non-Markovian Effects Research Articles

Nonperturbative treatment of giant atoms using chain transformations

Superconducting circuits coupled to acoustic waveguides have extended the range of phenomena that can be experimentally studied using tools from quantum optics. In particular, giant artificial atoms permit the investigation of systems in which the electric dipole approximation breaks down and pronounced non-Markovian effects become important. While previous studies of giant atoms focused on the realm of the rotating-wave approximation, we go beyond this and perform a numerically exact analysis of giant atoms strongly coupled to their environment, in regimes where counter-rotating terms cannot be neglected. To achieve this, we use a Lanczos transformation to cast the field Hamiltonian into the form of a one-dimensional chain and employ matrix-product state simulations. This approach yields access to a wide range of system-bath observables and to relatively unexplored parameter regimes.

Off-diagonal electron-phonon coupling effects on two-level system dynamics

Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.

Mechanical feedback controls the emergence of dynamical memory in growing tissue monolayers.

The growth of a tissue, which depends on cell-cell interactions and biologically relevant processes such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, pc. A cell can only grow and divide if its pressure, due to interaction with its neighbors, is less than pc. Because temperature is not a relevant variable, the cell dynamics is driven by self-generated active forces (SGAFs) that arise due to cell division. We show that even in the absence of intercellular interactions, cells undergo diffusive behavior. The SGAF-driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force-force autocorrelation function (FAF) that extends over a timescale of several cell division times. The time-dependence of the FAF reveals memory effects, which increases as pc increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback and are inherently a non-equilibrium phenomenon.

Non-Markovian effects for hybrid plasmonic systems in the strong coupling regime

We study the role of non-Markovian effects in the emission spectrum of a quantum emitter resonantly coupled to a surface plasmon in a metal-dielectric structure as the system transitions to strong coupling regime. By using a recent quantum approach to interacting plasmons that incorporates the effects of host material's optical dispersion and losses in the coupling parameters, we obtain analytically the emission spectrum for a plasmonic system of arbitrary shape with characteristic size below the diffraction limit. In the weak coupling regime, the dispersion-induced non-Markovian effects are weak and do not significantly affect the spectral shape of the emission peak. In contrast, in the strong coupling regime, the non-Markovian effects lead to dramatic changes in the emission spectra by causing inversion of spectral asymmetry, as compared to classical and quantum models based on the Markov approximation, which results in a strong enhancement of the lower frequency polaritonic band, consistent with the experiment.

Quantifying non-Markovian Memory in a Superconducting Quantum Computer

We analyze the temporal correlations in a sequence of gates by characterizing the performance of a gate conditioned on the gate that preceded it. With this method, we estimate (i) the size of fluctuations in the performance of a gate, i.e., errors due to non-Markovianity; (ii) the length of the memory; and (iii) the total size of the memory. Our results strongly indicate the presence of nontrivial non-Markovian effects in almost all gates in the universal set. However, based on our findings, we discuss the potential for cleaner computation by adequately accounting the non-Markovian nature of the machine.

Continuous-variable quantum sensing of a dissipative reservoir

We propose a continuous-variable quantum sensing scheme, in which a harmonic oscillator is employed as the probe to estimate the parameters in the spectral density of a quantum reservoir, within a non-Markovian dynamical framework. It is revealed that the sensing sensitivity can be effectively boosted by (i) optimizing the weight of the momentum-position-type coupling in the whole probe-reservoir interaction Hamiltonian, (ii) the initial quantum squeezing resource provided by the probe, (iii) the noncanonical equilibration induced by the non-Markovian effect, and (iv) applying an external driving field. Our results may have some potential applications in understanding and controlling the decoherence of dissipative continuous-variable systems.

Kinetics of Hawking-Page phase transition with the non-Markovian effects

Based on the free energy landscape description of Hawking-Page phase transition, the transition process from the Schwarzschild-anti-de Sitter black hole to the thermal anti-de Sitter space are considered to be stochastic under the thermal fluctuations. If the correlation time of the effective thermal bath is comparable or even longer than the oscillating time of the spacetime state in the potential well on the free energy landscape, the non-Markovian model of the black hole phase transition is required to study the kinetics of the transition processes. The non-Markovian or memory effect is represented by the time dependent friction kernel and the kinetics is then governed by the generalized Langevin equation complemented by the free energy potential. As the concrete examples, we study the effects of the exponentially decay friction kernel and the oscillatory friction kernel on the kinetics of Hawking-Page phase transition. For the exponentially decayed friction, the non-Markovian effects promote the transition process, and for the oscillatory friction, increasing the oscillating frequency also speeds up the transition process.

Quantum coherence protection by noise

In this paper, we propose a scheme to protect quantum coherence by adding another noise. We consider an example of a Jaynes–Cummings model coupled to an external non-Markovian bosonic bath. We solve this model by using the dressed state method in the presence of a stochastic coupling and obtain the density matrix by numerically averaging many stochastic trajectories. We show that the noisy atom-cavity coupling can effectively suppress both the relaxation and dephasing effects caused by the leakage of the cavity. Besides, we further illustrate the impacts of the standard deviation of the noisy coupling and the non-Markovian memory effect on the coherence protection. Then, the mechanism of the protection is analyzed. It is our hope that our research may open a new path to consider the role of noise in quantum coherence preservation.

Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation

We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise. We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading. Using the ΔN formalism, we find the probability distribution P(ℛ) of the comoving curvature perturbation ℛ. We consider inflationary potentials that fit the CMB and lead to PBH dark matter with i) asteroid, ii) solar, or iii) Planck mass, as well as iv) PBHs that form the seeds of supermassive black holes. We find that stochastic effects enhance the PBH abundance by a factor of \U0001d4aa(10)–\U0001d4aa(108), depending on the PBH mass. We also show that the usual approximation, where stochastic kicks depend only on the Hubble rate, either underestimates or overestimates the abundance by orders of magnitude, depending on the potential. We evaluate the gauge dependence of the results, discuss the quantum-to-classical transition, and highlight open issues of the application of the stochastic formalism to USR inflation.

Quantum coherence dynamics of displaced squeezed thermal state in a non-Markovian environment

The dynamical behavior of quantum coherence of a displaced squeezed thermal state in contact with an external bath is discussed in the present work. We use a Fano-Anderson type of Hamiltonian to model the environment and solve the quantum Langevin equation. From the solution of the quantum Langevin equation we obtain the Green's functions which are used to calculate the expectation value of the quadrature operators which are in turn used to construct the covariance matrix. We use a relative entropy based measure to calculate the quantum coherence of the mode. The single mode squeezed thermal state is studied in the Ohmic, sub-Ohmic and the super-Ohmic limits for different values of the mean photon number. In all these limits, we find that when the coupling between the system and the environment is weak, the coherence decays monotonically and exhibit a Markovian nature. When the system and the environment are strongly coupled, we observe that the evolution is initially Markovian and after some time it becomes non-Markovian. The non-Markovian effect is due to the environmental back action on the system. Finally, we also present the steady state dynamics of the coherence in the long time limit in both low and high temperature regime. We find that the qualitative behavior remains the same in both the low and high temperature limits. But quantitative values differ because the coherence in the system is lower due to thermal decoherence.

Dynamics of skew information-based quantum coherence under correlated noisy channels

In this paper, we study analytically the skew information-based coherence, and compare its dynamics with that of the norm of coherence for two-qubit Bell-diagonal states under the influence of correlated Pauli channels, such as correlated dephase, depolarizing and classical noisy channels, respectively. The similar as well as different features between the skew information-based coherence and norm of coherence are discussed. In addition, the physical mechanism of preserving quantum coherence based on memory coefficient of correlated channels and non-Markovian memory effect is also expounded.

Quantum Maxwell's demon assisted by non-Markovian effects.

Maxwell's demon is the quintessential example of information control, which is necessary for designing quantum devices. In thermodynamics, the demon is an intelligent being who utilizes the entropic nature of information to sort excitations between reservoirs, thus lowering the total entropy. So far, implementations of Maxwell's demon have largely been limited to Markovian baths. In our work, we study the degree to which such a demon may be assisted by non-Markovian effects using a superconducting circuit platform. The setup is two baths connected by a demon-controlled qutrit interface, allowing the transfer of excitations only if the overall entropy of the two baths is lowered. The largest entropy reduction is achieved in a non-Markovian regime and, importantly, due to non-Markovian effects, the demon performance can be optimized through proper timing. Our results demonstrate that non-Markovian effects can be exploited to boost the information transfer rate in quantum Maxwell demons.

Non-Markovianity and efficiency of a q-deformed quantum heat engine

We consider a qubit as a working medium in a deformed quantum Otto cycle using Tsallis statistics. To analyze the engine, we obtain the time evolution of the deformed density matrix in different steps of the cycle using the Lindblad equation. We calculate deformed work done, exchange heat, and cycle efficiency. We present a new and exact formula for the dependence of the above parameters with the non-Markovianity of the system, based on mutual information. It finds that the non-Markovian effects can be a resource to extract work from an Otto cycle.

Approximating invertible maps by recovery channels: Optimality and an application to non-Markovian dynamics

We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics. We show how this strategy attenuates non-Markovian effects, such as the backflow of information.

Non-Markovian rate theory on a multidimensional reaction surface: Complex interplay between enhanced configuration space and memory

A theory of barrier crossing rate on a multidimensional reaction energy surface is presented. The theory is a generalization of the earlier theoretical schemes to higher dimensions, with the inclusion of non-Markovian friction along both the reactive and the nonreactive coordinates. The theory additionally includes the bilinear coupling between the reactive and the nonreactive modes at the Hamiltonian level. Under suitable conditions, we recover the rate expressions of Langer and Hynes and establish a connection with the rate treatment of Pollak. Within the phenomenology of generalized Langevin equation description, our formulation provides an improvement over the existing ones because we explicitly include both the non-Markovian effects along the reaction coordinate and the bilinear coupling at the Hamiltonian level. At intermediate-to-large friction, an increase in dimensionality by itself tends to reduce the rate, while the inclusion of the memory effects increases the rate. The theory predicts an increase in rate when off-diagonal friction terms are included. We present a model calculation to study isomerization of a stilbene-like molecule using the prescription of Hochstrasser and co-workers on a two-dimensional reaction energy surface, employing Zwanzig-Bixon hydrodynamic theory of frequency-dependent friction. The calculated rate shows a departure from the predictions of Langer's theory and also from the two-dimensional transition state theory.

Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion.

The theory of hierarchical equations of motion (HEOM) is one of the standard methods to give exact evaluations of the dynamics as coupled to harmonic oscillator environments. However, the theory is numerically demanding due to its hierarchy, which is the set of auxiliary elements introduced to capture the non-Markovian and non-perturbative effects of environments. When system-bath coupling becomes relatively strong, the required computational resources and precision move beyond the regime that can be currently handled. This article presents a new representation of HEOM theory in which the hierarchy is mapped into a continuous space of a collective bath coordinate and several auxiliary coordinates as the form of the quantum Fokker-Planck equation. This representation gives a rigorous time evolution of the bath coordinate distribution and is more stable and efficient than the original HEOM theory, particularly when there is a strong system-bath coupling. We demonstrate the suitability of this approach to treat vibronic system models coupled to environments.

Mpemba effect of a mean-field system: The phase transition time.

The counterintuitive phenomenon-that an initially hotter water freezes faster than initially cooler water-is named the "Mpemba effect." Although it has been known for centuries, the underlying mechanism remains unclear. Recently, the Mpemba effect rekindled the interest of researchers since several studies identified that it might occur in some Markovian systems, and a general statistical-physical Mpemba effect framework was correspondingly proposed. In our previous study [Z.-Y. Yang and J.-X. Hou, Phys. Rev. E 101, 052106 (2020)10.1103/PhysRevE.101.052106], we observed the non-Markovian Mpemba effect in a mean-field system (MFS), where the Mpemba effect originates from the back-reaction of the thermal reservoir. Naturally, the phase transition time is the key to the occurrence of the Mpemba effect, which, however, has not been quantitatively described. Following the direction of previous work, this study rigorously derives the phase transition time under different conditions, and quantitatively describes the mechanism of the non-Markovian Mpemba effect in a MFS. In addition, the validation of our theory was further verified via the microcanonical Monte Carlo simulation. An accurate description of the underlying mechanism of our proposed MFS facilitates the generalization of the Mpemba effect framework in statistical physics and may benefit in answering the riddle of the century, the original Mpemba effect in water.

Real-Time GW: Toward an AbInitio Description of the Ultrafast Carrier and Exciton Dynamics in Two-Dimensional Materials.

We demonstrate the feasibility of the time-linear scaling formulation of the GW method [Phys. Rev. Lett. 124, 076601 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.076601] for abinitio simulations of optically driven two-dimensional materials. The time-dependent GW equations are derived and solved numerically in the basis of Bloch states. We address carrier multiplication and relaxation in photoexcited graphene and find deviations from the typical exponential behavior predicted by the Markovian Boltzmann approach. For a resonantly pumped semiconductor we discover a self-sustained screening cascade leading to the Mott transition of coherent excitons. Our results draw attention to the importance of non-Markovian and dynamical screening effects in out-of-equilibrium phenomena.

Non-Markovian measure independent of initial states of open systems

In recent years, quantifying non-Markovian effect in open quantum system has become an important subject in the quantum decoherence control field. In this paper, a non-Markovian measure independent of the initial state of open system is proposed, thereby extending non-Markovian measure based on quantum Fisher information from the case where the initial state of the system is a pure state to the case where the initial state of the system is an arbitrary mixed state. As its application, the non-Markovian process is quantified by quantum Fisher information about a two-level system undergoing the three well-known dissipative channels, i.e. amplitude dissipative channel, phase damping channel, and random unitary channel. The results show that the conditions of non-Markovian processes in the three dissipative channels are independent of the selection of the initial state of the system by means of the quantum Fisher information of a phase parameter. Further, for amplitude dissipation channel and phase damping channel, the conditions for the non-Markovian processes to occur are equivalent to those given by trace distance, divisibility, quantum mutual information, quantum Fisher-information matrix, et al. As expected, for the case of amplitude dissipation channel, the corresponding results can reduce to the one in other paper (Lu X M, Wang X G, Sun C P <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1103/PhysRevA.82.042103">2010 <i>Phys. Rev. A</i><italic/> <b>82</b> 042103</ext-link>) by selecting the initial state of the system as an optimal pure state. However, for random unitary channel, the conditions of non-Markovian process are not equivalent to those for other measures. In addition, we also obtain an interesting relationship between quantum Fisher information and quantum coherence of the open system in the three dissipative channels, namely the square of quantum <inline-formula><tex-math id="M2">\begin{document}$l_1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221053_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221053_M2.png"/></alternatives></inline-formula> coherence for the evolved state of system is exactly equal to the quantum Fisher information of the phase parameter. In a word, the obtained results not only improve the application scope of using the quantum Fisher information to detect non-Markovian effects in open systems, but also further highlight its important role in quantum information processing.

Convergence Guarantees for Discrete Mode Approximations to Non-Markovian Quantum Baths.

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this Letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.