A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic multistability emerges, associated with dynamical bifurcations so that the often-used modeling as a Duffing oscillator, which can exhibit bistability at most, is insufficient. The present work analyzes in this regime corresponding quantum properties by mapping the problem onto a highly nonlinear quasienergy operator in a rotating frame. This allows us to identify in detail parameter regions where simplifications such as the Duffing approximation are valid, to explore classical-quantum correspondences, and to study how quantum fluctuations impact the effective junction parameters as well as the dynamics around higher-amplitude classical fixed points.
We theoretically study the phase dynamics in Josephson junctions, which maps onto the oscillatory motion of a pointlike particle in the washboard potential. Under appropriate driving and damping conditions, the Josephson phase undergoes intriguing bistable dynamics near a saddle point in the quasienergy landscape. The bifurcation mechanism plays a critical role in superconducting quantum circuits with relevance to nondemolition measurements such as high-fidelity readout of qubit states. We address the question "what is the probability of capture into either basin of attraction?" and answer it concerning both classical and quantum dynamics. Consequently, we derive the Arnold probability and numerically analyze its implementation of the controlled dynamical switching between two steady states under the various nonequilibrium conditions.
The properties of phase escape in a dc superconducting quantum interference device (SQUID) at 25 mK, which is well below quantum-to-classical crossover temperature
Tcr, in the presence of strong resonant ac driving have been investigated. The SQUID contains two
Nb/Al-AlOx/Nb tunnel junctions with Josephson inductance much larger than the loop inductance so it can be viewed as a single junction having adjustable critical current. We find that with increasing microwave power
W and at certain frequencies $\ensuremath{\nu}$ and $\ensuremath{\nu}/2$, the single primary peak in the switching current distribution, which is the result of macroscopic quantum tunneling of the phase across the junction, first shifts toward lower bias current
I and then a resonant peak develops. These results are explained by quantum resonant phase escape involving single and two photons with microwave-suppressed potential barrier. As
W further increases, the primary peak gradually disappears and the resonant peak grows into a single one while shifting further to lower
I. At certain
W, a second resonant peak appears, which can locate at very low
I depending on the value of $\ensuremath{\nu}$. Analysis based on the classical equation of motion shows that such resonant peak can arise from the resonant escape of the phase particle with extremely large oscillation amplitude resulting from bifurcation of the nonlinear system. Our experimental result and theoretical analysis demonstrate that at
T⪡Tcr, escape of the phase particle could be dominated by classical process, such as dynamical bifurcation of nonlinear systems under strong ac driving.
We performed a novel phase-sensitive microwave reflection experiment which directly probes the dynamics of the Josephson plasma resonance in both the linear and the nonlinear regime. When the junction was driven below the plasma frequency into the nonlinear regime, we observed for the first time the transition between two different dynamical states predicted for nonlinear systems. In our experiment, this transition appears as an abrupt change in the reflected signal phase at a critical excitation power. This controlled dynamical switching can form the basis of a sensitive amplifier, in particular, for the readout of superconducting qubits.
We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits, in particular, with application to quantum readout. The developed quantitative description demonstrates strong influence of higher harmonics on their characteristics. While this effect is relevant for various circuits, including the conventional Josephson bifurcation amplifier and the parametrically driven circuit, we first focus on the period-doubling bifurcation under a force driving. This kind of bifurcation is due to nominally quadratic nonlinearity, which enables parametric down-conversion of the driving signal at nearly double resonance frequency to the basic mode. We analyze the effect of higher harmonics on the dynamics of the basic mode, inherent in a nonlinear circuit, which in our case is based on a Josephson junction with a sinusoidal current-phase relation as the origin of nonlinearity. We demonstrate that effects beyond the monochromatic approximation significantly modify the bare characteristics and evaluate their contribution. Due to high sensitivity of this circuit to small variations of parameters, it can serve as an efficient detector of the quantum state of superconducting qubits.