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

We investigate the quantum versus classical dynamics of a microwave cavity-coupled-Cooper pair transistor (CPT) system, where an applied dc bias causes the system to self-oscillate via the ac Josephson effect. Varying the dc bias allows the self-oscillation frequency to be tuned. An unusual feature of the system design is that the dc bias does not significantly affect the high quality factor of the cavity mode to which the CPT predominantly couples. The CPT-cavity mode system has a mechanical analogue involving a driven coupled pendulum-oscillator system. The corresponding, nonlinear classical dynamical equations exhibit chaotic, as well as aperiodic motions depending on the initial conditions and the nature and strengths of the damping/noise forces. The quantum master equation exhibits such phenomena as dynamical tunneling and the generation of non-classical 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 behavior.