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Register a new userMarkovian and non-Markovian dynamics induced by a generic environment
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We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of the whole parameter space, reveals a wide range of different regimes, ranging from strongly non-Markovian to Markovian dynamics. In contrast to analytical models, all non-Markovianity measures and criteria have to be applied to data with fluctuations and statistical uncertainties. We discuss the practical usefulness of the different approaches.
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We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e. the open dynamics is modelled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ancillas, which are subsequently traced out. In this setting non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of memory depth where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a non-monotonic time behaviour of the heat flux serves as an indicator of non-Markovian behaviour.
We investigate what a snapshot of a quantum evolution - a quantum channel reflecting open system dynamics - reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of `Markovianity is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations.
The time evolution of the distribution and shareability of quantum coherence of a tripartite system in a non-Markovian environment is examined. The total coherence can be decomposed into various contributions, ranging from local, global bipartite and global tripartite, which characterize the type of state. We identify coherence revivals for non-Markovian systems for all the contributions of coherence. The local coherence is found to be much more robust under the environmental coupling due to an effective smaller coupling to the reservoir. This allows us to devise a characterization of a quantum state in terms of a coherence tuple on a multipartite state simply by examining various combinations of reservoir couplings. The effect of the environment on the shareability of quantum coherence, as defined using the monogamy of coherence, is investigated and found that the sign of the monogamy is a preserved quantity under the decoherence. We conjecture that the monogamy of coherence is a conserved property under local incoherent processes.
We investigate theoretically the non-Markovian dynamics of a degenerate V-type quantum emitter in the vicinity of a metallic nanosphere, a system that exhibits quantum interference in spontaneous emission due to the anisotropic Purcell effect. We calculate numerically the electromagnetic Greens tensor and employ the effective modes differential equation method for calculating the quantum dynamics of the emitter population, with respect to the resonance frequency and the initial state of the emitter, as well as its distance from the nanosphere. We find that the emitter population evolution varies between a gradually total decay and a partial decay combined with oscillatory population dynamics, depending strongly on the specific values of the above three parameters. Under strong coupling conditions, coherent population trapping can be observed in this system. We compare our exact results with results when the flat continuum approximation for the modified by the metallic nanosphere vacuum is applied. We conclude that the flat continuum approximation is an excellent approximation only when the spectral density of the system under study is characterized by non-overlapping plasmonic resonances.
We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime; however, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale ($propto t^2$) than in the Markovian one ($propto t$). Moreover, although the singular coupling limit of non-Markovian dynamics yields Markovian ones, we show that the same limit does not lead from non-Markovian entanglement generation conditions to Markovian ones. Also, the entanglement generation conditions do not depend on the initial time for non-Markovian open dynamics resulting from couplings to bosonic Gaussian baths, while they may depend on time for open dynamics originated by couplings to classical, stochastic Gaussian environments.
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