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.
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.
In thin superconducting wires, phase-slip by thermal activation near the critical temperature is a well-known effect. It has recently become clear that phase-slip by quantum tunnelling through the energy barrier can also have a significant rate at low temperatures. In this paper, it is suggested that quantum phase-slip can be used to realize a superconducting quantum bit without Josephson junctions. A loop containing very thin nanofabricated wire is biased with an externally applied magnetic flux of half a flux quantum, resulting in two states with opposite circulating current and equal energy. Quantum phase-slip should provide coherent coupling between these two macroscopic states. Numbers are given for a wire of amorphous niobium-silicon that can be fabricated with advanced electron beam lithography.
Quantum mechanics reveals a world that defies classical determinism, where uncertainty, superposition, and fluctuations are fundamental aspects. Engineering devices that harness these quantum features requires not only precision, but also a deep understanding of how they interact with their surrounding environment. Superconducting circuits, which exploit macroscopic quantum coherence in low-loss superconducting materials, provide a scalable platform for implementing such systems. Among the critical elements in these circuits, superinductors—high-impedance, dissipation-free inductive components—play a central role by suppressing charge fluctuations. They allow quantum states to be delocalized in phase space, protect qubits from environmental noise, and facilitate access to phenomena such as dual Josephson physics and ultra-strong coupling regimes. This thesis explores two complementary implementations of high-impedance circuits: geometric superinductors, demonstrating that high impedance can be achieved beyond kinetic inductance, and Josephson junction chains, used to investigate both microwave mode properties and DC transport across the superconductor-to-insulator transition. Part I addresses geometric superinductors. Contrary to the common belief that high-impedance superconducting circuits require kinetic inductance, we demonstrate that purely geometric designs can achieve characteristic impedance exceeding the resistance quantum. By exploiting mutual coupling between adjacent turns, coil-based inductors achieve enhanced self-inductance, creating a reliable platform for qubits and resonators. Modeling, simulation, fabrication, and characterization confirm that these elements behave as superinductor. With low loss, high linearity, and minimal stray capacitance, these elements are reproducible, free of uncontrolled tunneling events, and capable of strong magnetic coupling. This establishes geometric superinductors as robust, single-wave-function superconducting devices suitable for hardware protected qubits and hybrid systems. Part II presents classical numerical simulations of a Quantum Phase Slip circuit to study dual Shapiro steps. The circuit consists of an ideal Quantum Phase Slip element embedded in a resistive-inductive environment with a parasitic capacitance. Part III extends the investigation of high characteristic-impedance circuit elements to one-dimensional Josephson junction chains, which act as a quantum simulator for many-body physics and the superconductor–insulator transition. Different devices are realized on both sides of the DC phase transition, showing either a supercurrent branch or Coulomb blockade at zero bias. The effect of the crossover on microwave modes, however, remains insufficiently investigated. Studying these modes provides insight into the interplay between disorder and phase-slip events. Small differences in circuit component sizes determine which side of the transition a device falls on, making these results relevant not only for fundamental understanding but also for the design of quantum devices, emphasizing the crucial role of the electromagnetic environment in stabilizing and controlling fragile quantum states. Together, these results illustrate how carefully engineered high characteristic-impedance elements provide a link between macroscopic circuits and the inherently uncertain quantum world, enabling experiments that probe, control, and ultimately exploit quantum fluctuations for applications in quantum information, metrology, solid state physics and beyond.
This thesis describes a series of theoretical proposals of novel circuits that embed ultrathin superconducting nanowires with coherent quantum phase-slips (QPS). The motivation for our proposals is twofold: firstly, to facilitate unambiguous experimental verification of coherent phase-slips. Secondly, to suggest superconducting devices with new features and functionalities. The first circuit is a driven LC oscillator with the superconducting inductance subject to QPS. We have studied the effect of QPS in two limits: for small and for large phase-slip amplitudes. We expect that weakQPS (whereweakmeans that the QPS amplitude is small compared to the resonance frequency) have ameasurable effect when the oscillator is resonantly driven. The charge induced by the gate affects the quantum interference of QPS with opposite shifts and thus the effect of QPS is periodic in gate voltage. The experimental observation of such dependence would unambiguously identify the quantum coherence of phase-slips. The other crucial effect of QPS is that they produce uncommon non-linearities in the proposed device. The distinctive feature of these non-linearities is the oscillatory dependence on number of photons n with a local period of the order of pn. We analyzed the regime where the QPS correction becomes large by employing a semiclassical approximation as well as by solving the full quantum mechanical equations. At semiclassical level, the QPS-induced non-linearities persist until very high photon number and they result in amultitude ofmetastable states. This was illustrated in the responses of the oscillator: the QPS-induced non-linearities cause deviations fromthe otherwise Lorentzian curve that represents the number of photons N versus detuning. At sufficiently large phase-slip amplitudes this results in an impressive characteristic, a "corkscrew" shape. At any given detuning one finds a multitude of states that differ in the number of photons. About half of these states are stable. At quantum level, we have demonstrated that there is indeed a single quantum state corresponding to the semiclassical metastable states. We have found that these states are robust, their switching time is exponentially long, although they encompass only a few photons. The QPS oscillator is highly tunable: small changes of the driving force, detuning, or charge induced change the number of stable states, thereby enabling easy manipulation of the number of photons. All these features of the phase-slip oscillator make it useful for a wide range of applications, such as ultra-sensitive measurements, quantum manipula- tion and naturally, an unambiguous experimental verification of coherent QPS. In Chapter 3 we propose a series of devices that illustrate the emergence of Coulomb blockade from coherent QPS in thin superconducting wires. The basic ideas is that QPS create an isolation in a wire which is similar to the isolation required by Coulomb blockade. We exploit this idea and suggest setups that are derived from Cooper-pair box and Cooper-pair transistor, so we refer to them as QPS-box and QPS-transistor, respectively. Our main goal was to demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. We analyze the emergence of discrete charging in the limit of strong phaseslips. We investigated six distinct regimes that are realized depending on the relation between the three characteristic energy scales: inductive and charging energy, and QPS amplitude. In both cases the charge sensitivity appears already for small QPS amplitudes as a perturbative correction to the ground-state energy. In both cases, the charge-sensitive part of the perturbative correction is exponentially suppressed in the limit of low impedance. In contrast to the QPS-box, the QPStransistor exhibits both flux and charge sensitivity that makes it potentially useful for measurements. However, if the QPS amplitude becomes of the order of either charging energy (large impedance regime) or inductive energy (small impedance regime), both devices showdiscrete charge states that followthe commonCoulomb blockade pattern of "crossing parabolas". The crossover to Coulomb blockade occurs differently in the limits of large and small impedance. For QPS-transistor, we have analyzed the flux sensitivity (superconducting current) as well as combined flux-charge sensitivity. For a symmetric QPS-transistor we have found a variable separation at specific values of induced charge that leads to double degeneracy of the states at q/e = 1 and half-integer external flux. We have calculated the superconducting current through QPS-transistor to show the non-triviality of the device. Experimental realization of these devices (achievable with the state-or-theart technology), will unambiguously prove the Coulomb blockade as an effect of coherent phase-slip processes. For completeness, we discuss the Josephson-based devices that are dual to QPS-box and QPS-transistor. In Chapter 4 we propose a way to realize quantum synchronization of Josephson and Bloch oscillations in a superconducting device. Essentially, this implies the synchronization of quantumconjugated variables: phase and charge. A circuit comprising of a QPS junction, series resistor and biased by a d.c. voltage exhibits Bloch physics of the charge variable. To ensure well-defined classical oscillations, the resistor needs to be large compared to the resistance quantum. We couple this Bloch subcircuit with a Josephson subcircuit in which the phase variable performs thewell-known Josephson oscillations. Themain effect of the coupling is the transfer of oscillating voltage/current from Josephson/Bloch to Bloch/Josephson part, whereby the voltage/current is multiplied with an amplification coefficient. This amplification coefficient is required to be high for stable synchronization. This is achieved by using an LC-resonator with high quality factorQ. The synchronization takes place in a rather broad interval of frequencies near the LC oscillator’s resonant value. Owing to this synchronization, the transresistance of our device exhibits a typical devil’s staircase curve, very similar to (fractional) Quantum Hall samples. In principle, fluctuations of phase and charge could could destroy the synchronization. Using the quantum description in the framework of Keldysh action formalism, we have investigated the effect of fluctuations on our circuit. The minimum synchronization error rate is shown to be exponential in Q. There is also significant practical interest in the field on metrology. The suggested device can be used to close the famous "metrological triangle" for threemetrological standards: those of resistance, voltage and current—within a single device.
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 work is concerned with two fascinating circuit quantum electrodynamics components, the Josephson junction and the geometric superinductor, and the interesting experiments that can be done by combining the two. The Josephson junction has revolutionized the field of superconducting circuits as a non-linear dissipation-less circuit element and is used in almost all superconducting qubit implementations since the 90s. On the other hand, the superinductor is a relatively new circuit element introduced as a key component of the fluxonium qubit in 2009. This is an inductor with characteristic impedance larger than the resistance quantum and self-resonance frequency in the GHz regime. The combination of these two elements can occur in two fundamental ways: in parallel and in series. When connected in parallel the two create the fluxonium qubit, a loop with large inductance and a rich energy spectrum reliant on quantum tunneling. On the other hand placing the two elements in series aids with the measurement of the IV curve of a single Josephson junction in a high impedance environment. In this limit theory predicts that the junction will behave as its dual element: the phase-slip junction. While the Josephson junction acts as a non-linear inductor the phase-slip junction has the behavior of a non-linear capacitance and can be used to measure new Josephson junction phenomena, namely Coulomb blockade of Cooper pairs and phase-locked Bloch oscillations. The latter experiment allows for a direct link between frequency and current which is an elusive connection in quantum metrology. This work introduces the geometric superinductor, a superconducting circuit element where the high inductance is due to the geometry rather than the material properties of the superconductor, realized from a highly miniaturized superconducting planar coil. These structures will be described and characterized as resonators and qubit inductors and progress towards the measurement of phase-locked Bloch oscillations will be presented.
A superconducting condensate is characterized by the emergence of macroscopic and collective order, established between its constituent electrons. The degree of correlation at a given spatial position is a complex scalar: it is characterized both by an amplitude (proportional to the minimal energy to generate a fundamental excitation) and a complex phase. Through its gradient, the latter enables the flow of the condensate, demonstrating the quantum fingerprint of superconductivity. Superconductors exhibit strong coupling to electromagnetic fields, so that phase-dependent dissipationless transport through “weak link” circuital elements is easily manipulated by applying voltage or magnetic flux bias to superconducting terminals and loops, respectively. For these reasons, superconducting electronics is nowadays a core technology to enable robust access and manipulation of the fundamental degrees of freedom in quantum devices, from ultrasensitive electromagnetic sensors to superconducting qubits. In this work, we explore different designs of micro-magnetometers based on superconducting interferometers. Differently from conventional designs based on Superconductor, Insulator, Superconductor (SIS) tunnel junctions, here the core elements are nanoscale diffusive metal wires acting as superconducting weak links. These consist in circuital dishomogeneities that can be fabricated over scales much smaller than typical superconductor coherence lengths, typically yielding unique response properties. On the other hand, their intrinsic transparency is usually associated with strong supercurrent concentration, which can severely limit their practicality due to superconducting depairing and thermal-driven hysteresis upon switching to the dissipative regime. In this thesis we demonstrate how a judicious use of nanofabricated designs makes it possible to counter these drawbacks and achieve complete phase polarization in interferometers based on diffusive weak links. The resulting micro-magnetometers are characterized by extremely high magnetic responsivity.