Photon waiting time distributions: a keyhole into dissipative quantum chaos

Open quantum systems can exhibit complex states, which classification and quantification is still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intra-cavity 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 {\it et al.}, Chaos {\bf 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 intra-cavity dynamics.Comment: 7 pages, 5 figure

Control of a single-particle localization in open quantum systems

We investigate the possibility to control localization properties of the asymptotic state of an open quantum system with a tunable synthetic dissipation. The control mechanism relies on the matching between properties of dissipative operators, acting on neighboring sites and specified by a single control parameter, and the spatial phase structure of eigenstates of the system Hamiltonian. As a result, the latter coincide (or near coincide) with the dark states of the operators. In a disorder-free Hamiltonian with a flat band, one can either obtain a localized asymptotic state or populate whole flat and/or dispersive bands, depending on the value of the control parameter. In a disordered Anderson system, the asymptotic state can be localized anywhere in the spectrum of the Hamiltonian. The dissipative control is robust with respect to an additional local dephasing.Comment: 6 pages, 5 figure

Localization in open quantum systems

In an isolated single-particle quantum system a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that dissipation can drive a disordered system into a steady state with tunable localization properties. This can be achieved with a set of identical dissipative operators, each one acting non-trivially only on a pair of neighboring sites. Operators are parametrized by a uniform phase, which controls selection of Anderson modes contributing to the state. On the microscopic level, quantum trajectories of a system in a localized steady regime exhibit intermittent dynamics consisting of long-time sticking events near selected modes interrupted by jumps between them.Comment: 5 pages, 5 figure

Collective oscillations in spatially modulated exciton-polariton condensate arrays

We study collective dynamics of interacting centers of exciton-polariton condensation in presence of spatial inhomogeneity, as modeled by diatomic active oscillator lattices. The mode formalism is developed and employed to derive existence and stability criteria of plane wave solutions. It is demonstrated that $k_0=0$ wave number mode with the binary elementary cell on a diatomic lattice possesses superior existence and stability properties. Decreasing net on-site losses (balance of dissipation and pumping) or conservative nonlinearity favors multistability of modes, while increasing frequency mismatch between adjacent oscillators detriments it. On the other hand, spatial inhomogeneity may recover stability of modes at high nonlinearities. Entering the region where all single-mode solutions are unstable we discover subsequent transitions between localized quasiperiodic, chaotic and global chaotic dynamics in the mode space, as nonlinearity increases. Importantly, the last transition evokes the loss of synchronization. These effects may determine lasing dynamics of interacting exciton-polariton condensation centers.Comment: 9 pages, 3 figure

Lyapunov exponents of quantum trajectories beyond continuous measurements

Quantum systems interacting with their environments can exhibit complex non-equilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. Yet, despite many attempts, the toolbox for quantifying dissipative quantum chaos remains very limited. In particular, quantum generalizations of Lyapunov exponent, the main quantifier of classical chaos, are established only within the framework of continuous measurements. We propose an alternative generalization which is based on the unraveling of a quantum master equation into an ensemble of so-called 'quantum jump' trajectories. These trajectories are not only a theoretical tool but a part of the experimental reality in the case of quantum optics. We illustrate the idea by using a periodically modulated open quantum dimer and uncover the transition to quantum chaos matched by the period-doubling route in the classical limit.Comment: 5 pages, 4 figure

Macroscopic quantum tunneling in "small" Josephson junctions in magnetic field

We study the phenomenon of macroscopic quantum tunneling (MQT) in small Josephson junctions (JJ) with an externally applied magnetic field. The latter results in the appearance of the Fraunhofer type modulation of the current density along the barrier. The problem of MQT for a point-like JJ is reduced to the motion of the quantum particle in the washboard potential. In the case of a finite size JJ under consideration, this problem corresponds to a MQT in potential which itself, besides the phase, depends on space variables. Finally, the general expression for the crossover temperature T_0 between thermally activated and macroscopic quantum tunneling regimes and the escaping time tau_esc have been calculated

Periodic orbits, localization in normal mode space, and the Fermi-Pasta-Ulam problem

The Fermi-Pasta-Ulam problem was one of the first computational experiments. It has stirred the physics community since, and resisted a simple solution for half a century. The combination of straightforward simulations, efficient computational schemes for finding periodic orbits, and analytical estimates allows us to achieve significant progress. Recent results on $q$-breathers, which are time-periodic solutions that are localized in the space of normal modes of a lattice and maximize the energy at a certain mode number, are discussed, together with their relation to the Fermi-Pasta-Ulam problem. The localization properties of a $q$-breather are characterized by intensive parameters, that is, energy densities and wave numbers. By using scaling arguments, $q$-breather solutions are constructed in systems of arbitrarily large size. Frequency resonances in certain regions of wave number space lead to the complete delocalization of $q$-breathers. The relation of these features to the Fermi-Pasta-Ulam problem are discussed.Comment: 19 pages, 9 figures, to appear in Am. J. Phy

Mutagenic potential as an integral index of soil pollution by oil components

A study was made on soil samples contaminated by oil and oil-polluted waste waters of Tatarstan oil fields. The mutagenic ability of the samples was evaluated by the plate modification of the Ames test (Salmonella/microsomes). Oil-polluted soils were shown to exhibit medium and weak mutagenic potential. The mutagenic effect was increased by metabolic activation by microsome fractions of rat liver and human placenta. The soil samples contaminated by waste waters of oil wells did not exhibit mutagenic effect. No reliable correlation was revealed between mutagenic effect and some chemical indices (heavy metal and 3,4-Benzpyrene content in the samples). Copyright © 1996 by MAHK Hayka/Interperiodica Publishing