Abstract
In this paper we consider a system comprising a highly hysteretic, single Josephson weak link SQUID ring (i.e. where 2πL s I c/Φ 0 ≫ 1 for a SQUID ring inductance L s and weak link critical current I c with Φ 0 = h/2e) coupled to an finite quality factor LC parallel resonator (tank circuit), the schematic of which is shown in Fig. 1. The non-linear dynamics of this system has been the subject of a great deal of interest both for the quantum and classical operational regimes (see for example [1–3]). In this paper we confine ourselves to the semi-classical Resistively Shunted Junction plus Capacitance (RSJ+C) model of the SQUID ring [4]. For such a SQUID ring-tank circuit system, where the tank circuit is driven by a current I in, the equations of motion are
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References
R.J. Prance, R. Whiteman, T.D. Clark, H. Prance, V. Schollmann, J.F. Ralph, S. Al-Khawaja, and M.J. Everitt. Nonlinear multilevel dynamics of a coupled squid ring-resonator system in the hysteretic regime. Phys. Rev. Lett., 82:5401–5404, 1999.
A.R. Bulsara, K. Wiesenfeld, and M.E. Inchiosa. Nonlinear dynamics in a high-gain amplifier: the dc squid. Ann Phys-Berlin, 9:679–688, 2000.
J. Diggins, J.F. Ralph, T.P. Spiller, T.D. Clark, H. Prance, and R.J. Prance. Chaotic dynamics in the rf superconducting quantum-interference-device magnetometer - a coupled quantum-classical system. Phys. Rev. E., 49:1854–1859, 1994.
K. Likharev. Dynamics of Josephson Junctions and Circuits. Taylor & Francis, 1986.
J.R. Friedman, V. Patel, W. Chen, S.K. Tolpygo, and J.E. Lukens. Quantum superposition of distinct macroscopic states. Nature, 406:43–46, 2000.
I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij. Coherent dynamics of a flux qubit coupled to a harmonic oscillator. Nature, 431:159–162, 2004.
P.B. Stiffell, M.J. Everitt, T.D. Clark, C.J. Harland, and J.F. Ralph. Control of multilevel voltage states in a hysteretic superconducting-quantum-interferencedevice ring-resonator system. Phys. Rev. E., in publication, 2005.
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Stiffell, P., Everitt, M., Clark, T., Bulsara, A., Ralph, J. (2006). A SQUID Ring-Resonator Finate State Machine. In: Baglio, S., Bulsara, A. (eds) Device Applications of Nonlinear Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33878-0_12
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DOI: https://doi.org/10.1007/3-540-33878-0_12
Publisher Name: Springer, Berlin, Heidelberg
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