non-Markovian Interactions Research Articles

Spatial Coherence of Exciton–Polariton Bose–Einstein Condensates

The dynamics of an exciton–polariton Bose–Einstein condensate in an optical microcavity was considered. A novel version of the stochastic Gross–Pitaevskii equation was proposed to describe the condensate evolution under the non-Markovian interaction with the environment. The proposed version was used to analyze the condensate dynamics at various temperatures. The phase transition from the homogeneous to the fragmented state of the condensate near a temperature of 15 K was detected. This phase transition is accompanied by a sharp drop in the condensate density and a decrease in the correlation length. It was found that, at a temperature of 10 K, the correlation length oscillates with time. The results obtained indicated the necessity to take into account the non-Markovianity of the condensate interaction with the excitonic reservoir.

Emission enhancement in nanoassemblies with extremely small metal nanoparticles: Nonmonotonic effect of temperature and the non-Markovian interactions

Emission enhancement in nanoassemblies with extremely small metal nanoparticles: Nonmonotonic effect of temperature and the non-Markovian interactions

Reassessing thermodynamic advantage from indefinite causal order

Indefinite causal order is a key feature involved in the study of quantum higher order transformations. Recently, intense research has been focused on possible advantages related to the lack of definite causal order of quantum processes. Quite often the quantum switch is claimed to provide advantages in information-theoretic and thermodynamic tasks. We address here the question whether indefinite causal order is a resource for quantum thermodynamics. Inspired by previous results in the literature, we show that indefinite causal order is not necessary for the reported increase in free energy and ergotropy. More specifically, we show that a simple causally ordered process, which replaces the system's state with a new one before the final measurement, outperforms the quantum switch in all thermodynamic tasks considered so far. We further show that a similar advantage can be also achieved without completely discarding system, if we allow for non-Markovian interactions between the system and an environment. We extend the analysis to more extreme examples of indefinite causal order, showing that they do not provide an advantage either. Finally, we discuss a possible way to study the advantages that may arise from indefinite causal order in a general scenario.

Radiative decay of an emitter due to non-Markovian interactions with dissipating matter

It is known that the more tractable Markovian models of coupling suited for weak interactions may overestimate the Rabi frequency notably when applied to the strong-coupling regime. Here, a more significant consequence of the non-Markovian interaction between a photon emitter and dissipating matter such as resonant plasmonic nanoparticles is described. A large increase of radiative decay and a diminished non-radiative loss is shown, which unravels the origin of unexpected large enhancements of surface-enhanced-Raman-spectroscopy, as well as the anomalous enhancements of emission due to extremely small fully absorbing metal nanoparticles less than 10 nm in dimensions. We construct the mixture of pure states of the coupled emitter-nanoparticle system, unlike conventional methods that rely on the orthogonal modes of the nanoparticle alone.

Non-Markovian effects in dynamics of exciton-polariton Bose condensates

Formation of exciton-polariton condensate due to incoherent pumping of an excitonic reservoir is considered. The condensate dynamics is governed by a system of stochastic integro-differential equations of Langevin's type corresponding to the model developed by Elistratov and Lozovik [12]. Attention is concentrated on non-Markovian interaction of the condensate with the excitonic and photonic reservoirs. It is shown that dynamical memory caused by the non-Markovian interaction qualitatively changes the condensate behavior as compared to the Markovian regime. In particular, it diminishes the threshold of pumping strength for the condensate emergence. Also, it is found that the non-Markovian regime leads to relaxation oscillations corresponding to population exchange between the condensate and the excitonic reservoir. Increasing of incoherent pumping strength leads to chaos of relaxation oscillations that is accompanied by random-like transitions between the lower and upper polaritonic states.

Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts.

Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.

Revealing electronic open quantum systems with subsystem TDDFT.

Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.

Magnon dark modes and gradient memory.

Extensive efforts have been expended in developing hybrid quantum systems to overcome the short coherence time of superconducting circuits by introducing the naturally long-lived spin degree of freedom. Among all the possible materials, single-crystal yttrium iron garnet has shown up recently as a promising candidate for hybrid systems, and various highly coherent interactions, including strong and even ultrastrong coupling, have been demonstrated. One distinct advantage in these systems is that spins form well-defined magnon modes, which allows flexible and precise tuning. Here we demonstrate that by dissipation engineering, a non-Markovian interaction dynamics between the magnon and the microwave cavity photon can be achieved. Such a process enables us to build a magnon gradient memory to store information in the magnon dark modes, which decouple from the microwave cavity and thus preserve a long lifetime. Our findings provide a promising approach for developing long-lifetime, multimode quantum memories.

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism.

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.

Non-Markovian quantum measurements in the non-invasive limit

In many real quantum systems the measurement is much less invasive than described by the projection postulate. For example, it is performed by weakly coupling a detector for a finite time to the system. The finite coupling time might lead to different measurement outcomes depending on the details of the interaction. We first investigate a generalized measurements scheme by means of positive operator-valued measures in the weak coupling limit and discuss the consequences appearing due to the non-Markovian interaction. Second we discuss the resulting quasiprobabilities, which in the case of a Markovian measurement scheme obey the so-called weak positivity, i.e. second-order correlation functions are positive semi-definite. In particular, we show a possible violation of weak positivity by second-order correlation functions for a frequency dependent detector measuring a spin-1/2 system. When both are themselves in an equilibrium state but at different respective temperatures, we find that the detection of the quantum behavior vanishes if the system temperature is larger than that of the detector.

Gaussian entanglement induced by an extended thermal environment

We study stationary entanglement among three harmonic oscillators which are dipole coupled to a one-dimensional or a three-dimensional bosonic environment. The analysis of the open-system dynamics is performed with generalized quantum Langevin equations which we solve exactly in Fourier representation. The focus lies on Gaussian bipartite and tripartite entanglement induced by the highly non-Markovian interaction mediated by the environment. This environment-induced interaction represents an effective many-parties interaction with a spatial long-range feature: a main finding is that the presence of a passive oscillator is detrimental for the stationary two-mode entanglement. Furthermore, our results strongly indicate that the environment-induced entanglement mechanism corresponds to uncontrolled feedback which is predominantly coherent at low temperatures and for moderate oscillator-environment coupling as compared to the oscillator frequency.

How Much Time Does a Measurement Take?

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.

Efficient estimation of energy transfer efficiency in light-harvesting complexes

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their realistic with surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long-time behavior of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for system-bath interactions with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulfur bacteria with respect to variations in reorganization energy and bath correlation time scales.

Decoherence of many-body systems due to many-body interactions

We study a spin-gas model, where N_S system qubits are interacting with N_B bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decohenerce induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between baths that are coupled to different individual system qubit and compare Markovian with non-Markovian interactions. As examples we consider specific quantum many-body states and investigate their evolution under several different decoherence models. As a complementary investigation we study how the coupling to the environment can be employed to generate a desired multipartite state.

Emission spectra of atoms with non-Markovian interaction: Fluorescence in a photonic crystal

We present a formula to evaluate the spontaneous emission spectra of an atom in contact with a radiation field with non-Markovian effects. This formula is written in terms of a two-time correlation of system observables and the environmental correlation function, and depends on the distance between the emitting atom and the detector. As an example, we use it to analyze the fluorescence spectra of a two level atom placed as an impurity in a photonic crystal. The radiation field within those materials has a gap or discontinuity where electromagnetic modes cannot propagate in the stationary limit. In that situation, the atomic emission occurs in the form of evanescent waves which are detected with less efficiency the farther we place the detector. The methodology presented in this paper may be useful to study the non-Markovian dynamics of any quantum open system in linear interaction with a harmonic oscillator reservoir and within the weak coupling approximation.

Multiple-Time Correlation Functions for Non-Markovian Interaction: Beyond the Quantum Regression Theorem

We derive the dynamical equation of the reduced propagator, an object that evolves state vectors of the system conditioned to the dynamics of its environment, which is not necessarily in the vacuum state at the initial time. Such a reduced propagator is essential to obtain multiple-time correlation functions (MTCFs). We also study the evolution of MTCFs within the weak-coupling limit and show that the quantum regression theorem is, in general, not satisfied. We illustrate the theory in two different cases: first, solving an exact model, and, second, presenting the results of the numerical integration for a system coupled with a thermal environment through a nondiagonal interaction.

Non-Markovian dynamics and barrier crossing rates at high viscosity

Using the formulation developed in the preceding paper we explain the anomalous simulation results of Straub, Borkovec, and Berne for barrier crossing rates in a double well potential. We find that even in the high friction regime the well dynamics may have a significant effect on rate constants. By using model potentials and memory kernels we show that the dynamics can resemble not only spatial diffusion but also energy diffusion. This is due to the viscoelastic nature of a non-Markovian interaction with a bath. In general, the well dynamics is a complicated mixture of energy and spatial diffusion processes. We find analytical expressions for rate constants valid when the well dynamics is near or far from the Markovian limit.

Preparation and decay of unstable molecular states undergoing memory effects: Excitation by coherent electromagnetic pulses of arbitrary strength

It is shown that the preparation and decay of non-markovian dissipative systems can be handled without any restriction on both excitation intensity and memory strength. Any perturbative approximation in the treatment of non-markovian interaction is avoided. The theory is explicity related to physical models relevant to the problem of molecular radiationless decay. In this respect, it is shown that a quantitative evaluation of the “radiative state” time evolution along the lines of the recent paper by Rhodes can easily be performed whatever the strength of external interaction. It is emphasized that no quantum beat phenomenon may be interpreted in an unambiguous way in the absence of any information on the dissipation coupling. As a new effect of coherent excitation on the nature of the excited state, it is shown that increasing light intensity may allow the molecule to be prepared in the “radiative state” without using § excitations. It is stressed, furthermore, that the excitation of a discrete set of states by long duration pulses has the effect of invalidating the replacement of a complex molecular system by a more simple one, which in turn is to be regarded as the basic idea of the theory. The above physical circumstance seems to be the unique one under which the present approach is no longer applicable. Evidence for this statement is provided by a quantitative simulation of hypothetical experiments of the same kind as the recent ones by Zewail et al.

Wave packet formulation of nonlinear plasma wave kinetics

A theory of nonlinear plasma wave propagation is presented which contains, as particular cases, both the nonlinear Schrödinger equation for coherent waves and the kinetic wave equation for weak plasma turbulence. Fluctuations are represented as a superposition of “micro” wave packets, with finite spread but negligible overlap in wavenumber and frequency. For the case of coherent wave propagation a nonlinear Schrödinger equation is derived, generalized over precious versions in that linear Landau damping nonlinear frequency shift, nonlinear damping, and three-dimensional effects are all included, as well as the non-local, non-Markovian interaction characteristic of this equation. In the case of weak plasma turbulence, the kinetic wave equation is generalized to include self-interaction of the micro packets, which, just as in the coherent case, results in non-local, non-Markovian terms, not heretofore considered in weak turbulence formulations.