Realization of robust coherent quantum phase slips represents a significant experimental challenge. Here we propose a design consisting of multiple nanowire junctions to realize a phase-slip flux qubit. It admits good tunability provided by gate voltages applied on superconducting islands separating nanowire junctions. In addition, the gates and junctions can be identical to or distinct from each other, leading to symmetric and asymmetric setups. We find that the asymmetry can improve the performance of the proposed device compared with the symmetric case. In particular, it can enhance the effective rate of collective quantum phase slips. Furthermore, we demonstrate how to couple two such devices via a mutual inductance. This is potentially useful for quantum gate operations. Our investigation on how symmetry in multiple nanowire junctions affects the device performance should be useful for the application of phase-slip flux qubits in quantum information processing and quantum metrology.
Realization of robust coherent quantum phase slips represents a significant experimental challenge. Here we propose a design consisting of multiple nanowire junctions to realize a phase-slip flux qubit. It admits good tunability provided by gate voltages applied on superconducting islands separating nanowire junctions. In addition, the gates and junctions can be identical to or distinct from each other, leading to symmetric and asymmetric setups. We find that the asymmetry can improve the performance of the proposed device compared with the symmetric case. In particular, it can enhance the effective rate of collective quantum phase slips. Furthermore, we demonstrate how to couple two such devices via a mutual inductance. This is potentially useful for quantum gate operations. Our investigation on how symmetry in multiple nanowire junctions affects the device performance should be useful for the application of phase-slip flux qubits in quantum information processing and quantum metrology.
Realization of robust coherent quantum phase slips represents a significant experimental challenge. Here we propose a new design consisting of multiple nanowire junctions to realize a phase-slip flux qubit. It admits good tunability provided by gate voltages applied on superconducting islands separating nanowire junctions. In addition, the gates and junctions can be identical or distinct to each other leading to symmetric and asymmetric setups. We find that the asymmetry can improve the performance of the proposed device, compared with the symmetric case. In particular, it can enhance the effective rate of collective quantum phase slips. Furthermore, we demonstrate how to couple two such devices via a mutual inductance. This is potentially useful for quantum gate operations. Our investigation on how symmetry in multiple nanowire junctions affects the device performance should be useful for the application of phase-slip flux qubits in quantum information processing and quantum metrology.
A phase-slip flux qubit, exactly dual to a charge qubit, is composed of a superconducting loop interrupted by a phase-slip junction. We propose a tunable phase-slip flux qubit by replacing the phase-slip junction with a charge-related superconducting quantum interference device (SQUID) consisting of two phase-slip junctions connected in series with a superconducting island. This charge-SQUID acts as an effective phase-slip junction controlled by the applied gate voltage and can be used to tune the energy-level splitting of the qubit. In addition, we show that a large inductance inserted in the loop can reduce the inductance energy and consequently suppress the dominating flux noise of the phase-slip flux qubit. This enhanced phase-slip flux qubit is exactly dual to a transmon qubit.
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 phenomenon of coherent quantum phase-slips (CQPS) in superconducting nanowires was some time ago proposed to be the exact dual of the Josephson effect, a proposal accompanied by predictions of a new quantum current standard dual to the Josephson voltage standard. Unambiguous experimental observation of CQPS in nanowire structures has only recently been achieved through microwave spectroscopy which showed an avoided crossing between flux states for a superconducting ring interrupted by a superconducting nanowire. This observation raises expectations that the CQPS quantum current standard and a slew of CQPS devices dual to devices containing Josephson junction might be realised, including a tunable capacitance, a sensitive charge detector and small-signal detector. To date, experimental evidence for CQPS in a dc transport geometry has not been considered conclusive, and the impact of decoherence in CQPS devices still remains to be evaluated. We present experimental work which has enabled us to crystallise pertinent issues which have prevented the realisation of CQPS in dc transport experiments to date.
Abstract Quantum phase slips represent a coherent mechanism to couple flux states of a superconducting loop. Since their first direct observation, there have been substantial developments in building charge-insensitive quantum phase-slip circuits. At the heart of these devices is a weak link, often a nanowire, interrupting a superconducting loop. Owing to the very small cross-sectional area of such a nanowire, quantum phase slip rates in the gigahertz range can be achieved. Instead, here we present the use of a bias voltage across a superconducting loop to electrostatically induce a weak link, thereby amplifying the rate of quantum phase slips without physically interrupting the loop. Our simulations reveal that the bias voltage modulates the free energy barrier between subsequent flux states in a very controllable fashion, providing a route towards a phase-slip flux qubit with a broadly tunable transition frequency.
In thin superconducting wires, phase-slip by thermal activation near the critical temperature is a well-known effect. It has recently become clear that phase-slip by quantum tunnelling through the energy barrier can also have a significant rate at low temperatures. In this paper, it is suggested that quantum phase-slip can be used to realize a superconducting quantum bit without Josephson junctions. A loop containing very thin nanofabricated wire is biased with an externally applied magnetic flux of half a flux quantum, resulting in two states with opposite circulating current and equal energy. Quantum phase-slip should provide coherent coupling between these two macroscopic states. Numbers are given for a wire of amorphous niobium-silicon that can be fabricated with advanced electron beam lithography.