Signatures of many-body localization in steady states of open quantum systems

Many-body localization (MBL) is a result of the balance between interference-based Anderson localization and many-body interactions in an ultra-high dimensional Fock space. It is usually expected that dissipation is blurring interference and destroying that balance so that the asymptotic state of a system with an MBL Hamiltonian does not bear localization signatures. We demonstrate, within the framework of the Lindblad formalism, that the system can be brought into a steady state with non-vanishing MBL signatures. We use a set of dissipative operators acting on pairs of connected sites (or spins), and show that the difference between ergodic and MBL Hamiltonians is encoded in the imbalance, entanglement entropy, and level spacing characteristics of the density operator. An MBL system which is exposed to the combined impact of local dephasing and pairwise dissipation evinces localization signatures hitherto absent in the dephasing-outshaped steady state.Comment: 6 pages, 3 figure

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables $\beta_2$ and $\beta_3$. The system is considered to oscillate between positive and negative $\beta_3$-values, by rounding an infinite potential core in the $(\beta_2,\beta_3)$-plane with $\beta_2>0$. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole-octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.Comment: 25 pages, 13 figures. Accepted in Phys. Rev.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work we consider time-periodically modulated quantum systems which are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a non-trivial computational task. To go beyond the current size limits, we use the quantum trajectory method which unravels master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long 'leaps' forward in time, and is numerically exact in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, $\{\eta_1, \eta_2,...,\eta_n\}$, one could propagate a quantum trajectory (with $\eta_i$'s as norm thresholds) in a numerically exact way. %Since the quantum trajectory method falls into the class of standard sampling problems, performance of the algorithm %can be substantially improved by implementing it on a computer cluster. By using a scalable $N$-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with $N = 2000$ states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed

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

Resonant ratcheting of a Bose-Einstein condensate

We study the rectification process of interacting quantum particles in a periodic potential exposed to the action of an external ac driving. The breaking of spatio-temporal symmetries leads to directed motion already in the absence of interactions. A hallmark of quantum ratcheting is the appearance of resonant enhancement of the current (Europhys. Lett. 79 (2007) 10007 and Phys. Rev. A 75 (2007) 063424). Here we study the fate of these resonances within a Gross-Pitaevskii equation which describes a mean field interaction between many particles. We find, that the resonance is i) not destroyed by interactions, ii) shifting its location with increasing interaction strength. We trace the Floquet states of the linear equations into the nonlinear domain, and show that the resonance gives rise to an instability and thus to the appearance of new nonlinear Floquet states, whose transport properties differ strongly as compared to the case of noninteracting particles