of single photons. We also present preliminary experimental results of nanobridge-based Josephson junctions to be used in the realization of the coincidence detector circuit. Evidence of the nanobridges exhibiting Josephson behavior (SQUID modulation) are presented.

This paper investigates the feasibility of using weak link nanobridges as Josephson junction elements for the purpose of creating Josephson circuits. We demonstrate the development of a single-step electron beam lithography procedure to fabricate niobium nanobridges with dimensions down to 40 nm x 100 nm. The single-step process facilitates fabrication that is scalable to complex circuits that require many junctions. We measure the IV-characteristics (IVC) of the nanobridges between temperatures of 4.2 and 9 K and find agreement with numerical simulations and the analytical resistively shunted junction (RSJ) model. Furthermore, we investigate the behaviour of the nanobridges under rf irradiation and observe the characteristic microwave-induced Shapiro steps. Our simulated IVC under rf irradiation using both the RSJ model and circuit simulator JSIM are in agreement with the experimental data. As a potential use of nanobridges in circuits requiring many junctions, we investigate the theoretical performance of a nanobridge-based Josephson comparator circuit using JSIM.

Nanoscale superconducting quantum interference devices (nanoSQUIDs) most commonly use Dayem bridges as Josephson elements to reduce the loop size and achieve high spin sensitivity. Except at temperatures close to the critical temperature Tc, the electrical characteristics of these bridges exhibit undesirable thermal hysteresis which complicates device operation. This makes proper thermal analysis an essential design consideration for optimising nanoSQUID performance at ultralow temperatures. However the existing theoretical models for this hysteresis were developed for micron-scale devices operating close to liquid helium temperatures, and are not fully applicable to a new generation of much smaller devices operating at significantly lower temperatures. We have therefore developed a new analytic heat model which enables a more accurate prediction of the thermal behaviour in such circumstances. We demonstrate that this model is in good agreement with experimental results measured down to 100 mK and discuss its validity for different nanoSQUID geometries.

NanoSQUIDs made from Nb thin films have been produced with nanometre loop sizes down to 200 nm, using weak-link junctions with dimensions less than 60 nm. These composite (W/Nb) single layer thin film devices, patterned by FIB milling, show extremely good low-noise performance ~170 nΦo at temperatures between 5 and 8.5 K and can operate in rather high magnetic fields (at least up to 1 T) . The devices produced so far have a limited operating temperature range, typically only 1-2 K. We have the goal of achieving operation at 4.2 K, to be compatible with the best SQUID series array (SSA) preamplifier available. Using the SSA to readout the nanoSQUIDs provides us with a means of investigating the intrinsic noise of the former. In this paper we report improved white noise levels of these nanoSQUIDs, enabling potential detection of a single electronic spin flip in a 1-Hz bandwidth. At low frequencies the noise performance is already limited by SSA preamplifier noise.

Superconducting quantum interference devices (SQUIDs) incorporating thin film nanobridges as weak links have sensitivities approaching that required for single spin detection at 4.2 K. However, due to thermal hysteresis they are difficult to operate at much lower temperatures which hinder their application to many quantum measurements. To overcome this, we have developed nanoscale SQUIDs made from titanium-gold proximity bilayers. We show that their electrical properties are consistent with a theoretical model developed for heat flow in bilayers and demonstrate that they enable magnetic measurements to be made on a sample at system temperatures down to 60 mK.

We report on the low-frequency noise performance of niobium dc superconducting quantum interference devices (SQUIDs), which contain nanobridges fabricated by focused ion beam lithography as the active Josephson elements. The devices have feature sizes down to 70 nm. We have measured devices of different loop sizes in two readout configurations: nano-scale loop sizes in small signal mode using a series SQUID array as a low-temperature pre-amplifier, and larger micron-scale loop sizes in a conventional flux-locked loop. We investigate the different contributions to the low frequency noise and report on electrical measurements made in applied magnetic fields of up to 0.5 T (in-plane) and 0.1 T (perpendicular to the plane) at operating temperatures around 7 K. We compare the measurements with the existing theories of noise in a dc SQUID.