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Register a new userTheory for frequent measurements of spontaneous emissions in non-Markovian environment: beyond Lorentzian spectrum
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The measurement-result-conditioned evolution of a system (e.g. an atom) with spontaneous emissions of photons is well described by the quantum trajectory (QT) theory. In this work we generalize the associated QT theory from infinitely wide bandwidth Markovian environment to the case of finite bandwidth non-Markovian environment. In particular, we generalize the treatment for arbitrary spectrum, which is not restricted by the specific Lorentzian case. We rigorously prove a general existence of a perfect scaling behavior jointly defined by the bandwidth of environment and the time interval between successive photon detections. For a couple of examples, we obtain analytic results to facilitate QT simulations based on the Monte-Carlo algorithm. For the case where analytical result is not available, numerical scheme is proposed for practical simulations.
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In this work we present a large-deviation analysis for the counting statistics of atomic spontaneous emissions continuously detected in finite-bandwidth non-Markovian environment. We show that the statistics of the spontaneous emissions depends on the response time of the detector, which can result in big differences such as dynamical phase transition. This feature excludes the idea of regarding the spontaneous emissions as detection-free objective events. Possible experiment is briefly discussed in connection with the state-of-the-art optical cavity set-up.
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 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 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.
The study of quantum dynamics featuring memory effects has always been a topic of interest within the theory of open quantum system, which is concerned about providing useful conceptual and theoretical tools for the description of the reduced dynamics of a system interacting with an external environment. Definitions of non-Markovian processes have been introduced trying to capture the notion of memory effect by studying features of the quantum dynamical map providing the evolution of the system states, or changes in the distinguishability of the system states themselves. We introduce basic notions in the framework of open quantum systems, stressing in particular analogies and differences with models used for introducing modifications of quantum mechanics which should help in dealing with the measurement problem. We further discuss recent developments in the treatment of non-Markovian processes and their role in considering more general modifications of quantum mechanics.
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