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Superconductor Science and Technology

Characterization of superconducting devices spanning the charging to Josephson regimes

Maria Gabriella Castellano, Roberto Leoni, G. Torrioli, B. Buonomo, Daniela Simeone, P. Carelli, F. Chiarello, F. Mattioli, C. Cosmelli

Published Nov 21, 2001• 1 citation
Publisher

Abstract

Charge states in mesoscopic Josephson devices are considered promising candidates for a solid-state implementation of quantum computing. We studied three superconducting single electron transistors (SSETs) fabricated with small Al/AlO x /Al tunnel junctions, which, with a different choice of the construction parameters, can realize both the quantum bit and the readout system for the qubit charge state. We varied the junction capacitance and barrier transparency, making the Josephson energy E J of the device smaller, comparable and larger than the charging energy E C : the first case is suitable to build the qubit, while the latter can be suitable for the qubit readout.

DOI
10.1088/0953-2048/14/12/338

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Charge states in mesoscopic Josephson devices are considered promising candidates for a solid-state implementation of quantum computing. We studied three superconducting single electron transistors (SSETs) fabricated with small Al/AlO x /Al tunnel junctions, which, with a different choice of the construction parameters, can realize both the quantum bit and the readout system for the qubit charge state. We varied the junction capacitance and barrier transparency, making the Josephson energy E J of the device smaller, comparable and larger than the charging energy E C : the first case is suitable to build the qubit, while the latter can be suitable for the qubit readout.
In view of future macroscopic quantum experiments, we have fabricated prototypes of charge qubits (with tunable Josephson coupling and capacitive gate) provided with capacitively coupled readout single-electron transistor electrometers. The devices are prepared by electron beam direct-writing in conjunction with material deposition by sputtering. All leads are made of Al, and the AlO/sub x/ tunnel barriers are generated by local thermal oxidizing of the surface of the base striplines. The island electrodes are made of Al or Nb in a subsequent deposition step. In the case of Nb it is suitable to protect the barriers by a thin sputtered Al film first. The small-area (100 nm/spl times/100 nm) tunnel junctions have capacitances in the order of a few 10/sup -16/ F; their resistances can be adjusted in a wide range from k/spl Omega/ to M/spl Omega/ with an on-chip spread of less than 10%. The (double) superconducting gap energy was determined to be about 0.4 meV for Al and 1.4 meV for Nb, respectively. Measuring the so-called Coulomb staircase, we have demonstrated the operation of both qubit boxes and sub-e electrometers.
Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions, exploiting the coherence of tunneling in the superconducting state combined with the possibility to control individual charges by Coulomb blockade effects (cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits, with logical states differing by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits the resulting quantum state has to be read out. This can be accomplished by coupling a single-electron transistor capacitively to the qubit (cond-mat/9801125). To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. Only when a transport voltage is turned on, the transistor destroys the phase coherence of the qubit; in this case within a short time. The measurement is accomplished after a longer time scale, when the signal resolves the different quantum states. At still longer times the measurement process itself destroys the information about the initial state. We present a suitable set of system parameters, which can be realized by present-day technology.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.
The field of quantum computing is growing at a rapid rate with the promise of dramatic improvements in the ability to solve critical computational problems. A leading approach for implementing fault-tolerant quantum computers is based on superconducting circuits containing Josephson junctions to form qubits. These qubits have many attractive qualities, but predicting the device performance requires detailed knowledge of the junction properties. Thus, precise characterization is crucial for realizing different qubit designs. The coherence of superconducting qubits is limited by several sources in the circuit en- vironment. Building a quantum computer requires effort to reduce gate errors caused by decoherence. This is typically achieved with quantum error correction. An alternative ap- proach involves designing qubits that are intrinsically protected from noise sources. One such design is the charge-parity qubit, which combines Josephson junctions in a novel regime. The capacitance of the junctions is a critical parameter for this qubit design that directly affects the engineered protection against decoherence. Beyond the conventional geometric capaci- tance, there is an excess contribution from virtual quasiparticle tunneling; we refer to this component as the electronic capacitance. This thesis focuses on the characterization of the capacitance of Josephson junctions, with the goal of isolating and measuring the electronic capacitance contribution, particularly for use in the charge-parity qubit. The thesis first reviews the initial implementation of the charge-parity qubit and the challenges that were encountered. Next, the theoretical origin is described and a framework for measuring the junction capacitance using superconducting resonant circuits is described. This technique is then applied to arrays of junctions fabricated with different parameters and the scaling of the electronic capacitance is presented. Finally, based on this knowledge of the junction capacitance, second-generation charge-parity qubits are implemented and the experimental results are presented.
Quantum information processing systems can be used in a variety of applications. Among proposed realizations of quantum bits nano-electronic circuits appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. In one limit, two logic states of the quantum bit differ by a Cooper pair charge, 2e, on a superconducting island. In the other limit different magnetic fluxes penetrate a superconducting loop in two states. Single-qubit and two-qubit logic operations can be performed by means of voltage or current pulses. Weak coupling to the environment allows a series of these elementary steps before the phase coherence is lost. To read out the result of the computation a quantum measurement is needed. For charge qubits this can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. Monitoring the current in the transistor one can extract the information about the state of the qubit. We discuss recent experiments and present a suitable set of circuit parameters available with the present-day technology.
Quantum-state engineering, i.e., active control over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. With concepts developed in atomic and molecular physics and in the context of NMR, the field has been stimulated further by the perspectives of quantum computation and communication. Low-capacitance Josephson tunneling junctions offer a promising way to realize quantum bits (qubits) for quantum information processing. The article reviews the properties of these devices and the practical and fundamental obstacles to their use. Two kinds of device have been proposed, based on either charge or phase (flux) degrees of freedom. Single- and two-qubit quantum manipulations can be controlled by gate voltages in one case and by magnetic fields in the other case. Both kinds of device can be fabricated with present technology. In flux qubit devices, an important milestone, the observation of superpositions of different flux states in the system eigenstates, has been achieved. The Josephson charge qubit has even demonstrated coherent superpositions of states readable in the time domain. There are two major problems that must be solved before these devices can be used for quantum information processing. One must have a long phase coherence time, which requires that external sources of dephasing be minimized. The review discusses relevant parameters and provides estimates of the decoherence time. Another problem is in the readout of the final state of the system. This issue is illustrated with a possible realization by a single-electron transistor capacitively coupled to the Josephson device, but general properties of measuring devices are also discussed. Finally, the review describes how the basic physical manipulations on an ideal device can be combined to perform useful operations.