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WORLD SCIENTIFIC eBooks

SUPERCONDUCTING QUANTUM CIRCUITS

Johannes Majer

Published Jul 21, 2019• 25 citations
Publisher

Abstract

This thesis describes a number of experiments with superconducting cir- cuits containing small Josephson junctions. The circuits are made out of aluminum islands which are interconnected with a very thin insulating alu- minum oxide layer. The connections form a Josephson junction. The current trough the junction is related to the superconducting phase difference across the junction and described by the well-known Josephson relation. The char- acteristic energy scale for this effect is the Josephson energy, which is a measure for the strength of the coupling of the islands. Due to the parallel plate geometry of the junction a capacitance is formed. This capacitance leads to a charging effect. The characteristic energy scale for this effect is given by the charging energy. With the shadow evaporation technique it is possible to make the Josephson junction area very small and the two characteristic energy scales of the same order of magnitude. Charge and phase are conju- gate variables. Therefore a circuit containing such small Josephson junctions exhibits quantum effects. The microfabrication technique used in this the- sis allows fabrication of solid circuits with controlled quantum mechanical behavior.

DOI
10.1142/9789811201400_0004

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This thesis describes a number of experiments with superconducting cir- cuits containing small Josephson junctions. The circuits are made out of aluminum islands which are interconnected with a very thin insulating alu- minum oxide layer. The connections form a Josephson junction. The current trough the junction is related to the superconducting phase difference across the junction and described by the well-known Josephson relation. The char- acteristic energy scale for this effect is the Josephson energy, which is a measure for the strength of the coupling of the islands. Due to the parallel plate geometry of the junction a capacitance is formed. This capacitance leads to a charging effect. The characteristic energy scale for this effect is given by the charging energy. With the shadow evaporation technique it is possible to make the Josephson junction area very small and the two characteristic energy scales of the same order of magnitude. Charge and phase are conju- gate variables. Therefore a circuit containing such small Josephson junctions exhibits quantum effects. The microfabrication technique used in this the- sis allows fabrication of solid circuits with controlled quantum mechanical behavior.
This thesis presents experimental research on Josephson junction devices that behave quantum mechanically. The devices are formed by micrometer-sized superconducting islands, that are interconnected by a Josephson tunnel junction: a thin insulating layer between two superconductors. With current microfabrication technology it is possible to make very clean and well-defined junctions. The research that is presented in this thesis aimed at investigating whether Josephson junction circuits can have quantum coherent dynamics with a long decoherence time.
This thesis describes fabrication, measurements and analysisof two different Josephson junction circuits; the Cooper pairtransistor (CPT) and the one dimensional Josephson junctionarray (JJA). All experiments are conducted in a dilutionrefrigerator with a base temperature of 15{30 mK.In the experiments on CPTs the maximum supercurrent,called the switch- ing current, is measured versus the gatecharge. The importance of filtering of the measurement leads inorder to suppress quasi-particle excitations and to get2e-periodic switching currents is demonstrated. Normal metalgold leads close to the CPTs are introduced to further reducethe effect of quasi-particles. To prove that switching currentis 2e-periodic, magnetic fields and increased temperatures areused to induce a transition to e-periodicity. CPTs where eachJosephson junction is replaced by a Superconducting QuantumInterference de- vice (SQUID) have also been fabricated andmeasured. The SQUIDs make it possible to tune the effectiveJosephson energy with an external magnetic field. The measuredswitching current is tunable in magnitude and 2e-periodic. Theswitching currents are compared with theory. Good agreementbetween the- ory and experiments is found using a model of theCPT in an electrodynamic environment with a high effectivetemperature.The JJAs are also fabricated with a SQUID geometry toenable tuning of the effective Josephson energy. The currentvoltage characteristics (IVCs) of the measured JJAs exhibit aCoulomb blockade of Cooper pair tunneling which is tunable withmagnetic field and periodic with the ux quanta. The IVCs of theJJA show a region of negative differential resistance, alsocalled back- bending. This is interpreted as evidence of Blochoscillations in the JJAs. Two different models are discussed toexplain the measured IVC.The thesis ends by presenting a theoretical proposal ona Josephson junction charge qubit, called the array-qubit. Thearray-qubit consists of an array with N SQUIDs and N +1islands. The two basis states of the qubit corresponds to anexcess Cooper pair on either island 1 or N +1. These two statesare coupled through an Nth-order tunneling process which makesit possible to effectively suppress the Josephson coupling.This facilitate a long relaxation time so that the state of thequbit can be read with a slow detector.
Besides serving as promising candidates for realizing quantum computing, superconducting quantum circuits are one of a few macroscopic physical systems in which fundamental quantum phenomena can be directly demonstrated and tested, giving rise to a vast field of intensive research work both theoretically and experimentally. In this paper we report our work on the fabrication of superconducting quantum circuits, starting from its building blocks: Al/AlO x /Al Josephson junctions. By using electron beam lithography patterning and shadow evaporation, we have fabricated aluminum Josephson junctions with a controllable critical current density ( j c ) and wide range of junction sizes from 0.01 μm 2 up to 1 μm 2 . We have carried out systematical studies on the oxidation process in fabricating Al/AlO x /Al Josephson junctions suitable for superconducting flux qubits. Furthermore, we have also fabricated superconducting quantum circuits such as superconducting flux qubits and charge-flux qubits.
. In circuits of underdamped, small-capacitance Josephson junctions, the charge and phase variables behave quantum mechanically. Superpositions of charge states and flux states have been demonstrated, as well as microwave induced quantum dynamics (see e.g. refs [3, 4]). These e#ects have their origin in the conjugation of the phase and charge variables of Josephson circuits. The qubit design that we present here also contains small-capacitance Josephson junctions. However, even though charge-phase conjugation underlies the quantum behavior of the qubit, it was explicitly designed to be very insensitive to charge e#ects. In practice, random background charges and 1/f charge noise are always present in Josephson circuits, but these charge e#ects have negligible influence on the qubit. The qubit loop contains three Josephson junctions. Two junctions have Josephson coupling E J , the third junction has a coupling of #E J .Weaim
The recent interest in developing highly controllable quantum bits (qubits) based on superconducting circuits makes it necessary to get a deeper understanding of the physics of small Josephson junctions. Such devices have to be wisely engineered and well isolated from the noisy environment to observe non-classical physics. In this thesis, a real-time noise analysis was implemented by an autocorrelation calculation to identify the type of environmental effects affecting a superconducting circuit. This was used during switching current measurements of small Josephson junctions to track the effects of unwanted signals and identify their frequency components. The temperature dependence of the switching current distribution was used to further characterise the small Josephson junctions. Furthermore the fabrication of smal1 Josephson junctions is further developed by analysing the reliability and reproducibility of them. A systematic approach is shown to solve typical fabrication problems for example identifying and reducing mechanical stress between resist layers. As Josephson junctions show quantum mechanical effects on a macroscopic scale they are used in a wide range of applications especially in superconducting circuits.
The Josephson effect, as an example of a macroscopic quantum phenomenon, reveals itself in the three-layer heterostructures formed by two superconductors coupled by a weak link that usually consists of a 1-2 nm-thick insulating barrier.The traditional way of modelling such-systems' dynamics is based on an equivalent circuit that comprises three parallel elements: a pure superconducting element with a certain supercurrent-versus-Josephson phase difference dependence, a resistor R, and a capacitor C. In this short review, we analyse the practical problem of reducing the junction capacitance while maintaining or slightly impairing other characteristics.Some arguments are presented to explain why the capacitance should be suppressed and how it will affect performance of superconducting quantum interference devices (SQUIDs) and digital electronics circuits.As a solution for low-capacitance junctions, we propose a weak link made of an amorphous-silicon interlayer doped with nanoscale metallic drops between the two superconducting Mo-Re-alloy electrodes.