Recent experimental demonstration of the quantum coherent phase slip and current quantization in the superconductors, the fundamental phenomena dual to the coherent Cooper pair tunneling and voltage quantization (Shapiro steps), enables the development of a new quantum device, the Bloch transistor (BT). BT has a unique functionality: it can deliver quantized non-dissipative current to the quantum circuit. BT consists of two coupled Josephson Junctions (JJ) in the regime of coherent quantum phase slip. At the heart of the BT operation is a new mechanism for phase-locking the Bloch oscillations in JJs to microwaves via induced charge. The charge phase locking allows not only quantization of current but also gate voltage control of this quantization through the Aharonov-Casher effect. We study the operation of the BT and analyze its parameters. BT technology is scalable and compatible with other superconducting quantum devices, making it part of an emerging cryogenic quantum technology platform.
Recent experimental demonstration of the quantum coherent phase slip and current quantization in the superconductors, the fundamental phenomena dual to the coherent Cooper pair tunneling and voltage quantization (Shapiro steps), enables the development of a new quantum device, the Bloch transistor (BT). BT has a unique functionality: it can deliver quantized non-dissipative current to the quantum circuit. BT consists of two coupled Josephson Junctions (JJ) in the regime of coherent quantum phase slip. At the heart of the BT operation is a new mechanism for phase-locking the Bloch oscillations in JJs to microwaves via induced charge. The charge phase locking allows not only quantization of current but also gate voltage control of this quantization through the Aharonov-Casher effect. We study the operation of the BT and analyze its parameters. BT technology is scalable and compatible with other superconducting quantum devices, making it part of an emerging cryogenic quantum technology platform.
We propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions, connected in series and having a small superconducting island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency fJ=2eVJ/h, related to the average transistor voltage VJ, and Bloch oscillations of frequency fB=IB/2e, related to the average current IB injected into the transistor island. We show that due to the Bloch transistor properties, these two types of oscillations are coupled and can mutually phase-lock, i.e., fJ=fB. This leads to the formation of a current step on the current-voltage curve at IB=2efJ, which is similar to the dual Shapiro step, appearing under microwave irradiation of frequency f on the current-voltage curve of a small Josephson Junction at current I=2ef. Moreover, the Bloch transistor transconductance IB/VJ takes the fundamental value of 1/RQ, where RQ=h/4e2 is the resistance quantum. The obtained results pave the way to an alternative quantum standard of resistance, based on the superconducting circuit and operating without applying a strong magnetic field.
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.
The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.
A resistively shunted Josephson junction with a DC-bias exhibits Josephson oscillations that link voltage and frequency through fundamental constants. These oscillations can synchronize their frequency to an external microwave signal achieving the metrological precision that underlies the modern Josephson voltage standard. Its electromagnetic dual, the phase-slip junction, exhibits Bloch oscillations that connect current to frequency in an analogous way. A current standard based on synchronized Bloch oscillations could close the quantum metrology triangle, providing a consistent test of the underlying fundamental relations between voltage, current, and resistance. The experimental realization, however, remains challenging, as external microwave lines introduce parasitic capacitances that can destroy the high-impedance environment required for Bloch oscillations. This work explores the use of on-chip synchronization to stabilize both Josephson and Bloch oscillations without the need for an external microwave drive. We review the theoretical framework of the synchronization between two coupled oscillators and the dynamics of superconducting circuits with a focus on quantum metrology. Building on this, we analyze a recent experiment on the mutual synchronization of Bloch oscillations in a pair of ultrasmall Josephson junctions. Our model in terms of correlated phase-slip junctions realized in the ground state of the device shows good agreement with the experimental results, confirming synchronized Bloch oscillations. At larger currents, nonadiabatic transitions wash out the coherence of the Bloch oscillations and therefore the synchronization features. Motivated by these findings, we propose an alternative circuit setup where the Bloch oscillations in a single phase-slip junction are stabilized by synchronization to on-chip Josephson oscillations. We study the back-action of the Bloch oscillations on the Josephson oscillations and identify a parameter regime in which it is minimized, rendering the latter an effectively rigid driving signal. Moreover, we find that the small remaining back-action further enhances the thermal stability of the synchronized Bloch oscillations compared to the externally driven case. Without a back-action mechanism, the coherence of Josephson oscillations is severely limited by thermal fluctuations. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings show, that the TUR can be broken by a classical pendulum clock. We propose a circuit that mimics the dynamics of a pendulum clock as a flexible on-chip microwave source for high impedance environments. Due to an internal synchronization, the clock circuit emits coherent radiation beyond the limits of the TUR. Finally, we explore the use of symmetry breaking drives as a resource for nonreciprocal transport in superconducting circuits. We demonstrate that a biharmonic microwave signal applied to a conventional Josephson junction induces an ideal supercurrent diode effect with a tunable direction.
To illustrate the emergence of Coulomb blockade from coherent quantum phase-slip processes in thin superconducting wires, we propose and theoretically investigate two elementary setups, or devices. The setups are derived from the Cooper-pair box and Cooper-pair transistor, so we refer to them as the QPS box and QPS transistor, respectively. We demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of these devices will unambiguously prove the Coulomb blockade as an effect of coherence of phase-slip processes. We analyze the emergence of discrete charging in the limit of strong phase slips. We have found and investigated six distinct regimes that are realized depending on the relation between three characteristic energy scales: inductive energy, charging energy, and phase-slip amplitude. For completeness, we include a brief discussion of dual Josephson-junction devices.
Abstract Bloch oscillations in small Josephson junctions were predicted theoretically as the quantum dual to Josephson oscillations. A significant consequence of this prediction is the emergence of quantized current steps, so-called dual Shapiro steps, when synchronizing Bloch oscillations to an external microwave signal. These steps potentially enable a fundamental standard of current I, defined via the frequency f of the external signal and the elementary charge e, I = ± n × 2ef, where n is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlOx/Al Josephson junctions to sinusoidal drives with frequencies from 1 to 6 GHz and observe dual Shapiro steps up to I ≈ 3 nA. Inspired by today’s voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime and observe an asymmetric pattern of dual Shapiro steps. This work confirms quantum duality effects in Josephson junctions and paves the way towards a range of applications in quantum metrology based on well-established fabrication techniques and straightforward circuit design.