Non-Markovian non-stationary completely positive open quantum system dynamics

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is defined by a set of disruptive events, consisting in the action of a completely positive superoperator over the system density matrix. The random time intervals between events are described by an arbitrary waiting-time distribution. We show that, in contrast to the Markovian case, if one performs a system-preparation (measurement) at an arbitrary time, the subsequent evolution of the density matrix evolution is modified. The non-stationary character refers to the absence of an asymptotic master equation even when the preparation is performed at arbitrary long times. In spite of this property, we demonstrate that operator expectation values and operators correlations have the same dynamical structure, establishing the validity of a non-stationary quantum regression hypothesis. The non-stationary property of the dynamic is also analyzed through the response of the system to an external weak perturbation.Comment: 13 pages, 3 figure

Lindblad rate equations

In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the structure of a classical rate equation. The system dynamics may develops strong non-local effects such as the dependence of the stationary properties with the system initialization. These equations are derived from alternative microscopic interactions, such as complex environments described in a generalized Born-Markov approximation and tripartite system-environment interactions, where extra unobserved degrees of freedom mediates the entanglement between the system and a Markovian reservoir. Conditions that guarantees the completely positive condition of the solution map are found. Quantum stochastic processes that recover the system dynamics in average are formulated. We exemplify our results by analyzing the dynamical action of non-trivial structured dephasing and depolarizing reservoirs over a single qubit.Comment: 12 pages, 2 figure

Solvable class of non-Markovian quantum multipartite dynamics

We study a class of multipartite open quantum dynamics for systems with an arbitrary number of qubits. The non-Markovian quantum master equation can involve arbitrary single or multipartite and time-dependent dissipative coupling mechanisms, expressed in terms of strings of Pauli operators. We formulate the general constraints that guarantee the complete positivity of this dynamics. We characterize in detail the underlying mechanisms that lead to memory effects, together with properties of the dynamics encoded in the associated system rates. We specifically derive multipartite “eternal” non-Markovian master equations that we term hyperbolic and trigonometric due to the time dependence of their rates. For these models we identify a transition between positive and periodically divergent rates. We also study non-Markovian effects through an operational (measurement-based) memory witness approach

A classical appraisal of quantum definitions of non-Markovian dynamics

We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behavior is analyzed in detail for quantum dynamics which can be built taking as input a class of classical processes.Comment: 15 pages, 6 figures; to appear in J. Phys. B, Special Issue on "Loss of coherence and memory effects in quantum dynamics

Detection of quantum non-Markovianity close to the Born-Markov approximation

We calculate in an exact way the conditional past-future correlation for the decay dynamics of a two-level system in a bosonic bath. Different measurement processes are considered. In contrast to quantum memory measures based solely on system propagator properties, here memory effects are related to a convolution structure involving two system propagators and the environment correlation. This structure allows to detect memory effects even close to the validity of the Born-Markov approximation. An alternative operational-based definition of environment-to-system backflow of information follows from this result. We provide experimental support to our results by implementing the dynamics and measurements in a photonic experiment.Fil: Silva, Thais De Lima. Universidade Federal do Rio de Janeiro; BrasilFil: Walborn, Stephen P.. Universidade Federal do Rio de Janeiro; BrasilFil: Santos, Marcelo F.. Universidade Federal do Rio de Janeiro; BrasilFil: Aguilar, Gabriel H.. Universidade Federal do Rio de Janeiro; BrasilFil: Budini, Adrian Adolfo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad Tecnológica Nacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin

Functional characterization of generalized Langevin equations

We present an exact functional formalism to deal with linear Langevin equations with arbitrary memory kernels and driven by any noise structure characterized through its characteristic functional. No others hypothesis are assumed over the noise, neither the fluctuation dissipation theorem. We found that the characteristic functional of the linear process can be expressed in terms of noise's functional and the Green function of the deterministic (memory-like) dissipative dynamics. This object allow us to get a procedure to calculate all the Kolmogorov hierarchy of the non-Markov process. As examples we have characterized through the 1-time probability a noise-induced interplay between the dissipative dynamics and the structure of different noises. Conditions that lead to non-Gaussian statistics and distributions with long tails are analyzed. The introduction of arbitrary fluctuations in fractional Langevin equations have also been pointed out

Squeezing generation and revivals in a cavity-ion system in contact with a reservoir

We consider a system consisting of a single two-level ion in a harmonic trap, which is localized inside a non-ideal optical cavity at zero temperature and subjected to the action of two external lasers. We are able to obtain an analytical solution for the total density operator of the system and show that squeezing in the motion of the ion and in the cavity field is generated. We also show that complete revivals of the states of the motion of the ion and of the cavity field occur periodically.Comment: 9 pages, 3 figure

The interpretation of non-Markovian stochastic Schr\"odinger equations as a hidden-variable theory

Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function $z(t)$ appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value $z(t)$ even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system ``conditioned'' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.Comment: 9 page

A perturbative approach to non-Markovian stochastic Schr\"odinger equations

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two level atom immersed in a environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensembled average state $\rho_{\rm red}(t)$ approach the exact reduced state found via Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure