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AIP conference proceedings

Phase Dynamics of a Closed 0-π Josephson Junction

T. Koyama, Masahiko Machida, Masaru Kato, Takekazu Ishida

Published Jan 1, 2006• 2 citations
Publisher

Abstract

The phase dynamics of a closed 0‐π junction is investigated. Such a system can be realized, for example, in a small d(x2−y2)‐wave superconductor embedded in a conventional s‐wave superconducting matrix. The Hamiltonian of the system is derived. We prove that the system can be mapped on a quantum two‐level system when the system size is small enough.

DOI
10.1063/1.2354936

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The phase dynamics of a closed 0‐π junction is investigated. Such a system can be realized, for example, in a small d(x2−y2)‐wave superconductor embedded in a conventional s‐wave superconducting matrix. The Hamiltonian of the system is derived. We prove that the system can be mapped on a quantum two‐level system when the system size is small enough.
Abstract We propose the Josephson junctions linked by a normal metal between a d + id superconductor and another d + id superconductor, a d-wave superconductor, or a s-wave superconductor for identifying the chiral d + id superconductivity. The time-reversal breaking in the chiral d-wave superconducting state is shown to result in a Josephson φ0-junction state where the current-phase relation is shifted by a phase φ0 from the sinusoidal relation, other than 0 and π. The ground-state phase difference φ0 and the critical current can be used to definitely confirm and read the information about the d + id superconductivity. A smooth evolution from conventional 0-π transitions to tunable φ0-states can be observed by changing the relative magnitude of two types of d-wave components in the d + id pairing. On the other hand, the Josephson junction involving the d + id superconductor is also the simplest model to realize a φ0- junction, which is useful in superconducting electronics and superconducting quantum computation.
Berry's phase often appears in quantum two-level systems with a degeneracy. An example of such a system is a spin-1/2 particle in a magnetic field. As the magnetic field is slowly evolved through a closed path, the particle has been shown to acquire an additional phase called Berry's phase, in addition to the usual dynamical phase. This phase has been found in two-level quantum systems intrinsic to many superconducting qubits and has particularly been calculated for the charge, flux and Josephson phase qubit. Here, we present an alternative derivation of the Berry's phase in a current-biased Josephson junction qubit. We also calculate the complete Berry's phase evaluated over a closed loop in a frequency parameter space and compare this with the geometric phase. From this comparison, we examine the possibility of using a single phase qubit for topological quantum computing.
Reentrant superconducting behavior of the critical supercurrent temperature dependencies has been observed for the Nb–Cu/Ni–Nb Josephson SFS (superconductor–ferromagnet–superconductor) junctions. The Ic(T) oscillations detected are associated with a crossover of the SFS junctions from '0'- to 'π'-state that is related to a special feature of superconducting pair flow through a ferromagnet (spatial oscillations of induced superconducting order parameter in presence of the exchange field). A triangular array of the junctions in the π-state shows evidence for a phase shift of π on the Ic(H) dependence. We have argued advantages of the SFS π-junction use for the quantum bit implementation based on the superconducting loop with quantum Josephson junctions. While designs proposed previously are based on magnetically frustrated superconducting loops, we discuss the advantages offered by the π-junctions in obtaining naturally degenerate two-level systems.
We shall present our theoretical studies of a Josephson junction of small size in a lossless cavity. When the size of two superconductors are at order of micrometres and the Josephson coupling constant is adjusted to the correct magnitude, the Josephson junction is found to be reduced to a two-level system owing to the finite-size effect and the quenching of the low-lying single-electronic excitations by the superconducting gap. When such a two-level system is placed in a high-quality microwave cavity, the coupling constant with a single photon g may be extremely large, for instance of the order of 108 s−1. On the other hand, the damping rate of the cavity field is much less than g. Therefore, this two-level system may be used to study the quantum nature of photons and to control the dynamics of quantum fields in the framework of the Jayne-Cummings model much more easily.
Josephson junctions constructed from superconductor-semiconductor-superconductor heterostructures have been used to realize a variety of voltage-tunable superconducting quantum devices, including qubits and parametric amplifiers. To date, theoretical descriptions of these systems have been restricted to small quantum fluctuations of the junction phase, making them inapplicable to many experiments. In this paper, we relax this, employing a path-integral formulation where the phase quantum dynamics is obtained self-consistently from an underlying many-body formalism. Our method recovers previously known results for small phase fluctuations, and predicts effects outside of that limit: (i) system capacitances undergo a gate-voltage-dependent renormalization; and (ii) an additional charge offset appears for asymmetric junctions. Our main results can be summarized in terms of a single-particle Hamiltonian, which can be directly compared to that of an ordinary Josephson junction. This more general theory could be a first step towards designing new quantum devices that go qualitatively beyond voltage-tunable variants of previously known circuits.