We present a detailed study of the non-Markovian two-state system dynamics for the regime of incoherent quantum tunneling. Using perturbation theory in the system tunneling amplitude $Δ$, and in the limit of strong system-bath coupling, we determine the short time evolution of the reduced density matrix and thereby find a general equation of motion for the non-Markovian evolution at longer times. We relate the nonlocality in time due to the non-Markovian effects with the environment characteristic response time. In addition, we study the incoherent evolution of a system with a double-well potential, where each well consists several quantized energy levels. We determine the crossover temperature to a regime where many energy levels in the wells participate in the tunneling process, and observe that the required temperature can be much smaller than the one associated with the system plasma frequency. We also discuss experimental implications of our theoretical analysis.
We introduce a measure of non-Markovianity based on the minimal amount of extra Markovian noise we have to add to the process via incoherent mixing, in order to make the resulting transformation Markovian too at all times. We show how to evaluate this measure by considering the set of depolarizing evolutions in arbitrary dimension and the set of dephasing evolutions for qubits.
We introduce a method of characterization of non-Markovianity using coherence of a system interacting with the environment. We show that under the allowed incoherent operations, monotonicity of a valid coherence measure is affected due to non-Markovian features of the system-environment evolution. We also define a measure to quantify non-Markovianity of the underlying dynamics based on the non-monotonic behavior of the coherence measure. We investigate our proposed non-Markovianity marker in the behavior of dephasing and dissipative dynamics for one and two qubit cases. We also show that our p…
We have recently presented a collision-model-based framework to approach non-Markovian quantum dynamics [Ciccarello F Palma G M and Giovannetti V 2013 Phys. Rev. A 87, 040103(R)]. As a distinctive feature, memory is introduced in a dynamical way by adding extra inter-ancillary collisions to a standard (memoryless) collision model. Here, we focus on the case where such intra-bath collisions are described by incoherent partial swap operations. After briefly reviewing the model, we show how to include temperature as an additional parameter by relaxing the assumption that each bath ancilla is init…
We investigate the role of coherence and Markovianity in finding an answer to the question whether the outcomes of a projectively measured quantum stochastic process are compatible with a classical stochastic process. For this purpose we put forward an operationally motivated definition of incoherent dynamics applicable to any open system's dynamics. For non-degenerate observables described by rank-1 projective measurements we show that classicality always implies incoherent dynamics, whereas the converse is only true for invertible Markovian (but not necessarily time-homogeneous) dynamics. Fo…
We report a theoretical study of a quantum optical model consisting of an array of strongly nonlinear cavities incoherently pumped by an ensemble of population-inverted two-level atoms. Projective methods are used to eliminate the atomic dynamics and write a generalized master equation for the photonic degrees of freedom only, where the frequency-dependence of gain introduces non-Markovian features. In the simplest single cavity configuration, this pumping scheme gives novel optical bistability effects and allows for the selective generation of Fock states with a well-defined photon number. Fo…
The remote control of coherence is a crucial step for its application in quantum computation. We investigate the maximal steered coherence (MSC) and its conversion to entanglement in multiple bosonic reservoirs. It is shown that the MSC decays with time in the Markovian regime and behaves as damped oscillations in the non-Markovian regime. The MSC can also be connected directly to the strength of non-Markovianity, through which we show that it can be noticeably enhanced by taking full advantage of the non-Markovian effects. Besides, the MSC can be converted completely to entanglement via optim…
Understanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For {\it isolated} systems, a hydrodynamic theory explains the origin and spreading of entanglement via the propagation of quasi-particle pairs. However, when systems interact with their surrounding much less has been established. Here we show that the quasi-particle picture remains valid for open quantum systems: while information is still spread by quasiparticles, the environment modifies their correlation and introduces incoherent and mixing effects. For fre…
Semiconductor quantum dots (QDs) have been demonstrated to be versatile candidates to study the fundamentals of light-matter interaction [1-3]. In contrast with atom optics, dissipative processes are induced by the inherent coupling to the environment and are typically perceived as a major obstacle towards stable performances in experiments and applications [4]. In this paper we show that this is not necessarily the case. In fact, the memory of the environment can enhance coherent quantum optical effects. In particular, we demonstrate that the non-Markovian coupling to an incoherent phonon bat…
We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: $-$ amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by $l_1$ norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative $α$-entropies, while the bit flit channel does change for some special cases.
We discuss the use of incoherent light as a resource to control the atomic dynamics and review the proposed in Phys. Rev. A 84, 042106 (2011) method for a controlled transfer between any pure and mixed states of quantum systems using a combination of incoherent and coherent light. Formally, the method provides a constructive proof for an approximate open-loop Markovian state-transfer controllability of quantum system in the space of all density matrices---the strongest possible degree of quantum state control.
The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (1) the oscillatory dynamics close to a coherent-to-incoherent transition is surprisingly different from the one of the classical damped harmonic oscillator and that (2) non-markovian memory plays a prominent role in the time evolution after a quantum quench.
We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich and new non-Markovian phenomenology. This implies a dynamical difference between entanglement and coherence: the latter undergoes revivals whereas the former not, despite the induced dynamics being fully incoherent. In addition, the evolution presents "quasieternal" non-Markovianity, becoming non-divisible at any time period where the system evolves qualitatively. Furthermore, the meth…
We propose a systematic scheme to engineer quantum states of a quantum system governed by a time-convolutionless non-Markovian master equation. According to the idea of reverse engineering, the general algebraic equation to determine the control parameters, such as coherent and incoherent control fields, is presented. Without artificially engineering the time-dependent decay rates and retaining the environment-induced Lamb shifts, the quantum state can still be transferred into the target state in a finite period of time along an arbitrary designed trajectory strictly in Hilbert space. As an a…
We investigate memory effects in the spin-boson model using a recently proposed measure for non-Markovian behavior based on the information exchange between an open system and its environment. Employing the numerical exact multilayer multiconfguration time-dependent Hartree approach, we simulate the dynamics of the spin-boson model at zero temperature for a broad range of parameters. For a fast bath, i.e. in the scaling limit, we find non-Markovian dynamics for a coherently decaying spin at weak system-bath coupling, whereas memory effects are absent for stronger coupling in the regimes of inc…
We study the dynamics of a macroscopic superconducting qubit coupled to two independent non-stationary reservoirs by using time-dependent perturbation theory. We show that an equilibrium environment surpasses the coherent evolution of the macroscopic qubit completely. When the qubit couples to two different reservoirs, exemplifying a non-equilibrium environment, the short-time dynamics is affected by the interference between two reservoirs, implying the non-additivity of effects of two reservoirs. The non-additivity can be traced back to a non-Markovian effect, even though two reservoirs are i…
We investigate the dynamical information exchange between a two-state system and its environment which is measured by von Neumann entropy. It is found that in the underdamping regime, the entropy dynamics exhibits an extremely non-Markovian oscillation-hump feature, in which oscillations manifest quantum coherence and a hump of envelop demonstrates temporal memory of bath. It indicates that the process of entropy exchange is bidirectional. When the coupling strength increases a certain threshold, the hump along with ripple disappears, which is indicative of the coherent-incoherent dynamical cr…
Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a non-operational approach, defined by the istinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitat…
In this work we develop a numerical framework to investigate the renormalization of the non-Markovian dynamics of an open quantum system to which dynamical decoupling is applied. We utilize a non-Markovian master equation which is derived from the non-Markovian quantum trajectories formalism. It contains incoherent Markovian dynamics and coherent Schrödinger dynamics as its limiting cases and is capable of capture the transition between them. We have performed comprehensive simulations for the cases in which the system is either driven by the Ornstein-Uhlenbeck noise or or is described by the …
The dynamics of open quantum systems and manipulation of quantum resources are both of fundamental interest in quantum physics. Here, we investigate the relation between quantum Markovianity and coherence, providing an effective way for detecting non-Markovianity based on the \textit{quantum-incoherent relative entropy of coherence} ($\mathcal{QI}$ REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the $\mathcal{QI}$ REC. Also we implement an all-optical experiment to demonstrate that the behavior of the $\mathcal{QI}$ REC is co…
Under natural conditions, excitation of biological molecules, which display non-unitary open system dynamics, occurs via incoherent processes such as temperature changes or irradiation by sunlight/moonlight. The dynamics of such processes is explored analytically in a non-Markovian generic model. Specifically, a system S in equilibrium with a thermal bath TB is subjected to an external incoherent perturbation BB (such as sunlight) or another thermal bath TB', which induces time evolution in (S+TB). Particular focus is on (i) the extent to which the resultant dynamics is coherent, and (ii) the …
We introduce a generalized approach to characterize the non-Markovianity of quantum dynamical maps via breakdown of monotonicity of thermodynamic functions. By adopting an entropy-based formulation of quantum thermodynamics, we use the relationship between heat and entropy to propose a measure of non-Markovianity based on the heat flow for single-qubit quantum evolutions. This measure can be applied for unital dynamical maps that do not invert the sign of the internal energy. Under certain conditions, it can also be extended for other thermodynamic functions, such as internal energy and work f…
Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovi…
The performance requirements for fault-tolerant quantum computing are very stringent. Qubits must be manipulated, coupled, and measured with error rates well below 1%. For semiconductor implementations, silicon quantum dot spin qubits have demonstrated average single-qubit Clifford gate error rates that approach this threshold, notably with error rates of 0.14% in isotopically enriched $^{28}$Si/SiGe devices. This gate performance, together with high-fidelity two-qubit gates and measurements, is only known to meet the threshold for fault-tolerant quantum computing in some architectures when as…
We investigate the quantum coherent dynamics of an externally driven effective two-level system subjected to a slow Ohmic environment characteristic of biomolecular protein-solvent reservoirs in photosynthetic light harvesting complexes. By means of the numerically exact quasi adiabatic propagator path integral (QUAPI) method we are able to include non-Markovian features of the environment and show the dependence of the quantum coherence on the characteristic bath cut-off frequency omega_c as well as on the driving frequency omega_l and the field amplitude A. Our calculations extend from the w…
The time evolution of the distribution and shareability of quantum coherence of a tripartite system in a non-Markovian environment is examined. The total coherence can be decomposed into various contributions, ranging from local, global bipartite and global tripartite, which characterize the type of state. We identify coherence revivals for non-Markovian systems for all the contributions of coherence. The local coherence is found to be much more robust under the environmental coupling due to an effective smaller coupling to the reservoir. This allows us to devise a characterization of a quantu…
I investigate energy transfer in a donor-acceptor pair beyond weak system-bath coupling. I identify a transition from coherent to incoherent dynamics with increasing temperature, due to multi-phonon effects not captured by a standard weak-coupling treatment. The crossover temperature has a marked dependence on the degree of spatial correlation between fluctuations experienced at the two system sites. For strong correlations, this leads to the possibility of coherence surviving into a high temperature regime.
We examine the elements of the balance equation of entropy in open quantum evolutions and their response as we go from a Markovian to a non-Markovian situation. In particular, we look at the heat current and entropy production rate in the non-Markovian reduced evolution, as well as a Markovian limit of the same, experienced by one of two interacting systems immersed in a Markovian bath. The analysis naturally leads us to define a heat current deficit and an entropy production rate deficit, which are differences between the global and local versions of the corresponding quantities. The investig…
Within the lowest-order Born approximation, we calculate the exact dynamics of a single qubit in the presence of 1/f noise, without making any Markov approximation. We show that the non-Markovian qubit time-evolution exhibits asymmetries and beatings that cannot be explained within a Markovian theory. The present theory for 1/f noise is relevant for both spin- and superconducting qubit realizations in solid-state devices, where 1/f noise is ubiquitous.
Non-Markovian thermal reservoirs for autonomous entanglement distribution
Technical University of Munich（慕尼黑工业大学）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Institute of Fundamental Physics IFF-CSIC（西班牙国家科学研究委员会基础物理研究所）
We show how to simulate a model of many molecules with both strong coupling to many vibrational modes and collective coupling to a single photon mode. We do this by combining process tensor matrix product operator methods with a mean-field approximation which reduces the dimension of the problem. We analyze the steady-state of the model under incoherent pumping to determine the dependence of the polariton lasing threshold on cavity detuning, light-matter coupling strength, and environmental temperature. Moreover, by measuring two-time correlations, we study quadratic fluctuations about the mea…
The investigation of the phenomenon of dephasing assisted quantum transport, which happens when the presence of dephasing benefits the efficiency of this process, has been mainly focused on Markovian scenarios associated with constant and positive dephasing rates in their respective Lindblad master equations. What happens if we consider a more general framework, where time-dependent dephasing rates are allowed, thereby permitting the possibility of non-Markovian scenarios? Does dephasing assisted transport still manifest for non-Markovian dephasing? Here, we address these open questions in a s…
We consider the general open system problem of a charged quantum oscillator confined in a harmonic trap, whose frequency can be arbitrarily modulated in time, that interacts with both an incoherent quantized (blackbody) radiation field and with an arbitrary coherent laser field. We assume that the oscillator is initially in thermodynamic equilibrium with its environment, a non-factorized initial density matrix of the system and the environment, and that at $t=0$ the modulation of the frequency, the coupling to the incoherent and the coherent radiation are switched on. The subsequent dynamics, …
Optical interferometric tools for probing memory effects
S. N. Bose National Centre for Basic Sciences（S. N. Bose 基础科学国家中心）；Indian Statistical Institute（印度统计研究所）；International Institute of Information Technology（国际信息技术学院）；Indian Institute of Technology Goa（印度理工学院果阿分校）
The initial stages of the evolution of an open quantum system encode the key information of its underlying dynamical correlations, which in turn can predict the trajectory at later stages. We propose a general approach based on non-Markovian dynamical maps to extract this information from the initial trajectories and compress it into non-Markovian transfer tensors. Assuming time-translational invariance, the tensors can be used to accurately and efficiently propagate the state of the system to arbitrarily long timescales. The non-Markovian Transfer Tensor Method (TTM) demonstrates the coherent…
We study dynamics of an artificial two-level atom in an open 1D space by measuring evolution of its coherent and incoherent emission. States of the atom -- a superconducting flux qubit coupled to a transmission line -- are fully controlled by resonant excitation microwave pulses. The coherent emission -- a direct measure of superposition in the atom -- exhibits decaying oscillations shifted by $π/2$ from oscillations of the incoherent emission, which, in turn, is proportional to the atomic population. The emission dynamics provides information about states and properties of the atom. By measur…
We study non-Markovian dynamics of a two level atom using pseudomode method. Because of the memory effect of non-Markovian dynamics, the atom receives back information and excited energy from the reservoir at a later time, which causes more complicated behaviors than Markovian dynamics. With pseudomode method, non-Markovian dynamics of the atom can be mapped into Markovian dynamics of the atom and pseudomode. We show that by using pseudomode method and quantum jump approach for Markovian dynamics, we get a physically intuitive insight into the memory effect of non-Markovian dynamics. It sugges…
The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have investigated the non-Markovianity of the dynamics of a two-state system driven by continuous time random walk-type noise, which can be Markovian or non-Markovian depending on its residence time distribution parameters. Exact analytical expressions for the distinguishability as well as the trace distance and entropy-based non-Markovianity measures are ob…
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 dynamics of two spins coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system in the Markovian and Post-Markovian case with exponential memory kernel is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed.
The quantum jump approach allows to characterize the stochastic dynamics associated to an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to non-Markovian system dynamics. The results rely in studying a measurement process performed on a bipartite arrangement characterized by a Markovian Lindblad evolution. Both a renewal and non-renewal extensions are found. The general structure of non-local master equations that admit an unravelling in terms of the corresponding non-Markovian trajectories are also found…
The understanding of memory effects arising from the interaction between system and environment is a key for engineering quantum thermodynamic devices beyond the standard Markovian limit. We study the performance of measurement-based thermal machine whose working medium dynamics is subject to backflow of information from the reservoir via collision based model. In this study, the non-Markovian effect is introduced by allowing for additional unitary interactions between the environments. We present two strategies of realizing non-Markovian dynamics and study their influence on the performance o…
A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we investigate the Markovianity of a qubit system coupled to a single-qubit bath with the qubit bath being continuously refreshed by quantum cooling. A surprising result is that there exists a finite threshold for the cooling rate at which the system transitions from non-Markovian dynamics to Markovian dynamics, which is in sharp contrast to the usual understan…
The Markovian dynamics of a qubit is investigated in the scheme of random unitary dynamics, where Kraus operators are changed by an extra noise. The behavior of Markovianity is explored in the perturbed scenario. We provide a new algorithm for checking CP-divisibility (Markovianity) of a dynamical map.
Coherent and incoherent neutron-matter interaction is studied inside a recently introduced approach to subdynamics of a macrosystem. The equation describing the interaction is of the Lindblad type and using the Fermi pseudopotential we show that the commutator term is an optical potential leading to well-known relations in neutron optics. The other terms, usually ignored in optical descriptions and linked to the dynamic structure function of the medium, give an incoherent contribution to the dynamics, which keeps diffuse scattering and attenuation of the coherent beam into account, thus warran…
We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime; however, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale ($\propto t^2$) than in the Markovian one ($\propto t$). Moreover, although the singular coupling limit of non-Markovian dynamics yield…
Using random matrices, we study the reduced dynamics of a two level system interacting with a generic environment. In the weak coupling limit, the result can be obtained directly from known results for purity decay, and result in Markovian dynamics. We then focus on the case of strong coupling, when the dynamics is known to be non-Markovian. In this regime, the coupling dominates over the local parts of the Hamiltonian, and thus we treat the latter as a perturbation of the former. With the help of the linear response approximation, this allows us to obtain an analytical description of the redu…
We provide an analysis on non-Markovian quantum evolution based on the spectral properties of dynamical maps. We introduce the dynamical analog of entanglement witness to detect non-Markovianity and we illustrate its behaviour with several instructive examples. It is shown that for a certain class of dynamical maps the shape of the body of accessible states provides a simple non-Markovianity witness.
