non-Markovian Noise Research Articles

On a Class of Non-Markovian Langevin Equations

This paper proposes a generalized Langevin's equation for a small classical mechanical system embedded in a reservoir. The interaction of the main system with the reservoir is given by a Gaussian transform as introduced in our previous paper [8]. Thus, a first result proves the existence of a strong solution to this equation in the space where the Gaussian transform (or non-Markovian noise) is defined. The interpretation of the noise is obtained by considering a finite number n of oscillating particles with discrete frequencies in the reservoir. The action of this discrete reservoir on the small system is described by a memory kernel and a sequence of zero-mean Gaussian processes. So, an integro-differential equation for the evolution of a generic particle in the main system arises for each n. This equation has a unique solution Xn which converges in distribution towards the solution of the initial non-Markovian Langevin's equation.

Non-Markovian dynamics and noise characteristics in continuous measurement of a solid-state charge qubit

We investigate the non-Markovian characteristics in continuous measurement of a charge qubit by a quantum point contact. The backflow of information from the reservoir to the system in the non-Markovian domain gives rise to strikingly different qubit relaxation and dephasing in comparison with the Markovian case. The intriguing non-Markovian dynamics is found to have a direct impact on the output noise feature of the detector. Unambiguously, we observe that the non-Markovian memory effect results in an enhancement of the signal-to-noise ratio, which can even exceed the upper limit of “4,” leading thus to the violation of the Korotkov-Averin bound in quantum measurement. Our study thus may open new possibilities to improve detector's measurement efficiency in a direct and transparent way.

Divergence of fermionic correlations under non-Markovian noise in a non-inertial frame

Non-Markovian dynamics of correlations of fermionic systems is investigated beyond the single-mode approximations in a non-inertial frame. Two well known correlation measures, quantum discord and geometric quantum discord, are analyzed for the fermionic states influenced by the non-Markovian noise. Persistence of discord is seen for longer times depending upon the level of mixedness of the fermionic system. The dynamics of the fermionic systems heavily depends upon the degree of white noise. It is shown that fermionic systems remain dependent upon the choice of Unruh modes (qR) beyond the single-mode approximations under non-Markovian noise. Quantum discord is found to be more robust as compared to the geometric quantum discord. Furthermore, the non-Markovian effects are more stronger than the acceleration of Bob, the accelerated partner.

Magnetization-noise-induced collapse and revival of Rabi oscillations in circuit QED

We use a quasi-Hamiltonian formalism to describe the dissipative dynamics of a circuit-QED qubit that is affected by several fluctuating two-level systems with a $1/f$-noise power spectrum. The qubit-resonator interactions are described by the Jaynes-Cummings model. We argue that the presence of pure dephasing noise in such a qubit-resonator system will also induce an energy relaxation mechanism via a fluctuating dipole-coupling term. This random modulation of the coupling is seen to lead to rich physical behavior. For non-Markovian noise, the coupling can either worsen or alleviate decoherence, depending on the initial conditions. The magnetization noise leads to behavior resembling the collapse and revival of Rabi oscillations if the photons are in a coherent state. For a broad distribution of noise couplings, the frequency of these oscillations depends on the mean noise strength. We describe this behavior semianalytically and find it to be independent of the number of fluctuators. This phenomenon could be used as an in situ probe of the noise characteristics.

Quantum Metrology in Non-Markovian Environments

We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.

EFFECTS OF CLASSICAL ENVIRONMENTAL NOISE ON ENTANGLEMENT AND QUANTUM DISCORD DYNAMICS

We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy

We theoretically investigate an electron transfer (ET) process in a dissipative environment by means of two-dimensional (2D) correlation spectroscopy. We extend the reduced hierarchy equations of motion approach to include both overdamped Drude and underdamped brownian modes. While the overdamped mode describes the inhomogeneity of a system in the slow modulation limit, the underdamped mode expresses the primary vibrational mode coupled with the electronic states. We outline a procedure for calculating 2D correlation spectrum that incorporates the ET processes. The present approach has the capability of dealing with system-bath coherence under an external perturbation, which is important to calculate nonlinear response functions for non-markovian noise. The calculated 2D spectrum exhibits the effects of the ET processes through the presence of ET transition peaks along the Ω(1) axis, as well as the decay of echo signals.

Quantum Entanglement Swapping in a Non-Markovian Environment

We propose an entanglement swapping scheme for mixed states in a classical non-Markovian noises, which is modelled as the so-called Ornstein-Uhlenbeck processes. The two mixed states before entanglement swapping are two X-type mixed states, which are caused by the environment-induced decoherence on the initially Bell states. This is more practical than the pure state case in quantum information processing. The fidelity and concurrence of the post-swapping states are discussed.

Deterministic chaos can act as a decoherence suppressor

We propose a strategy to suppress decoherence of a solid-state qubit coupled to non-Markovian noises by attaching the qubit to a chaotic setup with the broad power distribution in particular in the high-frequency domain. Different from the existing decoherence control methods such as the usual dynamics decoupling control, high-frequency components of our control are generated by the chaotic setup driven by a low-frequency field, and the generation of complex optimized control pulses is not necessary. We apply the scheme to superconducting quantum circuits and find that various noises in a wide frequency domain, including low-frequency $1/f$, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubits to a Duffing oscillator as the chaotic setup. Significantly, the decoherence time of the qubit is prolonged approximately $100$ times in magnitude.

Generalized Langevin dynamics of a nanoparticle using a finite element approach: thermostating with correlated noise.

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

Comparison of different measures for quantum discord under non-Markovian noise

Two geometric measures for quantum discord were recently proposed by Modi et al (2010 Phys. Rev. Lett. 104 080501) and Dakić et al (2010 Phys. Rev. Lett. 105 190502). We study the similarities and differences for total quantum correlations of Bell-diagonal states using these two geometry-based quantum discord and the original quantum discord. We show that, under non-Markovian dephasing channels, quantum discord and one of the geometric measures remain constant for a finite amount of time, but not the other geometric measure. However, all the three measures share a common sudden change point. Our study on critical point of sudden transition might be useful for keeping long-time total quantum correlations under decoherence.

Quantum operation for a one-qubit system under a non-Markovian environment

This paper introduces a simple alternating-current (AC) control strategy to perform quantum state manipulations under non-Markovian noise. A genetic algorithm is adopted to optimize the parameters of the AC control, which can be further used to fulfil one-qubit quantum operations at a given final time. Theoretical analysis and simulations show that our method works almost equally well for 1/f noise, ohmic, sub-ohmic and super-ohmic noise, which demonstrates the robustness of our strategy for noise with various spectra. In comparison with the Markovian cases, our method is more suitable to be used to suppress non-Markovian noise.

Motor-driven dynamics of cytoskeletal filaments in motility assays

We model analytically the dynamics of a cytoskeletal filament in a motility assay. The filament is described as rigid rod free to slide in two dimensions. The motor proteins consist of polymeric tails tethered to the plane and modeled as linear springs and motor heads that bind to the filament. As in related models of rigid and soft two-state motors, the binding and unbinding dynamics of the motor heads and the dependence of the transition rates on the load exerted by the motor tails play a crucial role in controlling the filament's dynamics. Our work shows that the filament effectively behaves as a self-propelled rod at long times, but with non-Markovian noise sources arising from the coupling to the motor binding and unbinding dynamics. The effective propulsion force of the filament and the active renormalization of the various friction and diffusion constants are calculated in terms of microscopic motor and filament parameters. These quantities could be probed by optical force microscopy.

Non-Markovian Effect on the Classical and Quantum Correlations

We evaluate the dynamics of quantum and classical correlations in the presence of non-Markovian noises. By considering an entangled pair of spins in the noise environment described by Ornstein—Uhlenbeck processes, we show that the quantum discord of some states is completely unaffected by independent Ornstein—Uhlenbeck noises for long intervals of time, and that the inevitable onset of the sudden decrease of the quantum discord can be substantially delayed by the decrease of the noise bandwidth γ, where γ−1 = τc defines the environment's finite correlation time of the noise.

Non-Markovian shot noise spectrum of quantum transport through quantum dots

The generalized quantum master equation with transport particle number resolution, similar to its conventional unconditioned counterpart, also has time-local and time-nonlocal configurations. The latter is found to be more suitable for the effect of an electrode’s bandwidth on quantum transport and noise spectrum for weak system-reservoir coupling, as calibrated with the exact results in the absence of a Coulomb interaction. We further analyze the effect of the Coulomb interaction on the noise spectrum of the transport current through quantum dot systems, and show that the realistic finite Coulomb interaction and finite bandwidth are manifested only with the non-Markovian treatment. We demonstrate a number of non-Markovian characteristics of the shot noise spectrum, including that which is due to finite bandwidth and that which is sensitive to and enhanced by the magnitude of the Coulomb interaction.

Estimation and Inference of Diffusion Coefficients in Complex Biomolecular Environments.

The 1-D diffusion coefficient associated with a charged atom fluctuating in an ion-channel binding pocket is statistically analyzed. More specifically, unconstrained and constrained molecular dynamics simulations of potassium in gramicidin A are studied. Time domain transition density based inference methods are used to fit simple stochastic differential equations and also to carry out frequentist goodness of fit tests. Particular attention is paid to varying the time between adjacent time series observations due to the well-known "non-Markovian noise" that can appear in this system due to inertia and other unresolved coordinates influencing the dynamics. Different types of non-Markovian noise are shown by the goodness of fit tests to be statistically significant on vastly different time scales. On intermediate scales, a Markovian model is not rejected by the tests; models calibrated at these intermediate scales demonstrate a predictive capability for some physical quantities. However, in this intermediate regime, ergodic sampling does not occur over the length of a time series, but a local diffusion coefficient is deemed statistically acceptable for the observed raw data. It is demonstrated that a linear mixed effects model can be used to summarize the variation induced by slow unresolved degrees of freedom acting as a non-Markovian noise source. The utility of quantitative criteria for assessing low-dimensional stochastic models calibrated from time series generated by high-dimensional biomolecular systems is briefly discussed. Less coarse-grained data summaries of this type show promise for better understanding the kinetic signature of unresolved degrees of freedom in time series coming from simulations and single-molecule experiments.

Entanglement and entangling power of the dynamics in light-harvesting complexes

We study the evolution of quantum entanglement during exciton energy transfer (EET) in a network model of the Fenna-Matthews-Olson (FMO) complex, a biological pigment-protein complex involved in the early steps of photosynthesis in sulfur bacteria. The influence of Markovian as well as spatially and temporally correlated (non-Markovian) noise on the generation of entanglement across distinct chromophores (site entanglement) and different excitonic eigenstates (mode entanglement) is studied for different injection mechanisms, including thermal and coherent laser excitation. Additionally, we study the entangling power of the FMO complex under natural operating conditions. While quantum information processing tends to favor maximal entanglement, near unit EET is achieved as the result of an intricate interplay between coherent and noisy processes where the initial part of the evolution displays intermediate values of both forms of entanglement.

Entanglement evolution in a non-Markovian environment

We extend recent theoretical studies of entanglement dynamics in the presence of environmental noise, following the long-time interest of Krzysztof Wodkiewicz in the effects of stochastic models of noise on quantum optical coherences. We investigate the quantum entanglement dynamics of two spins in the presence of classical Ornstein–Uhlenbeck noise, obtaining exact solutions for evolution dynamics. We consider how entanglement can be affected by non-Markovian noise, and discuss several limiting cases.

Constitutive equations for weakly entangled linear polymers

To interpret the viscoelastic behaviour of entangled linear polymers in terms of dynamics of a single macromolecule, we have been developing the approach, which allows one to study systematically deviations from the Rouse dynamics, when adding non-Markovian and anisotropic noise. It was shown earlier, that the introduction of specific form of non-Markovian dynamics leads to emerging of an intermediate length, which has the meaning of a tube radius and/or the length of a macromolecule between adjacent entanglements. The additional introduction of local anisotropy of mobility of particles allows one to get the results of the conventional reptation-tube model for both mobility and relaxation times of macromolecular coil and, beyond it, to estimate a transition point between weakly (the length of macromolecules M < 10 M e , no reptation) and strongly (the length of macromolecules M > 10 M e , reptation) entangled polymer systems. The adequate mesoscopic equation allows us to develop theory of different relaxation phenomena, in particular, a theory of viscoelasticity and to formulate constitutive equations for linear polymers, which, due to the difference of mechanisms of relaxation, appear to be different for the two types of entangled systems.

Classical capacity of a qubit depolarizing channel with memory

The classical product state capacity of a noisy quantum channel with memory is investigated. A forgetful noise-memory channel is constructed by Markov switching between two depolarizing channels which introduces non-Markovian noise correlations between successive channel uses. The computation of the capacity is reduced to an entropy computation for a function of a Markov process. A reformulation in terms of algebraic measures then enables its calculation. The effects of the hidden-Markovian memory on the capacity are explored. An increase in noise correlations is found to increase the capacity.