We report on observations of a superconductor-normal pulsing regime in microwave (GHz) coplanar waveguide resonators consisting of superconducting MoGe films interrupted by a gap that is bridged by one or more suspended superconducting nanowires. This regime, which involves MHz-frequency oscillations in the amplitude of the supercurrent in the resonator, is achieved when the steady-state amplitude of the current in the driven resonator exceeds the critical current of the nanowires. Thus we are able to determine the temperature dependence of the critical current, which agrees well with the corresponding Bardeen formula. The pulsing regime manifests itself as an apparent ``crater'' on top of the fundamental Lorentzian peak of the resonator. Once the pulsing regime is achieved at a fixed drive power, however, it remains stable for a range of drive frequencies corresponding to subcritical steady-state currents in the resonator. We develop a phenomenological model of resonator-nanowire systems from which we are able to obtain a quantitative description of the amplitude oscillations and also, inter alia, to investigate thermal relaxation processes in superconducting nanowires. For the case of resonators comprising two parallel nanowires and subject to an external magnetic field, we find field-driven oscillations of the onset power for the amplitude oscillations, as well as the occurrence (for values of the magnetic field that strongly frustrate the nanowires) of a distinct steady state in which the pulsing is replaced by stochastic amplitude fluctuations. We conclude by giving a brief discussion of how circuit-quantum electrodynamics-based systems have the potential to facilitate nondestructive measurements of the current-phase relationship of superconducting nanowires and, hence, of the rate at which quantum phase slips take place in superconducting nanowires.
We report on observations of a superconductor-normal pulsing regime in microwave (GHz) coplanar waveguide resonators consisting of superconducting MoGe films interrupted by a gap that is bridged by one or more suspended superconducting nanowires. This regime, which involves MHz-frequency oscillations in the amplitude of the supercurrent in the resonator, is achieved when the steady-state amplitude of the current in the driven resonator exceeds the critical current of the nanowires. Thus we are able to determine the temperature dependence of the critical current, which agrees well with the corresponding Bardeen formula. The pulsing regime manifests itself as an apparent ``crater'' on top of the fundamental Lorentzian peak of the resonator. Once the pulsing regime is achieved at a fixed drive power, however, it remains stable for a range of drive frequencies corresponding to subcritical steady-state currents in the resonator. We develop a phenomenological model of resonator-nanowire systems from which we are able to obtain a quantitative description of the amplitude oscillations and also, inter alia, to investigate thermal relaxation processes in superconducting nanowires. For the case of resonators comprising two parallel nanowires and subject to an external magnetic field, we find field-driven oscillations of the onset power for the amplitude oscillations, as well as the occurrence (for values of the magnetic field that strongly frustrate the nanowires) of a distinct steady state in which the pulsing is replaced by stochastic amplitude fluctuations. We conclude by giving a brief discussion of how circuit-quantum electrodynamics-based systems have the potential to facilitate nondestructive measurements of the current-phase relationship of superconducting nanowires and, hence, of the rate at which quantum phase slips take place in superconducting nanowires.
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.
We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a ``crater'' at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. We also propose a concept of a nanowire-based qubit that relies on the current dependence of the kinetic inductance of a superconducting nanowire.
We have observed period-tripling subharmonic oscillations in a driven superconducting coplanar waveguide resonator operated in the quantum regime, ${k}_{B}T\ensuremath{\ll}\ensuremath{\hbar}\ensuremath{\omega}$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $\ensuremath{\omega}/2\ensuremath{\pi}\ensuremath{\sim}5\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$, when driving the resonator with a current at $3\ensuremath{\omega}$, with amplitude exceeding an instability threshold. We observed three stable radiative states with equal amplitudes, phase shifted by $2\ensuremath{\pi}/3$ rad, red detuned from the fundamental mode. The down-conversion from $3\ensuremath{\omega}$ to $\ensuremath{\omega}$ is strongly enhanced by near-resonant excitation of the second mode of the resonator and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.
We study current–voltage ( V – I ) characteristics of short superconducting nanowires of length ∼100 nm exposed to microwave (MW) radiation of frequencies between 2 and 15 GHz. The radiation causes a decrease of the average switching current of the wire. This suppression of the switching current is modeled assuming that there is one-to-one correspondence between Little's phase slips, which are microscopic stochastic events induced by thermal and quantum fluctuations, and the experimentally observed switching events. We also find that at some critical power P * of the radiation a dissipative dynamic superconducting state occurs as an extra step on the V – I curve. It is identified as a phase slip center (PSC), which is essentially a deterministic and periodic in-time phase rotation. With the dependence of the switching currents and the standard deviations observed at the transitions: (i) from the supercurrent state to the normal state and (ii) from the supercurrent state to the PSC regime, we conclude that both of the two types of switching events are triggered by the same microscopic event, namely a single-phase slip. We show that the Skocpol–Beasley–Tinkham model is not applicable to our MW-driven PSCs, probably due to the tendency of the PSC to synchronize with the MW. Through the analysis of the switching current distributions at a sufficiently low temperature, we also present evidence that quantum phase slips play a role in switching events even under MWs.
In this thesis, we first demonstrate that a disordered superconductor with high kinetic inductance can realise a microwave low-loss, non-dissipative circuit element with impedance greater than the quantum resistance. This element, known as a superinductor, can suppress the fluctuations of charge in a quantum circuit.For this purpose, we fabricated and characterised 20 nm thick, 40 nm wide niobium-nitride nanowires and determined the impedance to 6.795 kΩ. We demonstrate internal quality factors Qi = 2.5e4 in nanowire resonators at single photon excitation, which is significantly higher than values reported in devices with similar materials and geometries. Moreover, we show that the dominant dissipation in our nanowires is not an intrinsic property of the disordered films, but can instead be fully understood within the framework of two-level systems.To further characterise these losses, we then explore the geometrical scaling, toward nanowire dimensions, of dielectric losses in superconducting microwave resonators fabricated with the same techniques and from the same NbN thin-film as the nanowire superinductors. For this purpose, we perform an experimental and numerical study of dielectric loss at low temperatures. Using 3D finite-element simulation of the Maxwell--London equations, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. Finally, we study the effect of two-level systems on the performance of various superconducting quantum circuits. For this purpose, we measure coherence-time fluctuations in qubits and frequency fluctuations in resonators. In all devices, through statistical analysis, we identify the signature of individual Lorentzian fluctuators in the noise. We find that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems. Furthermore, when examining the low-frequency noise of three different types of superconducting resonator - one NbN nanowire, one Al coplanar waveguide, and one Al 3D cavity - we observe a similar power-law dependence of the Lorentzian switching time and amplitude on the circulating power in the resonators, suggesting a common noise mechanism in the three different types of devices.
We present a detailed report of microwave irradiation of ultranarrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage Vc, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous-wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and, thus, lead to the development of a QPS-based quantum current standard.