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Register a new userChaos in a double driven dissipative nonlinear oscillator
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We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum trajectories in quantum state diffusion approach. Quantum dynamical manifestation of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement are studied by numerical simulation of ensemble averaged Wigner function and von Neumann entropy.
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We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double well symmetry breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry breaking states, in form of a bistable pair, are associated to the single cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry breaking states and bistability disappear due to the quantum fluctuations. In quantum trajectory picture, we observe enhanced quantum jumps and switching which indicate the presence of the underlying semiclassical symmetry breaking states. Finally, we present a set of analytical solutions for the steady state correlation functions using the complex P-representation and discuss its regime of validity.
We study transitions between the Floquet states of a periodically driven oscillator caused by the coupling of the oscillator to a thermal reservoir. The analysis refers to the oscillator that is driven close to triple its eigenfrequency and displays resonant period tripling. The interstate transitions result in a random ``walk over the states. We find the transition rates and show that the walk is nonlocal in the state space: the stationary distribution over the states is formed by the transitions between remote states. This is to be contrasted with systems in thermal equilibrium, where the distribution is usually formed by transitions between nearby states. The analysis of period tripling allows us to explore the features of the multi-state Floquet dynamics including those missing in the previously explored models of driven oscillators such as the absence of detailed balance for low temperatures. We use the results to study switching between the period-3 states of the oscillator due to quantum fluctuations and find the scaling of the switching rates with the parameters.
We treat the double well quantum oscillator from the standpoint of the Ehrenfest equation but in a manner different from Pattanayak and Schieve. We show that for short times there can be chaotic motion due to quantum fluctuations, but over sufficiently long times the behaviour is normal.
We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, $Z_{2}$ symmetry breaking, $mathcal{PT}$ symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.
We present a heralded state preparation scheme for driven nonlinear open quantum systems. The protocol is based on a continuous photon counting measurement of the systems decay channel. When no photons are detected for a period of time, the system has relaxed to a measurement-induced pseudo-steady state. We illustrate the protocol by the creation of states with a negative Wigner function in a Kerr oscillator, a system whose unconditional steady state is strictly positive.
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