This doctorate thesis focuses on the effects of the electromagnetic environment on applied electromagnetic fields in single small junctions as well as arrays. We apply radio-frequency (RF) microwaves in the sub-gigahertz frequency range on a one-dimensional array of small Josephson junctions exhibiting distinct Coulomb blockade characteristics. We observed a gradual lifting of Coulomb blockade with increase in the microwave power which we interpret is due to photon-assisted tunneling of Cooper pairs in the classical (multi-photon absorption) regime. We observe that, due to its high sensitivity to microwave power, the array is well-suited for in situ microwave detection applications in low temperature environments. A detailed analysis of the characteristics in the classical (multi-photon absorption) limit reveals that the microwave amplitude is rescaled (renormalized), which we attribute to the difference in dc and ac voltage response of the array. We proceed to rigorously consider the origin of the aforementioned renormalization effect by considering the effect of the electromagnetic environment of the Josephson junction on applied oscillating voltages. We theoretically demonstrate that its effect is simply to renormalize the amplitude of oscillation in a predictable manner traced to the physics of wave function renormalization (Lehmann weights) consistent with circuit-QED. We also introduce Einstein's A and B coefficients for small Josephson junctions, in a bid to relate the renormalization effect to the modification of photon absorption and emission amplitudes. Such renormalization implies that the sensitivity of the single junction and the array to oscillating electromagnetic fields (e.g. microwaves) is modulated and depends on the environmental impedance. The renormalization effect can be exploited to configure `opaque', `translucent' or `transparent' quantum circuits to microwaves.
This doctorate thesis focuses on the effects of the electromagnetic environment on applied electromagnetic fields in single small junctions as well as arrays. We apply radio-frequency (RF) microwaves in the sub-gigahertz frequency range on a one-dimensional array of small Josephson junctions exhibiting distinct Coulomb blockade characteristics. We observed a gradual lifting of Coulomb blockade with increase in the microwave power which we interpret is due to photon-assisted tunneling of Cooper pairs in the classical (multi-photon absorption) regime. We observe that, due to its high sensitivity to microwave power, the array is well-suited for in situ microwave detection applications in low temperature environments. A detailed analysis of the characteristics in the classical (multi-photon absorption) limit reveals that the microwave amplitude is rescaled (renormalized), which we attribute to the difference in dc and ac voltage response of the array. We proceed to rigorously consider the origin of the aforementioned renormalization effect by considering the effect of the electromagnetic environment of the Josephson junction on applied oscillating voltages. We theoretically demonstrate that its effect is simply to renormalize the amplitude of oscillation in a predictable manner traced to the physics of wave function renormalization (Lehmann weights) consistent with circuit-QED. We also introduce Einstein's A and B coefficients for small Josephson junctions, in a bid to relate the renormalization effect to the modification of photon absorption and emission amplitudes. Such renormalization implies that the sensitivity of the single junction and the array to oscillating electromagnetic fields (e.g. microwaves) is modulated and depends on the environmental impedance. The renormalization effect can be exploited to configure opaque', translucent' or `transparent' quantum circuits to microwaves.
The influence of radio frequency microwaves on the Coulomb blockade characteristics in small Josephson junctions was studied using a one-dimensional array of ten small Al tunnel junctions in the frequency range from 1 MHz to 1000 MHz. Coulomb blockade voltage (Vth) is diminished with increasing microwave power (Vac), where the Vth-Vac plots for varied frequencies fall on a single curve. We observed and theoretically analyzed a magnetic field dependent renormalization of the applied microwave power, in addition to a magnetic-field independent renormalization effect explained using an effective circuit approach of the array. Due to its high sensitivity to microwave power, the array is well-suited for on-chip detection applications in low temperature environments.
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.
This thesis presents the results of an experimental study onsmall-capacitance Josephson junctions in a high impedanceenvironment. In small-capacitance Josephson junctions the charging energyEC=e2/2C becomes relevant at low temperature and thecharging effects influence the transport properties. In theobservation of single-charge effects, a fundamental role isplayed by the impedance Z(ω) of the electromagneticenvironment surrounding the junction. To detect the tunnelingof single Cooper pairs in one junction, it is essential toembed the junction in a high impedance environment at all thefrequencies, such that Z(ω)>>RQ, where RQ=h/(2e)2= 6.45 kΩ is the quantum resistance forCooper pairs. This requirement is necessary in order to avoidthe fast discharge of the junction capacitance through theexternal circuit. In this work the effect of the high impedance environment isstudied on Cooper pair transistors (CPT) and single junctionswith tunable coupling (SQUID). The high impedance environmentis obtained by biasing the sample under test with four SQUIDarrays. The SQUID geometry, besides the modulation of thejunctions Josephson energy (EJ), allows the tuning in situ of the effective impedanceof the environment. By applying a magnetic field perpendicularto the SQUIDs loop, the zero bias resistance of the leads (R0) can be varied over several orders of magnitude(104<R0 (Ω)<108), providing the possibility to study the samesample in different electromagnetic environments. Measurements of the current-voltage (I-V) characteristic ofa single junction with SQUID geometry allow the investigationof the influence of both the electrodynamic environment and theEJ/ECratio in the same sample. As the impedance of thebiasing leads is increased (R0>>RQ), the I-V curve of the junction exhibits a welldefined Coulomb blockade feature with a region of negativedifferential resistance, evidence of the coherent tunneling ofsingle Cooper pairs. Measurements on CPT samples also show how the Coulombblockade feature in the I-V curve becomes sharper as theimpedance of the environment is increased. Furthermore theyindicate how the Coulomb blockade threshold voltage is modifiedwith the DC signal applied to the gate. When the SQUID arraysare highly resistive, the gate-induced modulation of the I-Vcurve changes frome-periodic to 2e-periodic, suggesting that high impedance leadseffectively reduce non-equilibrium quasiparticle poisoning.
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
Properties of weak links between two superconductors, or Josephson junctions, make them interesting for fundamental physics research. Since their discovery over four decades ago, they have provided a unique way to study the behavior of the superconducting quantum phase. More recently, ultra small, or mesoscopic, Josephson junctions with substantial single Cooper pair charging energy have gained interest due to their behavior as macroscopic quantum objects. In addition to the theoretical interest, Josephson junctions can be used as active elements in circuit applications. Particularly, in this Thesis we study two different devices. We develop the required theoretical treatments, derive device properties, and compare the results with experimental data. The first application is a Josephson voltage standard based on externally damped Superconductor - Insulator - Superconductor junctions. It consists of an array of large Josephson junctions connected in series and irradiated with a 70 GHz microwave signal. Phase locking the Josephson dynamics into the signal leads to the quantization of the voltage. This is utilized in metrology. We introduce a new circuit solution based on frequency dependent damping of the junctions. Optimization and some designs for practical arrays are presented. The purpose is to find such a design that the array is fast, has low power consumption and is as stable as possible. Arrays able to generate DC voltages of order 1 volt with metrological accuracy are demonstrated experimentally and their applicability in AC voltage calibrations is analyzed. The second application is the Bloch Oscillating Transistor (BOT). The BOT is based on controlling the Cooper pair current in an ultra small Josephson junction by means of quasiparticles tunneling through a normal junction. As part of the thesis work, the principle of operation is first demonstrated computationally. The model is then refined to yield quantitative predictions of the characteristics. Finally, an analytic theory for the device is developed and the properties as an amplifier are derived.
We describe the fabrication and measurement of one-dimensional series arrays of small capacitance Josephson junctions and superconducting quantum interference devices. These arrays exhibit a Coulomb blockade of Cooper pair tunneling when the Josephson coupling energy is the order of the charging energy. The effectiveness of a resistive coaxial cable (ThermocoaxTM made by Philips) for attenuation of high frequency electromagnetic noise is demonstrated. This noise influences the measured dc current–voltage characteristic of the array, having qualitatively the same effect as raising the temperature.