The topic of superconducting nanowires has recently been an interesting field of research which has included the study of the superconductor to insulator transition (SIT), the observation of macroscopic quantum behavior such as quantum phase slips (QPS), and the potential use of nanowires as qubits. Superconducting coplanar microwave waveguide resonators have also become a popular way of studying superconducting junctions and qubits, as they provide an extremely low noise environment. For example, superconducting two-dimensional Fabry-Perot resonators have been used by other groups to make non-demolition measurements of a qubit. The motivation of this thesis will be the merging of the fields of superconducting nanowires and the technique of using superconducting microwave resonators to study junctions by incorporating a nanowire into the resonator itself at a current anti-node. By doing this, the nonlinear effects of the nanowire can be studied which may find application in single photon detectors, mixers, and the readout of qubits. We also employ the technique of molecular templating to fabricate some of the thinnest superconducting nanowires ever studied (down to ~ 5 nm in diameter in some cases). In this thesis, we extend the understanding of the nonlinear properties of a nanowire- resonator system and investigate a new type of nonlinearity that involves a pulsing regime between the superconducting and normal phases of the nanowire. We develop a model, which describes the results quantitatively and by modeling the system, we are able to extract information regarding the relaxation time of the nanowire back into the superconducting state. We also study double nanowire-resonator systems where two closely spaced parallel nanowires interrupt the resonator center conductor and form a loop where vortex tunneling processes can occur. Using a double nanowire-resonator we are able to observe the Little-Parks effect at low temperatures (where the resistance of the wires is immeasurably low) and are able to confirm the multivalued nature of the current phase relationship (CPR) in nanowires. Additionally, we observe an anomalous transmission regime where the periodic pulsing is replaced by stochastic amplitude fluctuations. In addition to microwave measurements on nanowires, we also study the normal state in resistively shunted nanowires with dc measurements where the inclusion of a shunt resistor is observed to change the nature of the normal state from the Joule heated state to a state that preserves phase coherence. Finally, the statistics on switching current events in graphene proximity junctions are analyzed and compared to the well known results for Josephson junctions. Only thermal activation (and no macroscopic quantum tunneling) is observed in graphene proximity superconducting junctions down to temperatures of ~ 300 mK.
The topic of superconducting nanowires has recently been an interesting field of research which has included the study of the superconductor to insulator transition (SIT), the observation of macroscopic quantum behavior such as quantum phase slips (QPS), and the potential use of nanowires as qubits. Superconducting coplanar microwave waveguide resonators have also become a popular way of studying superconducting junctions and qubits, as they provide an extremely low noise environment. For example, superconducting two-dimensional Fabry-Perot resonators have been used by other groups to make non-demolition measurements of a qubit. The motivation of this thesis will be the merging of the fields of superconducting nanowires and the technique of using superconducting microwave resonators to study junctions by incorporating a nanowire into the resonator itself at a current anti-node. By doing this, the nonlinear effects of the nanowire can be studied which may find application in single photon detectors, mixers, and the readout of qubits. We also employ the technique of molecular templating to fabricate some of the thinnest superconducting nanowires ever studied (down to ~ 5 nm in diameter in some cases). In this thesis, we extend the understanding of the nonlinear properties of a nanowire- resonator system and investigate a new type of nonlinearity that involves a pulsing regime between the superconducting and normal phases of the nanowire. We develop a model, which describes the results quantitatively and by modeling the system, we are able to extract information regarding the relaxation time of the nanowire back into the superconducting state. We also study double nanowire-resonator systems where two closely spaced parallel nanowires interrupt the resonator center conductor and form a loop where vortex tunneling processes can occur. Using a double nanowire-resonator we are able to observe the Little-Parks effect at low temperatures (where the resistance of the wires is immeasurably low) and are able to confirm the multivalued nature of the current phase relationship (CPR) in nanowires. Additionally, we observe an anomalous transmission regime where the periodic pulsing is replaced by stochastic amplitude fluctuations. In addition to microwave measurements on nanowires, we also study the normal state in resistively shunted nanowires with dc measurements where the inclusion of a shunt resistor is observed to change the nature of the normal state from the Joule heated state to a state that preserves phase coherence. Finally, the statistics on switching current events in graphene proximity junctions are analyzed and compared to the well known results for Josephson junctions. Only thermal activation (and no macroscopic quantum tunneling) is observed in graphene proximity superconducting junctions down to temperatures of ~ 300 mK.
This thesis investigates fundamental properties of Josephson junctions embedded in microwave circuits, and an application arising from this hybrid approach. We used the versatility of superconducting coplanar DC bias cavities to extract previously inaccessible information on phase coherent and subgap mechanisms of graphene Josephson junctions. Chapter 1 gives an introduction to the technology of Josephson field effect transistors, among which graphene junctions show promise for future improvements in quantum computation. Together with an overview of the Josephson effect in superconducting-semiconducting systems, we introduce the concept of coplanar DC bias cavities for probing Josephson junctions at gigahertz frequencies. In chapter 2, we describe the experimental methods developed for carrying out the subsequent measurements. We include details on fabrication, material properties and measurement setup. Results of graphene Josephson junctions embedded in DC bias microwave resonators are presented in chapters 3 and 4. By following the resonance frequency and losses of the circuit, we are able to extract the junctions’ Josephson inductance and subgap resistance. Studying the nonlinear power and bias current response reveals further information on the underlying loss mechanisms and current phase relation. We turn to an application of our hybrid bias cavity – Josephson junction devices to detect small, low-frequency currents in chapter 5. Our device is competitive with state-of-the-art techniques for microwave radiation detection and, with minor modifications, should be able to outperform existing technologies by orders of magnitude. Finally, we conclude the presented work in chapter 6 and provide an outlook on potential future research.
Macroscopic quantum tunneling is a process by which a macroscopic object, rather than a single electron, tunnels between two macroscopically distinct quantum states. In this dissertation, we will present the study of macroscopic quantum tunneling of phase-slips in superconducting devices, including one-dimensional nanowires, quasi-two-dimensional superconducting strips and doubly connected superconducting devices composed of two nanowires connected in parallel. We observe macroscopic quantum tunneling in these devices by measuring switching current distributions. It is known that the standard deviation of switching current distributions can be measured on a single nanowire to reveal temperatures at which macroscopic quantum tunneling is responsible for phase-slips. Therefore we begin by studying higher moments of the switching current distributions, namely the skewness S (a measure of the asymmetry of a distribution) and kurtosis K (a measure of its peakedness). We find that the skewness and kurtosis of the switching current distributions obtained via the Kurkijarvi process on devices composed of single nanowires do not depend on whether the switching events are initiated by quantum or thermal phase-slips. Skewness and kurtosis deviate considerably from the values associated with a Gaussian distribution (S=0 and K=3). If, in an experiment these higher moments approach Gaussian values they indicate the existence of noise. Next we study macroscopic quantum tunneling of phase-slips in quasi-two-dimensional superconducting strips, which are commercially available devices used as single-photon detectors. These devices are composed of (250 um) long, (120 nm) wide, meandering superconducting strips. Each time a photon with sufficient energy strikes the strip a voltage pulse is produced and counted. However, the accuracy of these detectors is limited by a rate of dark counts (false events). We find that at sufficiently low temperatures, the macroscopic quantum tunneling of a vortex through an edge barrier on the wire (which results in a phase-slip as the vortex crosses the wide wire) contributes a base-level dark count rate in these detectors which must be considered during operation at low enough temperatures. After studying tunneling in single one-dimensional nanowires and wide, quasi-two-dimensional strips, we move our focus to doubly connected superconducting samples composed of two nanowires connected in parallel. We characterize and model these devices, and show their applicability as nanometer-scale superconducting memory cells. We develop precise algorithms allowing us to write and read the information onto such memory cells. We also observe signatures of macroscopic quantum tunneling in these doubly connected devices by observing a saturation in the standard deviation of switching current distributions at low temperatures. We then discuss how macroscopic quantum tunneling of the memory state can lead to a dissipationless operation of the superconducting memory cell. In each of these devices, whether single one-dimensional nanowires, wide quasi-two-dimensional superconducting strips, or two nanowires in parallel, we find, quite surprisingly, that the same equations can be used to model macroscopic quantum tunneling at the high currents we apply. Therefore we argue that the physics of macroscopic quantum tunneling in wide quasi-two-dimensional strips and doubly connected nanowire devices can be well understood in the context of tunneling in a single, one-dimensional nanowire.
The key components in superconducting quantum computing architectures are qubits, couplers, microwave elements and low-noise amplifiers among others. In a variety of these subsystems, nonlinear circuit elements are an essential ingredient which enables their functionality. In this thesis, we study two different superconducting elements used to implement nonlinear capacitors. First we simulated a novel Josephson-junction-based tuneable nonlinear capacitor to couple flux qubits. Such a device implements a YY interaction, which has the potential to enhance the performance and extend the capabilities of current generation quantum annealers. We show that the interaction strength of the YY coupling is on the order of MHz and tuneable across zero. We discuss experimental realisations of this device to verify its function. Next, we present our study of a low temperature parametric amplifier utilizing the nonlinear capacitance of quantum phase-slip nanowires. We have fabricated a single-nanowire and two-nanowire variants which shunt a quarter-wavelength superconducting coplanar waveguide resonator. We characterised the nonlinear properties of the first variant such as the power-dependent resonance frequency, idler generation and signal gain, while in the second variant we developed a lock-in detection method to investigate the gate voltage response and demonstrate that the device acts as a gate-voltage-tuneable resonator. We also report on the progress towards a fabrication process for sputtered Al overlap junctions in the LCN cleanroom. Back-sputter and in-situ oxide growth techniques are developed as an alternative to shadow evaporation. These techniques are better suited for large-scale integration as they do not rely on angular deposition, but they require better control over the interfaces due to patterning the two electrodes separately. We characterised the processes using resistance measurements and characterised their low temperature properties. We show that our junctions exhibit overdamped dynamics and the critical current is suppressed with RF radiation.
The topic of the PhD project is a comparative study of phase dynamics and macroscopic quantum phenomena in moderately damped NbN, YBaCuO grain boundary (GB) Josephson junctions (JJs) and hybrid devices. This type of research activity responds to the needs of better identifying phase dynamics in JJs in the moderately damped regime, which is going to be more and more common in hybrid nanostructures. Issues on a more detailed understanding of coherence, dissipation and noise in the various devices have a relevant role in the progress of quantum circuits.
In the last few years, studies of phase dynamics and macroscopic quantum phenomena have been extended to junctions composed of materials other than the traditional low critical temperature superconductors (LTS) and to novel types of structures with unconventional barriers composed for instance of graphene sheets or of grain boundaries. Progress in engineering new materials into junctions and in understanding and controlling the physics of interfaces may offer novel solutions for junctions of superior quality and complementary functionalities, and therefore may lead in the long run to improve also specific qubit performances.
For LTS JJs, once the barrier thickness and the critical current density (Jc) have been fixed, a reduction in its size unavoidably leads to a lowering of the critical current and determines a quite different phase dynamics re-normalized to the new scaling energy. Lower critical currents Ic result in lower Josephson energies EJ, and higher levels of dissipation are expected. The range of the energy dynamical parameters is significantly enlarged, and it is technologically easier to reproducibly realize nontrivial configurations. These devices are characterized by intermediate levels of dissipation (moderately damped regime) and by phase diffusion phenomena. The low Jc limit seems to be characteristic also of all futuristic nanohybrids devices incorporating nanowires, and the moderately damped regime (MDR) is intrinsically more common than it could be expected.
Measurements of switching current distribution (SCD) in these last years have turned to be standard tools to investigate phase dynamics in unconventional and hybrid systems and nanostructures. High critical temperature superconductors (HTS) are an example of unconventional systems, because of the d-wave order parameter symmetry and of the presence of low-energy quasiparticles, which are expected to induce high level of dissipation and as a consequence to spoil macroscopic quantum coherence. A comparative study in systems so different and complementary is of great interest.
During the PhD program, we have performed measurements of SCD, both in the thermal and quantum regime down to 20 mK, on moderately damped NbN/MgO/NbN JJs and on YBCO biepitaxial GB JJs. The NbN JJs exhibit a crossover from thermal activation (TA) to macroscopic quantum tunneling (MQT) regime at about 90 mK. After the MQT saturation, the width of the SCD follows the expected dependence in the TA regime. Deviations are evident in proximity and above the crossover temperature T* (about 1.6K) where we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called phase diffusion (PD) are evident, such as the change of the switching distributions symmetry.
Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The combined analysis of these three regimes allowed us to extract the fundamental parameters, which completely characterize the dynamics of such moderately damped NbN JJs. In addition, clear signatures of the PD regime have been detected and numerical methods have been developed to estimate the dissipation level in the MDR.
As a term of comparison, the studies on moderately damped systems have been also carried out on HTS junctions, which have different levels of intrinsic dissipation induced by low energy quasi-particles, and are for this reason of great impact as a reference.
In such JJs we have clearly observed a direct transition from the MQT to the PD regime. The width of the SCDs is constant below 100mK, which is a clearly indication of a quantum activation regime. Above 100mK the negative temperature derivative of the width is consistent with a diffusive motion due to multiple escape and re-trapping in the potential wells. Thermal behavior of the width has been fitted through numerical simulations, thus providing the estimate of the damping factor. These conclusions of a PD regime also in YBaCuO JJs are supported by data in presence of an externally applied magnetic field, and are consistent with the numerical outcomes.
Numerical simulations of the thermal behavior of the SCD width for different values of the quality factor ranging from 1 to 10 have been carried out. Such numerical simulations allow us to reconstruct a (Q, kBT/EJ) phase diagram summarizing the various activation regimes. The transition curve between the PD regime and the running state following thermal or quantum activation has been determined numerically by varying the damping factor Q as function of the ratio between the thermal energy and the Josephson energy. The result of the calculation is a universal curve. A phase diagram valid in a large range of dissipation conditions emerges as a functional guide to classify the switching behavior and to settle the fundamental junction parameters and energies in the MDR. It is therefore a reference for phase dynamics of novel types of junction and system for which the nature of the current induced transition from the superconducting to the normal state has not been completely clarified.
Superconducting circuits combine zero electrical resistance with macroscopic quantum coherence, making them a versatile platform for both fundamental studies and technological applications. Modern thin-film deposition and lithography allow precise control over geometry, material composition, and dimensional scales, enabling the fabrication of complex superconducting structures with tailored properties. These capabilities give access to phenomena not achievable with conventional electronic components, establishing superconducting circuits as a unique tool for exploring quantum physics and developing devices with unique functionalities. In superconducting rings, macroscopic quantum coherence manifests as discrete circulating currents. Fluxoid quantization restricts these currents to discrete winding states. Transitions between winding states occur via phase-slip events. A phase slip event requires overcoming an energy barrier, which can be crossed either through thermal activation, resulting in thermally activated phase slips (TAPS), or via quantum tunneling, resulting in quantum phase slips (QPS) that have no classical analogue. Both processes depend sensitively on temperature, loop geometry, material properties, and the intrinsic properties of the superconductor. Embedding weak links or nanowires in a superconducting ring provides localized regions where phase slips preferentially occur, enabling controlled TAPS and QPS dynamics. When the QPS rate becomes sufficiently high, coherent tunneling between neighboring winding states generates an energy splitting, forming the basis of qubit states. The discrete winding states can thus be exploited for device applications: serving as robust memory elements when the energy barrier is high and phase slips are rare and well controlled, and as qubits when coherent quantum phase slips allow the system to occupy superpositions of distinct winding states, marking the transition from a classical bit to a quantum bit. Phase-slip dynamics in superconducting rings have traditionally been studied using switching-current measurements, in which the bias current is ramped until the ring or nanowire becomes resistive. While this approach provides statistical information about phase-slip rates, it is inherently dissipative and cannot detect events that do not drive the system in the normal state, leaving many phase slips hidden and preventing their unambiguous classification by origin or rate.This thesis develops a non-invasive, radio-frequency resonator-based platform for studying phase-slip dynamics in superconducting rings. Building on magnetooptical imaging of flux penetration in superconducting resonators, we first established methods to apply a local magnetic field to a loop without perturbing the resonator and couple it to the resonator, linking changes in circulating currents to shifts in the resonance frequency. This enabled continuous, timeresolved detection of individual phase-slip events on microsecond-to-nanosecond timescales. Using this platform, we systematically investigated how loop geometry, weak-link properties, kinetic inductance, and temperature govern phase-slip rates and dynamics. Deterministic control of discrete winding states in high-kinetic-inductance aluminum loops, our chosen material platform, was demonstrated, realizing a superconducting memory based on fluxoid quantization. By progressively reducing loop dimensions and introducing weak links, we observed quantum phase-slip events at millikelvin temperatures, providing the first experimental signatures of coherent tunneling between winding states, a first step toward realizing phase-slip-based qubits. Collectively, these results establish a robust experimental pathway from conventional DC measurements to non-invasive RF probing, provide a framework for controlled studies of superconducting phase-slip dynamics, and open the door to exploring and utilizing coherent phase slips in circuit-QED-compatible architectures with device geometries that are simple and easy to fabricate.
This thesis presents the results of the experimental studies on two kindof Superconducting circuits: one-dimensional Josephson junction chains andsuperconducting coplanar waveguide (CPW) resonators. One-dimensionalJosephson junction chains are constructed by connecting many Superconducting quantum interference devices (SQUIDs) in series. We have studied DC transport properties of the SQUID chains and model their nonlineardynamics with Thermally Activated Phase-Slips (TAPS). Experimental andsimulated results showed qualitative agreement revealing the existence of auniform phase-slipping and phase-sticking process which results in a voltage-independent current on the dissipative branch of the current-voltage char-acteristics (IVC). By modulating the effective Josephson coupling energy ofthe SQUIDs (EJ ) with an external magnetic field, we found that the ratio EJ /EC is a decisive factor in determining the qualitative shape of theIVC. A quantum phase transition between incoherent Quantum Phase Slip, QPS (supercurrent branch with a finite slope) to coherent QPS (IVC withwell-developed Coulomb blockade) via an intermediate state (supercurrentbranch with a remnant of Coulomb blockade) is observed as the EJ /EC ratio is tuned. This transition from incoherent QPS to the intermediate-statehappens around R0 ∼ RQ (RQ = h/4e^2 = 6.45kΩ). We also fabricated structured chains where a SQUID at the middle of the chain (central SQUID) has different junction size and loop area compared to other SQUIDs in the chain. Results showed that with these structured chains it is possible to localize andtune the amplitude of both TAPS and QPS at the central SQUID. The second part of the thesis describes the fabrication process and themeasurement results of superconducting CPW resonators. Resonators withdifferent design parameters were fabricated and measured. The transmissionspectra showed quality factors up to, Q ∼ 5 × 10^5 . We have observed bendingof the resonance curves to the lower frequencies due to existence of a nonlinear kinetic inductance. The origin of the nonlinear kinetic inductance isthe nonlinear relation between supercurrent density, Js, and superfluid veloc-ity, vs , of the charge carriers on the center line of the resonators. A simplemodel based on the Ginzburg-Landau theory is used in order to explain ob-served nonlinear kinetic inductance and estimates using this model showedgood agreement with the experimental results.