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Fluctuating Nonlinear OscillatorsFrom Nanomechanics to Quantum Superconducting Circuits$
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Mark Dykman

Print publication date: 2012

Print ISBN-13: 9780199691388

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199691388.001.0001

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Quantum‐classical correspondence for a dc‐biased cavity resonator–Cooper‐pair transistor system

Quantum‐classical correspondence for a dc‐biased cavity resonator–Cooper‐pair transistor system

(p.33) 2 Quantum‐classical correspondence for a dc‐biased cavity resonator–Cooper‐pair transistor system
Fluctuating Nonlinear Oscillators

M. P. Blencowe

A. D. Armour

A. J. Rimberg

Oxford University Press

This chapter investigates the quantum versus classical dynamics of a microwave cavity-coupled-Cooper-pair transistor (CPT) system, where a variable applied dc bias causes the system to tunably self-oscillate via the ac Josephson effect. An essential feature of the system is that the dc bias does not significantly affect the high quality factor of the cavity mode to which the CPT predominantly couples. The classical, nonlinear dynamics of the system exhibits chaotic, as well as aperiodic motions depending on the initial conditions and the nature and strengths of the damping/noise forces. The corresponding quantum dynamics exhibits such phenomena as dynamical tunnelling and the generation of nonclassical states from initial classical states. Obviating the need for an external ac-drive line, which typically is harder to noise filter than a dc bias line, the self-oscillating system described here has considerable promise for demonstrating macroscopic quantum dynamical behaviour.

Keywords:   quantum-classical correspondence, macroscopic quantum dynamics, open quantum systems, nonlinear dynamics, chaos, dynamical tunnelling, superconducting circuits, Cooper-pair transistor, Wigner function

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