We investigate the relaxation of a superconducting qubit for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The qubit relaxation rates are different in different states. They can display strong dependence on the qubit frequency and resonant enhancement, which is due to quasienergy resonances. Coupling to the driven oscillator changes the effective temperature of the qubit.
We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded dc-SQUID. The dc-SQUID allows to control the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change of the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either $0$ or $π$, whose probability can be control…
In this paper, we investigate theoretically the quantum state transfer in a laser driven hybrid optomechanical cavity with two Duffing-like anharmonic movable end mirrors containing an ensemble of identical two-level trapped atoms. The quantum state transfer from the Bogoliubov modes of the two anharmonic oscillators to the atomic mode results in the atomic quadrature squeezing beyond the standard quantum limit of 3 dB which can be controlled by both the optomechanical and atom-field coupling strengths. Interestingly, the generated atomic squeezing can be made robust against the noise sources …
We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings under varying semiclassical approximations. Using spatial (based on Kullback-Leibler distances between phase-space attractors) and temporal (Lyapunov exponent-based) complexity metrics, we isolate the effect of the environment on quantum-classical differences. Moreover, we quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. Remarkably, we find that a parametrically invariant meta-attractor emerges at a speci…
In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric non…
The paper shows mechanisms of both the pumping and energy decay of an "isolated" oscillator. The oscillator is only non-resonantly coupled with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the "isolated" oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian, with the latter being the Hamiltonian of two oscillators and environment of one of them.
Periodically-driven oscillators are commonly described in a frame co-rotating with the drive and using the rotating-wave approximation (RWA). This description, however, is known to induce errors for off-resonant driving. Here we show that the standard quantum description, using creation and annihilation of particles with the oscillator's natural frequency, necessarily leads to incorrect results when combined with the RWA. We demonstrate this on the simple harmonic oscillator and present an alternative operator basis which reconciles the RWA with off-resonant driving. The approach is also appli…
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 multi-stability emerges associated with dynamical bifurcations so that the often used modeling as a Duffing oscillator, which can exhibit bi-stability at the most, is insufficient. The present work analyzes in this regime corresponding quantum properties by mapping the problem onto a highly-nonlinear quasi-energy operator in a rotating frame. This allows us to identify in detail parameter regions wher…
