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arXiv:1607.04977 · Physical Review A

Energy backflow in strongly coupled non-Markovian continuous-variable systems

Giacomo Guarnieri, Johannes Nokkala, Rebecca Schmidt, Sabrina Maniscalco, Bassano Vacchini

Published Dec 1, 2016• 24 citations
arXivHTMLPDF

Abstract

By employing the full counting statistics formalism, we characterize the first moment of energy that is exchanged during a generally non-Markovian evolution in nondriven continuous-variable systems. In particular, we focus on the evaluation of the energy flowing back from the environment into the open quantum system. We apply these results to the quantum Brownian motion, where these quantities are calculated both analytically, under the weak-coupling assumption, and numerically also in the strong-coupling regime. Finally, we characterize the non-Markovianity of the reduced dynamics through a recently introduced witness based on the so-called Gaussian interferometric power and we discuss its relationship with the energy backflow measure.

DOI
10.1103/physreva.94.062101

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By employing the full counting statistics formalism, we characterize the first moment of energy that is exchanged during a generally non-Markovian evolution in nondriven continuous-variable systems. In particular, we focus on the evaluation of the energy flowing back from the environment into the open quantum system. We apply these results to the quantum Brownian motion, where these quantities are calculated both analytically, under the weak-coupling assumption, and numerically also in the strong-coupling regime. Finally, we characterize the non-Markovianity of the reduced dynamics through a recently introduced witness based on the so-called Gaussian interferometric power and we discuss its relationship with the energy backflow measure.
We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al. [Phys. Rev. Lett. 103, 210401 (2009);], that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.
We explore the behavior in time of the energy exchange between a system of interest and its environment, together with its relationship to the non-Markovianity of the system dynamics. In order to evaluate the energy exchange we rely on the full counting statistics formalism, which we use to evaluate the first moment of its probability distribution. We focus in particular on the energy backflow from environment to system, to which we associate a suitable condition and quantifier, which enables us to draw a connection with a recently introduced notion of non-Markovianity based on information backflow. This quantifier is then studied in detail in the case of the spin-boson model, described within a second-order time-convolutionless approximation, observing that non-Markovianity allows for the observation of energy backflow. This analysis allows us to identify the parameters region in which energy backflow is higher.
Nonequilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady-state nonequilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to establish general relationships between transport coefficients in the transient regime which take the form of fluctuation-dissipation theorems in the steady state. This result becomes most conspicuous in the transient dynamics of open quantum systems under strong-coupling to non-Markovian environments in nonequilibrium settings. In order to explore this regime, a new simulation method based in a hierarchy of equations of motion has been developed. We instantiate our proposal with the study of energetic conductance between two baths connected via a few level system.
We explore signatures of the non-Markovianity in the time-resolved energy transfer processes for quantum open systems. Focusing on typical systems such as the exact solvable damped Jaynes-Cummings model and the general spin-boson model, we establish quantitative links between the time-resolved energy current and the symmetric logarithmic derivative quantum Fisher information (SLD-QFI) flow, one of measures quantifying the non-Markovianity, within the framework of non-Markovian master equations in time-local forms. From the relationships, we find in the damped Jaynes-Cummings model that the SLD-QFI backflow from the reservoir to the system always correlates with an energy backflow, thus we can directly witness the non-Markovianity from the dynamics of the energy current. In the spin-boson model, the relation is built on the rotating-wave approximation, calibrated against exact numerical results, and proven reliable in the weak coupling regime. We demonstrate that whether the non-Markovianity guarantees the occurrence of an energy backflow depends on the bath spectral function. For the Ohmic and sub-Ohmic cases, we show that no energy backflow occurs and the energy current always flow out of the system even in the non-Markovian regime. While in the super-Ohmic case, we observe that the non-Markovian dynamics can induce an energy backflow.
We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation approaches, we introduce an effective master equation whose solution can be used to generate arbitrary moments of the heat statistics for any number of reservoirs. This theory applies equally to fermionic and bosonic systems, holds at arbitrarily strong coupling, and resolves out-of-equilibrium transient dynamics determined by the system's initial state. In the steady-state, weak-coupling limit, we recover results analogous to those of the well-known Landauer-Büttiker formalism. We conclude our discussion by demonstrating an application of the method to a prototypical fermionic system. Our results uncover a regime of transient negative heat conductance contingent upon the initial system preparation, providing a clear signature of non-trivial out-of-equilibrium dynamics.
In quantum open systems, non-Markovianity is an important phenomenon that allows a backflow of information from the environment to the system. In this work, we investigate the non-Markovianity problems in two different types of channels, where the system–environment interactions are treated with and without the rotating-wave approximation (RWA). We employ the quantum interferometric power (QIP) to quantify the non-Markovian dynamics, which is the minimal quantum Fisher information obtained by the local unitary evolution in a bipartite system. By the hierarchy equation method, we calculate the dynamical evolution of the QIP in the non-RWA case. The results show that the dynamical behavior under the non-RWA is significantly different from that under the RWA in both weak and strong coupling. Moreover, in the non-RWA case, we also find the nonmonotonic behavior of the non-Markovianity measure with the variation of coupling strength, which is caused by the competition between the rotating-wave terms and the counterrotating-wave terms. As a result, we highlight the importance of the counterrotating-wave terms for the influence of non-Markovianity.