Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency and a Liouville space implementation of a time-discrete quantum memory, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and structured acoustic phonon modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
We establish a quantum functional central limit for the dynamics of a system coupled to a Fermionic bath with a general interaction linear in the creation, annihilation and scattering of the bath reservoir. Following a quantum Markovian limit, we realize the open dynamical evolution of the system as an adapted quantum stochastic process driven by Fermionic Noise.
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level…
The non-Markovianity is a recently proposed characterization of the non-Markovian behavior in an open quantum system, based on which we first present a practical idea for directly measuring the non-Markovian character of a single qubit coupled to a zero-temperature bosonic reservoir, and then extend to investigate the dynamics of two noninteracting qubits subject to two reservoirs respectively with a lower bound of non-Markovianity. Our scheme, with no need of optimization procedures and quantum state tomography, is helpful for experimental implementation.
The reservoir memory effects can lead to information backflow and recurrence of the previously lost quantum correlations. We establish connections between the direction of information flow and variation of the geometric quantum discords (GQDs) measured respectively by the trace distance, the Hellinger distance, and the Bures distance for two qubits subjecting to the bosonic structured reservoirs, and unveil their dependence on a factor whose derivative signifies the (non-)Markovianity of the dynamics. By considering the reservoirs with Lorentzian and Ohmic-like spectra, we further demonstrated…
A theoretical investigation on slow light propagation based on eletromagnetically induced transparency in a three-level quantum-dot system is performed including non-Markovian effects and correlated dephasing reservoirs. It is demonstraonated that the non-Markovian nature of the process is quite essential even for conventional dephasing typical of quantum dots leading to significant enhancement or inhibition of the group velocity slow-down factor as well as to the shifting and distortion of the transmission window. Furthermore, the correlation between dephasing reservoirs may also either enhan…
We study two distinct multi-level atomic models in which one transition is coupled to a Markovian reservoir, while another linked transition is coupled to a non-Markovian reservoir. We show that by choosing appropriately the density of modes of the non-Markovian reservoir the spontaneous emission to the Markovian reservoir is greatly altered. The existence of `dark lines' in the spontaneous emission spectrum in the Markovian reservoir due to the coupling to specific density of modes of the non-Markovian reservoir is also predicted.
The decoherence of two initially entangled qubits in a non-Markovian reservoir has been investigated exactly without Born Markovian approximation and rotating-wave approximation(RWA). The non-perturbative quantum master equation is derived and its exact solution is obtained. The decoherence behaviors of two qubits, initially entangled in Bell states, has been investigated in three different cases of parameters. The results show that the counter-rotating wave terms have great influence on the decoherence behavior, and there are differences between the exact solution of the Hamiltonian with RWA …
The interaction of quantum emitters with structured baths modifies both their individual and collective dynamics. In González-Tudela \emph{et al} we show how exotic quantum dynamics emerge when QEs are spectrally tuned around the middle of the band of a two-dimensional structured reservoir, where we predict the failure of perturbative treatments, anisotropic interactions and novel super and subradiant behaviour. In this work, we provide further analysis of that situation, together with a complete analysis for the quantum emitter dynamics in spectral regions different from the center of the ban…
We investigate the non-Markovian dynamics of two-state systems in structured reservoirs. We establish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] and the recently developed non-Markovian quantum jump method [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. This connection provides a clear physical picture of how the structured reservoir affects the system dynamics, indicating the role of the pseudomodes as an effective description of the environmental memory.
By using the effective non-Markovian measure [H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local reservoir. We show that subsystem dynamics can be controlled by manipulating the coupling between TLAs, temperature and relaxation rate of the atoms. Moreover, the correlation between non-Markovianity of subsystem and entanglement between the subsystem and the structured bath is investigated, the results show that the emergence of non-Markovianity has a nega…
In this paper, we investigate preservation of quantum coherence of a single-qubit interacting with a zero-temperature thermal reservoir through the addition of noninteracting qubits in the reservoir. Moreover, we extend this scheme to preserve quantum entanglement between two and three distant qubits, each of which interacts with a dissipative reservoir independently. At the long time limit, we obtained analytical expressions for the coherence measure and the concurrence of two and three qubits in terms of the number of additional qubits. It is observed that, by increasing the number of additi…
Non-Markovian evolution of an open quantum system can be induced by the memory effects of a reservoir. Although a reservoir with stronger memory effects may seem like it should cause stronger non-Markovian effects on the system of interest, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a qubit (a two-level atom) that is coupled to a hierarchical environment, which contains a single-mode cavity and a reservoir consisting of infinite numbers of modes. We show how the non-Markovian character of the system is influenced by the coupling strength be…
The squeezing dynamics of a damped harmonic oscillator are studied for different types of environment without making the Markovian approximation. The squeezing dynamics of a coherent state depend on the reservoir spectrum in a unique way that can, in the weak coupling approximation, be analyzed analytically. Comparison of squeezing dynamics for Ohmic, sub-Ohmic and super-Ohmic environments is done showing a clear connection between the squeezing--non-squeezing oscillations and reservoir structure. Understanding the effects occurring due to structured reservoirs is important both from a purely …
In this paper, we provide a mechanism of decoherence suppression for open quantum systems in general, and that for "Schrodinger cat-like" state in particular, through the strong couplings to non-Markovian reservoirs. Different from the usual strategies of suppressing decoherence by decoupling the system from the environment in the literatures, here the decoherence suppression employs the strong back-reaction from non-Markovian reservoirs. The mechanism relies on the existence of the singularities (bound states) of the nonequilibrium retarded Green function which completely determines the dissi…
We evaluate exactly the non-Markovian effect on the decoherence dynamics of a qubit interacting with a dissipative vacuum reservoir and find that the coherence of the qubit can be partially trapped in the steady state when the memory effect of the reservoir is considered. Our analysis shows that it is the formation of a bound state between the qubit and its reservoir that results in this residual coherence in the steady state under the non-Markovian dynamics. A physical condition for the decoherence suppression is given explicitly. Our results suggest a potential way to decoherence control by …
The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a quantum system will unavoidably suffer from decoherence. Here, we investigate the dynamic behaviors of the entropic uncertainty relation of an atom-cavity interacting system under a bosonic reservoir during the crossover between Markovian and non-Markovian regimes. Specifically, we explore the dynamic behavior of the entropic uncertainty relation for a pair of inc…
We present a formalism that enables the study of the non-Markovian dynamics of a three-level ladder system in a single structured reservoir. The three-level system is strongly coupled to a bath of reservoir modes and two quantum excitations of the reservoir are expected. We show that the dynamics only depends on reservoir structure functions, which are products of the mode density with the coupling constant squared. This result may enable pseudomode theory to treat multiple excitations of a structured reservoir. The treatment uses Laplace transforms and an elimination of variables to obtain a …
An exactly solvable model for the multi-level system interacting with several reservoirs at zero temperatures is presented. Population decay rates and decoherence rates predicted by exact solution and several approximate master equations, which are widespread in physical literature, are compared. The space of parameters is classified with respect to different inequities between the exact and approximate rates.
We study the non-Markovianity and quantum speedup of a two-level atom (quantum system of interest) in a dissipative Jaynes-Cumming model, where the atom is embedded in a single-mode cavity, which is leaky being coupled to an external reservoir with Ohmic spectral density. We obtain the non-Markovianity characterized by using the probability of the atomic excited state and the negative decoherence rate in the time-local master equation. We also calculate the quantum speed limit time (QSLT) of the evolution process of the atom. The results show that, the atom-cavity coupling is the main physical…
The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature is studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics is completely determined by the propagating (retarded) and correlation Green functions. Compare the non-Markovian behavior at finite temperature with those at zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory eff…
The model of a multi-level system interacting with several reservoirs is considered. The exact reduced density matrix evolution could be obtained for this model without Markov approximation. Namely, this evolution is fully defined by the finite set of linear differential equations. In this work the results which were obtained previously for only one Lorentz peak in the spectral density are generalized to the case of an arbitrary number of such peaks. The case of the Ohmic contribution in the spectral density is also taken here into account.
In this paper, the exact dynamics of open quantum systems in the presence of initial system-reservoir correlations is investigated for a photonic cavity system coupled to a general non-Markovian reservoir. The exact time-convolutionless master equation incorporating with initial system-reservoir correlations is obtained. The non-Markovian dynamics of the reservoir and the effects of the initial correlations are embedded into the time-dependent coefficients in the master equation. We show that the effects induced by the initial correlations play an important role in the non-Markovian dynamics o…
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 study the decoherence properties of an entangled bipartite qubit system, represented by two two-level atoms that are individually coupled to non-Markovian reservoirs. This coupling ensures that the dynamical equations of the atoms can be treated independently. The non-Markovian reservoirs are described by a model which leads to an exact non-Markovian master equation of the Nakajima-Zwanzig form [J. Salo, S. M. Barnett, and S. Stenholm, Optics Commun. 259, 772 (2006)]. We consider the evolution of the entanglement of a two-atom state that is initially completely entangled, quantified by its …
We study the non-Markovian dynamics of a two-mode bosonic system interacting with two uncorrelated thermal bosonic reservoirs. We present the solution to the exact microscopic Master equation in terms of the quantum characteristic function and study in details the dynamics of entanglement for bipartite Gaussian states. In particular, we analyze the effects of short-time system-reservoir correlations on the separability thresholds and show that the relevant parameter is the reservoir spectral density. If the frequencies of the involved modes are within the reservoir spectral density entanglemen…
This paper deals with the dissipative dynamics of a quantum harmonic oscillator interacting with a bosonic reservoir. The Master Equations based on the Rotating Wave and on the Feynman-Vernon system--reservoir couplings are compared highlighting differences and analogies. We discuss quantitatively and qualitatively the conditions under which the counter rotating terms can be neglected. By comparing the analytic solution of the heating function relative to the two different coupling models we conclude that, even in the weak coupling limit, the counter rotating terms give rise to a significant c…
We investigate the entanglement dynamics of two initially entangled qubits interacting independently with two uncorrelated reservoirs beyond the Markovian approximation. Quite different from the Markovian reservoirs [C. E. Lopez et al., Phys. Rev. Lett. 101 (2008) 080503], we find that entanglement sudden birth (ESB) of the two reservoirs occurs without certain symmetry with respect to the entanglement sudden death (ESD) of the two qubits. A phenomenological interpretation of entanglement revival is also given.
The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubits system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.
We show that the effects of decoherence on quantum steering ellipsoids can be controlled by a specific reservoir manipulating, in both Markovian and non-Markovian realms. Therefore, the so-called maximal steered coherence could be protected through reservoir engineering implemented by coupling auxiliary qubits to the reservoir.
We investigate the optimal control problem for non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle is specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions: ω_0\llω_c, ω_0\approxω_c or ω_0\ggω_c, where ω_0 is the characteristic frequency of the quantum system of interest, and ω_c the cut-off frequency of Ohmic reservoir. The optimal control process shows its remarkable influences on the decoherence dynamics. The temperature is a k…
We propose an effective Hamiltonian approach to investigate decoherence of a quantum system in a non-Markovian reservoir, naturally imposing the complete positivity on the reduced dynamics of the system. The formalism is based on the notion of an effective reservoir, i.e., certain collective degrees of freedom in the reservoir that are responsible for the decoherence. As examples for completely positive decoherence, we present three typical decoherence processes for a qubit such as dephasing, depolarizing, and amplitude-damping. The effects of the non-Markovian decoherence are compared to the …
We show that non-Markovian effects of the reservoirs can be used as a resource to extract work from an Otto cycle. The state transformation under non-Markovian dynamics is achieved via a two-step process, namely an isothermal process using a Markovian reservoir followed by an adiabatic process. From second law of thermodynamics, we show that the maximum amount of extractable work from the state prepared under the non-Markovian dynamics quantifies a lower bound of non-Markovianity. We illustrate our ideas with an explicit example of non-Markovian evolution.
The decay dynamics of the classical electromagnetic field in a leaky optical resonator supporting a single mode coupled to a structured continuum of modes (reservoir) is theoretically investigated, and the issue of threshold condition for lasing in presence of an inverted medium is comprehensively addressed. Specific analytical results are given for a single-mode microcavity resonantly coupled to a coupled resonator optical waveguide (CROW), which supports a band of continuous modes acting as decay channels. For weak coupling, the usual exponential Weisskopf-Wigner (Markovian) decay of the fie…
In this paper we present a method to derive an exact master equation for a bosonic system coupled to a set of other bosonic systems, which plays the role of the reservoir, under the strong coupling regime, i.e., without resorting to either the rotating-wave or secular approximations. Working with phase-space distribution functions, we verify that the dynamics are separated in the evolution of its center, which follows classical mechanics, and its shape, which becomes distorted. This is the generalization of a result by Glauber, who stated that coherent states remain coherent under certain circ…
Quantum sensing explores protocols using the quantum resource of sensors to achieve highly sensitive measurement of physical quantities. The conventional schemes generally use unitary dynamics to encode quantities into sensor states. In order to measure the spectral density of a quantum reservoir, which plays a vital role in controlling the reservoir-caused decoherence to microscopic systems, we propose a nonunitary-encoding optical sensing scheme. Although the nonunitary dynamics for encoding in turn degrades the quantum resource, we surprisingly find a mechanism to make the encoding time a r…
We consider four two-level atoms interacting with independent non-Markovian reservoirs with detuning. We mainly investigate the effects of the detuning and the length of the reservoir correlation time on the decoherence dynamics of the multipartite entanglement. We find that the time evolution of the entanglement of atomic and reservoir subsystems is determined by a parameter, which is a function of the detuning and the reservoir correlation time. We also find that the decay and revival of the entanglement of the atomic and reservoir subsystems are closely related to the sign of the decay rate…
We propose the generalized stochastic Liouville equation to investigate the coherent dynamics in single molecule systems coupled to environments which exhibit both nonstationary and non-Markovian features. The generalized stochastic Liouville equation contains a generalized memory kernel associated with both the intrinsic system Hamiltonian and the non-Markovian features of the environmental noise, which returns to the well-known framework established by Kubo in the limit case that the environmental noise is stationary and memoryless. The coherence of the quantum system can be derived by means…
We study a driven two-state system interacting with a structured environment. We introduce the non-Markovian master equation ruling the system dynamics, and we derive its analytic solution for general reservoir spectra. We compare the non-Markovian dynamics of the Bloch vector for two classes of reservoir spectra: the Ohmic and the Lorentzian reservoir. Finally, we derive the analytic conditions for complete positivity with and without the secular approximation. Interestingly, the complete positivity conditions have a transparent physical interpretation in terms of the characteristic timescale…
The dynamics of a three-level atom in a cascade configuration with both transitions coupled to a single structured reservoir of quantized field modes is treated using Laplace transform methods applied to the coupled amplitude equations. Results are also obtained from master equations by two different approaches, that is, involving either pseudomodes or quasimodes. Two different types of reservoir are considered, namely a high-Q cavity and a photonic band-gap system, in which the respective reservoir structure functions involve Lorentzians. Non-resonant transitions are included in the model. In…
The decoherence of two initially entangled qubits in a squeezed vacuum cavity has been investigated exactly. The results show that, first, in principle, the disentanglement time decreases with the increasing of squeeze parameter r, due to the augmenting of average photon number of every mode in squeezed vacuum cavity. Second, there are entanglement revivals after complete disentanglement for the case of even parity initial Bell state, while there are entanglement decrease and revival before complete disentanglement for the case of odd parity initial Bell state. The results are quite different …
The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the correspon…
Memory effects can be studied through a conditional past-future correlation, which measures departure with respect to a conditional past-future independence valid in a memoryless Markovian regime. In a quantum regime this property leads to an operational definition of quantum non-Markovianity based on three consecutive system measurement processes and postselection [Budini, Phys. Rev. Lett. 121, 240401 (2018)]. Here, we study the conditional past-future correlation for a qubit system coupled to different dephasing environments. Exact solutions are obtained for a quantum spin bath as well as fo…
In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study dependence of the steady states of the two-level…
We study non-Markovianity as backflow of information in two-qubit systems. We consider a setting where, by changing the distance between the qubits, one can interpolate between independent reservoir and common reservoir scenarios. We demonstrate that non-Markovianity can be induced by the common reservoir and single out the physical origin of this phenomenon. We show that two-qubit non-Markovianity coincides with instances of non-divisibility of the corresponding dynamical map, and we discuss the pair of states maximizing information flowback. We also discuss the issue of additivity for the me…
We present a non-Markovian quantum trajectory method for treating atoms radiating into a reservoir with a non-flat density of states. The results of an example numerical simulation of the case where the free space modes of the reservoir are altered by the presence of a cavity are presented and compared with those of an extended system approach.
Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a p…
We explore the dynamics of $N$ coupled atoms to a generic bosonic reservoir under specific system symmetries. In the regime of multiple atoms coupled to a single reservoir with identical couplings, we identify remarkable effects, notably that the initial configuration of the atomic excited state amplitudes strongly impacts the dynamics of the system and can even fully sever the system from its environment. Additionally, we find that steady state amplitudes of the excited states become independent of the choice of the reservoir. The framework introduced is applied to a structured photonic reser…
We investigate the relationship between non-Markovianity and the effectiveness of a dynamical decoupling protocol for qubits undergoing pure dephasing. We consider an exact model in which dephasing arises due to a bosonic environment with a spectral density of the Ohmic class. This is parametrised by an Ohmicity parameter by changing which we can model both Markovian and non-Markovian environments. Interestingly, we find that engineering a non-Markovian environment is detrimental to the efficiency of the dynamical decoupling scheme, leading to a worse coherence preservation. We show that each …
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…
Quantum transport along a tight-binding chain connected to Markovian reservoirs
Kirensky Institute of Physics, Federal Research Centre KSC SB RAS（基连斯基物理研究所，俄罗斯科学院西伯利亚分院克拉斯诺亚尔斯克科学中心联邦研究中心）；IRC SQC, Siberian Federal University（西伯利亚联邦大学量子系统与量子控制国际研究中心）；School of Engineering Physics and Radio Electronics, Siberian Federal University（西伯利亚联邦大学工程物理与无线电电子学院）
We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see remarkable difference between the non-Markovian entanglement dynamics with its Markovian counterpart. We show that a non-Markovian decoherence free state is also decoherence free in the Markovian regime, but all the Markovian decoherence free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from squeezed vacuum bath to squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is expressed in terms of the standard deviation of the measured observables. In quantum information theory, it is shown that the uncertainty principle can be expressed by Shannon's entropy. The entopic uncertainty lower bound can be altered by considering a particle as the quantum memory which is correlated with the measured particle. We assume that the quantum memory…
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…
