The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.
The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.
In this thesis the single Cooper pair box (SCB) is investigated with a radio frequency single electron transistor (RF-SET). The RF-SET is used as an electrometer to detect the charge of the SCB. The SCB can be regarded as a quantum two-level system and could therefore be a possible qubit. Both the SCB and the RF-SET have been fabricated with e-beam lithography followed by two-angle shadow evaporation of aluminium. The system has been measured in a dilution refrigerator at temperatures of ~30 mK. A charge sensitivity of 2.3 μe/square root of Hz was measured for an optimized RF-SET with a bandwidth of 7 MHz, operated in the superconducting state. In a phase sensitive measurement of the RF-SET reflected signal, the gate dependence of the quantum capacitance, due to avoided level crossing, was detected in a superconducting SET. Coulomb staircases for the SCB were obtained by changing the charge of the SCB by ramping a gate voltage and continuously measuring the charge with the RF-SET. To prevent quasiparticle poisoning of the SCB island, we have used a method of graded gaps. Here we exploit the greater reduction of the superconducting gap for the connecting leads with an external magnetic field applied, resulting in a higher gap for the island. This creates an effective barrier against quasiparticle tunnelling. The charging energy and the Josephson coupling energy of the SCB were measured with microwave spectroscopy. The SCBs were fabricated in a SQUID geometry, which made it possible to tune the Josephson coupling energy of the box. This tuning was verified through microwave spectroscopy. The effect of tuning could also be seen in the pure 2e Coulomb staircase, as a predicted smearing of the staircase, which was in excellent agreement with the independent spectroscopy data. Coherent quantum oscillation of the SCB charge state was measured by applying nonadiabatic DC-pulses to the SCB gate. The measured amplitude of the charge oscillations was higher than 70%. The deviation from 100% can be explained by the initial charge state purity and the finite rise time of the pulses. The longest decoherence time of the charge oscillations was T2 = 9 ns at the charge degeneracy point. It was found to be limited by relaxation. Away from the degeneracy point the decoherence time was limited by pure dephasing, due to low frequency charge fluctuators.
This thesis presents measurements of quantum coherence in a single Cooper pair box, where quantum oscillations of charge between a reservoir and a small superconducting island have been observed. The single Cooper pair box (SCB) consists of a small metallic island which is connected to a reservoir via a tunnel junction. In the superconducting state, Cooper pairs are free to tunnel to and from the island, whose potential can be controlled by a gate voltage. A graded gap method was used to prevent quasiparticles from tunneling onto the island. For this purpose, a magnetic field suppressed the superconducting gap in the SCB leads more than in the island. This created an additional energy barrier for quasiparticles to tunnel to the island, making the gate voltage modulation periodic in Cooper pair charge. For a limited range of gate voltage, the SCB was found to behave as a model two-level quantum mechanical system. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T2=9 ns at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate, ?1. Away from this point, the coherence time was limited by the dephasing rate, ??. Away from the charge degeneracy, the dependence of T2 on gate charge suggested that low frequency fluctuators were the main source of dephasing. The charge of the Cooper pair box was measured by coupling the SCB capacitively to a radio frequency single electron transistor (RF-SET). The RF-SET was used as an electrometer by measuring the amount of reflection from a resonant microwave circuit in which a single electron transistor (SET) was embedded. A best charge sensitivity of 2.3·10-6 e/sqrt(Hz) and a 7 MHz bandwidth was reached in an improved setup. Another part of this thesis concerns an investigation of electrical filters for use in single electronics experiments. The characteristics of seven different types of cryogenic filters were evaluated.
In the field of nanoelectronics, one seeks to combine quantum mechanical effects with macroscopic entities such as currents in order to find new ways of storing and manipulating information. One possibility to accomplish this is to use the quantum correlations found in superconductors. Teaming superconductors with normal metals and magnetic systems, one can obtain novel correlation and fluctuation effects. \n\nIn the first work of this thesis, we examine how charge correlations in a metallic dot are modified due to the presence of a capacitively coupled superconducting island. It is possible to overcome the Coulomb repulsion between electrons in a hybrid double-dot system consisting of a metallic island coupled capacitively to a Cooper-pair box. The superconducting island S acts as a dynamic gate on the metallic island N and in the strong coupling regime the electric charge of the Cooper pairs in S and their fluctuations are able to overscreen the repulsion between electrons in N. This produces an attractive interaction between two additional electrons in the metallic island and results in a non-monotonous charging curve of the metallic island. \n\nThe second part of the thesis considers how the dynamics of a precessing molecular magnetic moment affects the Josephson current. The precession gives rise to a time-dependent tunnel potential which not only creates different tunneling probabilities for spin-up and spin-down quasiparticles, but also introduces a time-dependent spin-flip term. In particular, we study the effects of the spin-flip term alone on the Josephson current between two spin-singlet superconductors as a function of precession frequency and junction transparency. The system displays a nonequilibrium steady-state solution which depends on the precession frequency of the classical spin.\n\n\n
Micro-fabricated superconducting circuits have emerged as a leading candidate for quantum computers. However, typical error rates of 10-3 for quantum gates remain a challenge for performing error correction and need to be further decreased for achieving practical quantum computation. Improving qubit coherence times for superconducting qubits is a continuous endeavor in order to decrease error rates. As part of this effort, a topic addressed in this dissertation is the study of the generation mechanism and dynamics of non-equilibrium quasiparticles (QPs), which are electron-like excitations of a superconductor. This source of decoherence was studied by measuring the rate of single-electron changes in the parity state of multiple charge-sensitive transmon qubits under different conditions. The presence of non-equilibrium QPs in superconducting resonators and qubits operating at millikelvin temperature has been known for decades. Understanding the sources and dynamics of these QPs is crucial to evaluate and improve the performance of the devices. Specifically, for superconducting qubits, a single QP tunneling across the Josephson junction changes the total charge parity from even to odd or vice versa, and can induce energy relaxation and dephasing, limiting the coherence of the device. To study the dynamics of non-equilibrium QPs, I utilized a Ramsey-like pulse sequence to measure the rate of single-electron parity changes in transmon qubits, which had a weak charge dispersion, with different shunting capacitor geometries and materials. I started out by measuring a charge parity rate of ~ 33 s-1 for a grounded "x-mon" qubit and ~ 17 s-1 for a galvanically isolated "two-pads" qubit with our standard setup. These rates decreased to ~ 5 s-1 and ~ 2 s-1 for the x-mon and two-pads respectively when IR-filters and extra layers of shielding were installed. From my measurements, I found that the charge parity rates are sensitive to the geometry of the shunting capacitor, weakly depend on the amount of shielding surrounding the device, and independent of using Al or Ta for the superconducting shunting capacitor. To distinguish between two possible mechanisms for the parity switching, I measured the parity rates after cooling one of the qubit devices in an external magnetic field to induce vortices in the superconducting electrodes. After increasing the magnetic field above 23 μT, I measured a faster QP trapping rate and a much smaller T1, suggesting that at least one vortex was added to the superconducting electrode near the Josephson junction. On the other hand, the measured charge parity rates exhibited no clear dependence on the background QP trapping rates. These data suggest that a large portion of parity switching events occurs from QPs being produced at the Josephson junction, where pair-breaking radiation is rectified into QPs by the junction, as opposed to tunneling of QPs residing in the electrodes. To understand the difference in the measured parity rates, I simulated the absorption efficiency of pair-breaking radiation for my two designs and observed a similar difference in absorption rates when a single-mode blackbody radiation with an effective temperature T* ~ 300 mK was assumed to be illuminating the devices. This large T*, which is significantly higher than the device's nominal temperature of 20 mK, is consistent with values reported in the literature. However, its physical origin remains not fully understood. For the other part of my dissertation, I developed a new simplified process for making superconducting air bridges. Air bridges are used to suppress unwanted extraneous high frequency chip modes parasitic to superconducting quantum circuits that can couple to qubits and cause decoherence. Traditional ways of making air bridges utilize thermal reflow to create arched photoresist scaffolds that are limited in heights. This results in insufficient mechanical strength of the bridges which tend to collapse when spanning to larger lengths. My simplified fabrication method that utilizes two-photon lithography, a technique that enables creation of three-dimensional micron-scale structures, relaxes this limitation and is capable of making mechanically stable bridges with lengths up to 100 μm. The resulting Al air bridges, having a superconducting transition temperature of Tc = 1.08 mK and a dc residual resistivity ratio of 3.85, were confirmed to form a good electrical contact with the base metal layers and exhibit a small measurable amount of rf loss when placed over coplanar waveguide resonators, on par with other air bridge fabrication methods.
The detection of single microwave photons remains a difficult challenge because of their low energy. The authors demonstrate that an aluminum superconducting double dot can be tuned to a regime in which a photon creating a single quasiparticle pair changes the quantum capacitance of the device. By using high-bandwidth reflectometry techniques, they observe the absorption of photons in real time. They also exploit the band structure of the device to tune the frequencies to which it is sensitive and use this to carry out spectroscopy on the ambient black-body radiation environment in their dilution refrigerator.
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.