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 a nonlinear Josephson oscillator (Josephson junction) in the effective potential, which form is a result of a driving current. We first consider the phase dynamics in the classical regime and then explore the problem in the quantum regime by solving the energy eigenvalue problem. Here we are going to pay special attention to the study of the effects of switching between the states of a nonlinear oscillator separated by a separatrix. For this purpose, we consider controlling the oscillator with a "two-color" current. In the classical view, the first high-frequency current component brings the oscillator to the bifurcation point. A second modulated high-frequency component produces a programmed system switching. A similar scenario is considered in the quantum regime.
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 tackle the problem of accurate simulations of switching currents arising from tunnel events in the washboard potentials associated to Josephson junctions. The measurements of the probability distribution of the switching currents is essential to determine the quantum character of the device, and therefore is at the core of technological applications, as Josephson junctions, that have been proposed for quantum computers. In particular, we show how to accurately calibrate the parameters of the boundary conditions to avoid spurious reflections of the wavefunction from the finite border of numerical simulations. The proposed approximate numerical scheme exploits a quantum version of a perfect matched layers for the boundary problems associated with this class of potentials. Thus, we employ the analogous of a well established electromagnetic method to deal with radiation in mesoscopic quantum systems. Numerical simulations demonstrate that the known analytic results are well recovered in the appropriated limits of quantum measurements. We also find that a relaxation time shows up in the dynamics of the quantum evolution in between two consecutive measurements.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.
A Josephson tunnel junction which is rf driven near a dynamical bifurcation point can amplify quantum signals. However, the bifurcation point will exist robustly only if the electrodynamic environment of the junction meets certain criteria. We develop a general formalism for dealing with the nonlinear dynamics of a Josephson junction embedded in an arbitrary microwave circuit. We find sufficient conditions for the existence of the bifurcation regime: (a) the embedding impedance of the junction needs to present a resonance at a particular frequency ${\ensuremath{\omega}}_{R}$, with the quality factor
Q of the resonance and the participation ratio
p of the junction satisfying
Qp⪢1, and (b) the drive frequency should be low frequency detuned away from ${\ensuremath{\omega}}_{R}$ by more than $\sqrt{3}{\ensuremath{\omega}}_{R}∕(2Q)$.