ABSTRACT
The agenda of dissipative quantum chaos is to create a toolbox that would allow us to categorize open quantum systems into "chaotic" and "regular" ones. Two approaches to this categorization have been proposed recently. One of them is based on the spectral properties of generators of open quantum evolution. The other one utilizes the concept of Lyapunov exponents to analyze quantum trajectories obtained by unraveling this evolution. By using two quantum models, we relate the two approaches and try to understand whether there is an agreement between the corresponding categorizations. Our answer is affirmative.
ABSTRACT
When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed "chaotic." Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here, we consider quantum chaotic states emerging in a leaky cavity when the intracavity photonic mode is coherently pumped with the pumping intensity varying periodically in time. We show that a single spin when placed inside the cavity and coupled to the mode can moderate transitions between regular and chaotic regimes-that are identified by using quantum Lyapunov exponents or features of photon emission statistics-and thus can be used to control the degree of chaos.
ABSTRACT
Open quantum systems can exhibit complex states, for which classification and quantification are still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intracavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation of quantum Lyapunov exponents [I. I. Yusipov et al., Chaos 29, 063130 (2019)], we identify "chaotic" and "regular" regimes there. In particular, we show that chaotic regimes manifest an intermediate power-law asymptotics in the distribution of photon waiting times. This distribution can be retrieved by monitoring photon emission with a single-photon detector so that chaotic and regular states can be discriminated without disturbing the intracavity dynamics.
ABSTRACT
Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated open quantum dimer model, we report and investigate a quantum Neimark-Sacker bifurcation. Its classical counterpart is the birth of a torus (an invariant curve in the Poincaré section) due to instability of a limit cycle (fixed point of the Poincaré map). The quantum system exhibits a transition from unimodal to bagel shaped stroboscopic distributions, as for Husimi representation, as for observables. The spectral properties of Floquet map experience changes reminiscent of the classical case, a pair of complex conjugated eigenvalues approaching a unit circle. Quantum Monte-Carlo wave function unraveling of the Lindblad master equation yields dynamics of single trajectories on "quantumtorus" and allows for quantifying it by rotation number. The bifurcation is sensitive to the number of quantum particles that can also be regarded as a control parameter.
ABSTRACT
Quantum systems, when interacting with their environments, may exhibit nonequilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. However, different from the Hamiltonian case, the toolbox for quantifying dissipative quantum chaos remains limited. In particular, quantum generalizations of Lyapunov exponents, the main quantifiers of classical chaos, are established only within the framework of continuous measurements. We propose an alternative generalization based on the unraveling of quantum master equation into an ensemble of "quantum trajectories," by using the so-called Monte Carlo wave-function method. We illustrate the idea with a periodically modulated open quantum dimer and demonstrate that the transition to quantum chaos matches the period-doubling route to chaos in the corresponding mean-field system.
