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.
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.
The objective of this thesis is to evaluate a generic process for fabrication and characterization of the Superconductive coplanar waveguide (CPW) resonators. Superconductive CPW resonators with various lengths and shapes are designed to investigate their electrical and magnetic properties as well as resonance properties and sensitivities. In the first part of thesis, two different models are introduced in order to estimate the nonlinear kinetic inductance of a superconducting CPW resonator. The first model is based on Bean criticalstate model and the second one is based on current dependence of London penetration depth, λL(I). The existence of a shift in resonant frequency, f0, of Superconductive CPW resonator caused by a non-linear kinetic inductance is also shown experimentally. Simulations were carried out to estimate the nonlinear kinetic inductance due to the selfinduced magnetic field penetration. The rest of the thesis is concerned with development of very smooth Aluminum (Al) thin films with RMS (Root Mean Square) roughness ∼ 1 nm and CAD (Computer Aid Design) of superconductive CPW resonators. Experimental investigation of a generic fabrication technique for superconductive CPW resonator is carried out. Many resonators are fabricated with different design parameters, such as centerline or gap width, film thickness and gap capacitors length. The fabrication process is described in detail. Electron Beam Lithography is used to fabricate Nb and Al CPW resonators which are coupled to outer conductors via gap capacitors. We have fabricated GHz frequency CPW resonators with quality factors, Q up to 5× 10.
The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.
This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning.
The objective of this thesis is to evaluate a generic process for fabrication and characterization of the Superconductive coplanar waveguide (CPW) resonators. Superconductive CPW resonators with various lengths and shapes are designed to investigate their electrical and magnetic properties as well as resonance properties and sensitivities. In the first part of thesis, two different models are introduced in order to estimate the nonlinear kinetic inductance of a superconducting CPW resonator. The first model is based on Bean critical-state model and the second one is based on current dependence of London penetration depth. The existence of a shift in resonant frequency of Superconductive CPW resonator caused by a non-linear kinetic inductance is also shown experimentally. Simulations were carried out to estimate the nonlinear kinetic inductance due to the self- induced magnetic field penetration. The rest of the thesis is concerned with development of very smooth Aluminum (Al) thin films with RMS (Root Mean Square) roughness 1~nm and CAD (Computer Aid Design) of superconductive CPW resonators. Experimental investigation of a generic fabrication technique for superconductive CPW resonator is carried out. Many resonators are fabricated with different design parameters, such as centerline or gap width, film thickness and gap capacitors length. The fabrication process is described in detail. Electron Beam Lithography is used to fabricate Nb and Al CPW resonators which are coupled to outer conductors via gap capacitors. We have fabricated GHz frequency CPW resonators with quality factors, Q up 5X10^5.
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.