  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.
