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Physical review. B, Condensed matter

Quantum dynamics of a superconducting tunnel junction

Ulrich Eckern, Gerd Schön, Vinay Ambegaokar

Published Dec 1, 1984• 355 citations
Publisher

Abstract

Basing our model and method on the microscopic theory we formulate a quantum-mechanical description for the relevant variable in a superconducting tunnel junction, i.e., the phase difference across the junction. The quasiparticle degrees of freedom are responsible for dissipation and noise in the system. Because of the discreteness of the charge-transfer process, the noise is shot noise. The energy gaps in the superconductors lead to further interesting features. We discuss the consequences of these physical effects on macroscopic quantum phenomena.

DOI
10.1103/physrevb.30.6419

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Basing our model and method on the microscopic theory we formulate a quantum-mechanical description for the relevant variable in a superconducting tunnel junction, i.e., the phase difference across the junction. The quasiparticle degrees of freedom are responsible for dissipation and noise in the system. Because of the discreteness of the charge-transfer process, the noise is shot noise. The energy gaps in the superconductors lead to further interesting features. We discuss the consequences of these physical effects on macroscopic quantum phenomena.
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This paper discusses the observation of quantum effects in the macroscopic system of a Josephson tunnel junction. The macroscopic degree of freedom is the phase difference delta between the phases of the order parameters in the two superconductors on either side of the tunnel barrier. As we shall see, the anharmonicity enables us to observe the quantized energy levels because they are no longer equally spaced, and to observe the zero point motion by the demonstration that the system tunnels out of its initial state. 6 refs., (LSP)
The theory of charge partition noise of quasiparticles in a superconducting tunnel junction is developed. The charge fluctuations are shown to have a significant contribution from partition noise that arises from the quantum superposition of the electron and hole character of the quasiparticles. These fluctuations are dominant at small bias voltage. The charge fluctuations are compared to the usual Poisson ``shot noise'' of the current. The implications for the design of energy-resolving single-photon detectors are explored.
Experiments to investigate the quantum behavior of a macroscopic degree of freedom, namely the phase difference across a Josephson tunnel junction, are described. The experiments involve measurements of the escape rate of the junction from its zero voltage state. Low temperature measurements of the escape rate for junctions that are either nearly undamped or moderately damped agree very closely with predictions for macroscopic quantum tunneling, with no adjustable parameters. Microwave spectroscopy reveals quantized energy levels in the potential well of the junction in excellent agreement with quantum-mechanical calculations. The system can be regarded as a "macroscopic nucleus with wires."
Recently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system's response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/e2{e}^{2}e2. .AE
Intrinsic noise is known to be ubiquitous in Josephson junctions. We introduce a rough tunnel junction model characterized by a very small number of pinholes---transport channels possessing a transmission coefficient close to unity and analyze its transport properties. Although it may still have just a small total leakage current, it can lead to enormous current fluctuations in the low-voltage regime. We show that even fully transparent transport channels between superconductors contribute to shot noise due to the uncertainty in the number of Andreev cycles. We discuss shot-noise enhancement by multiple Andreev reflection in such a junction and investigate whether pinholes might contribute as a microscopic mechanism of two-level current fluctuators. We discuss the connection of these results to the junction resonators observed in Josephson phase qubits.