General non-Markovian dynamics of open quantum systems

Dephasing Dynamics in a Non-Equilibrium Fluctuating Environment

We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, of which the statistical properties are both non-stationary and non-Markovian. Due to the time-homogeneous property in the master equations for the multi-time probability distribution, the decoherence factor induced by the generalized RTN with a modulatable-type memory kernel can be exactly derived by means of a closed fourth-order differential equation with respect to time. In some special limit cases, the decoherence factor recovers to the expression of the previous ones. We analyzed in detail the environmental effect of memory modulation in the dynamical dephasing in four types of dynamics regimes. The results showed that the dynamical dephasing of the quantum system and the conversion between the Markovian and non-Markovian characters in the dephasing dynamics under the influence of the generalized RTN can be effectively modulated via the environmental memory kernel.

Hybrid quantum thermal machines with dynamical couplings

Quantum thermal machines can perform useful tasks, such as delivering power, cooling, or heating. In this work, we consider hybrid thermal machines, that can execute more than one task simultaneously. We characterize and find optimal working conditions for a three-terminal quantum thermal machine, where the working medium is a quantum harmonic oscillator, coupled to three heat baths, with two of the couplings driven periodically in time. We show that it is possible to operate the thermal machine efficiently, in both pure and hybrid modes, and to switch between different operational modes simply by changing the driving frequency. Moreover, the proposed setup can also be used as a high-performance transistor, in terms of output-to-input signal and differential gain. Owing to its versatility and tunability, our model may be of interest for engineering thermodynamic tasks and for thermal management in quantum technologies.

Disentanglement Dynamics in Nonequilibrium Environments

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

Unidirectional amplification in optomechanical system coupling with a structured bath

Nonreciprocity plays an indispensable role in quantum information transmission. We theoretically study the unidirectional amplification in the non-Markovian regime, in which a nanosphere surrounded by a structured bath is trapped in a single (dual)-mode cavity. The global mechanical response function of the nanosphere is markedly altered by the non-Markovian structured bath through shifting the effective frequency and magnifying the response function. Consequently, when there is a small difference in the transmission rate within the regime of Markovian, the unidirectional amplification is achieved in the super-Ohmic spectral environment. In the double-optomechanical coupling system, the phase difference between two optomechanical couplings can reverse the transmission direction. Meanwhile, the non-Markovian bath still can amplify the signal because of the XX-type coupling between nanosphere and its bath.

Nonequilibrium Dynamics of Renyi Entropy for Bosonic Many-Particle Systems

We propose a new field theoretic method for calculating Renyi entropy of a subsystem of many interacting bosons without using replica methods. This method is applicable to dynamics of both open and closed quantum systems starting from arbitrary initial conditions. Our method identifies the Wigner characteristic of a reduced density matrix with the partition function of the whole system with a set of linear sources turned on only in the subsystem, and uses this to calculate the subsystem's Renyi entropy. We use this method to study the evolution of Renyi entropy in a noninteracting open quantum system starting from an initial Fock state. We find a relation between the initial state and final density matrix which determines whether the entropy shows nonmonotonic behavior in time. For non-Markovian dynamics, we show that the entropy approaches its steady-state value as a power law with exponents governed by nonanalyticities of the bath. We illustrate that this field-theoretic method can be used to study large bosonic open quantum systems.

Strong coupling regime and bound states in the continuum between a quantum emitter and phonon-polariton modes

We investigate the population dynamics of a two-level quantum emitter (QE) placed near a hexagonal boron nitride (h-BN) layer. The h-BN layer supports two energy phonon-polariton bands. In the case that the transition energy of the QE is resonant to them, its relaxation rate is enhanced several orders of magnitude compared to its free-space value and the population of the QE excited state shows reversible dynamics. We further show that for specific parameters of the QE/h-BN layer system, the QE population can be trapped in the excited state, keeping a constant value over long periods of time, thus demonstrating that the h-BN layer is a platform that can provide the strong light-matter interaction conditions needed for the formation of bound states in the electromagnetic continuum of modes. Semi-analytical methods are employed for determining whether such a bound state can be formed for given coupling conditions, as well as for computing the amount of initial population trapped in it. The bound states in the continuum are important for designing practical future quantum applications.

Dissipatively Controlled Optomechanical Interaction via Cascaded Photon-Phonon Coupling

In an optomechanical system, we experimentally engineer the optical density of state to reduce or broaden the effective linewidth of the optical mode by introducing an ancillary mechanical mode, which has a large decay rate, i.e., stimulated backward Brillouin scattering. Based on this dissipation engineering, we could engineer the optical mode linewidth by one order of magnitude. In addition, we can either enhance or suppress the optomechanical cooling and amplification of the target mechanical oscillations. Our scheme demonstrates the cascaded photon-phonon coupling to control the mechanical interactions, and also presents a novel approach for engineering coherent light-matter interaction in hybrid systems, which consist of different types of nonlinear interactions and multiple modes, and promote the performance of quantum devices.

Universal non-Markovianity detection in hybrid open quantum systems

A universal characterization of non-Markovianity for any open hybrid quantum systems is presented. This formulation is based on the negativity volume of the generalized Wigner function, which serves as an indicator of the quantum correlations in any composite quantum systems. It is shown, that the proposed measure can be utilized for any single or multi-partite quantum system, containing any discrete or continuous variables. To demonstrate its power in revealing non-Markovianity in such quantum systems, we additionally consider a few illustrative examples.

Quantum thermodynamics of single particle systems

Thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two-level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system-reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system-reservoir coupling regime where the Born-Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non-Markovian memory effect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by inflationary dynamics associated with negative dynamical temperature. The corresponding dynamical criticality provides a border separating classical and quantum worlds. The inflationary dynamics may also relate to the origin of big bang and universe inflation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved.

Observing Information Backflow from Controllable Non-Markovian Multichannels in Diamond

The unavoidable interaction of a quantum open system with its environment leads to the dissipation of quantum coherence and correlations, making its dynamical behavior a key role in many quantum technologies. In this Letter, we demonstrate the engineering of multiple dissipative channels by controlling the adjacent nuclear spins of a nitrogen-vacancy center in diamond. With a controllable non-Markovian dynamics of this open system, we observe that the quantum Fisher information flows to and from the environment using different noisy channels. Our work contributes to the developments of both noisy quantum metrology and quantum open systems from the viewpoints of metrologically useful entanglement.

Rate Operator Unraveling for Open Quantum System Dynamics

Stochastic methods with quantum jumps are often used to solve open quantum system dynamics. Moreover, they provide insight into fundamental topics, such as the role of measurements in quantum mechanics and the description of non-Markovian memory effects. However, there is no unified framework to use quantum jumps to describe open-system dynamics in any regime. We solve this issue by developing the rate operator quantum jump (ROQJ) approach. The method not only applies to both Markovian and non-Markovian evolutions, but also allows us to unravel master equations for which previous methods do not work. In addition, ROQJ yields a rigorous measurement-scheme interpretation for a wide class of dynamics, including a set of master equations with negative decay rates, and sheds light on different types of memory effects which arise when using stochastic quantum jump methods.

Bound state and non-Markovian dynamics of a quantum emitter around a surface plasmonic nanostructure

A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time. We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics. We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists. A general criterion for identifying the existence of a bound state is presented. The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity. Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value. In addition, it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface, but nearly independent on the size of the nanosphere or the rod. Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.

Multipartite Entanglement Generation in a Structured Environment

In this paper, we investigate the entanglement generation of n-qubit states in a model consisting of n independent qubits, each coupled to a harmonic oscillator which is in turn coupled to a bath of N additional harmonic oscillators with nearest-neighbor coupling. With analysis, we can find that the steady multipartite entanglement with different values can be generated after a long-time evolution for different sizes of the quantum system. Under weak coupling between the system and the harmonic oscillator, multipartite entanglement can monotonically increase from zero to a stable value. Under strong coupling, multipartite entanglement generation shows a speed-up increase accompanied by some oscillations as non-Markovian behavior. Our results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance non-Markovian dynamics and make it take a very long time for the entanglement to reach a stable value. Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation. Finally, the entanglement generation of the additional harmonic oscillators is also discussed.

Quantum dephasing induced by non-Markovian random telegraph noise

We theoretically study the dynamical dephasing of a quantum two level system interacting with an environment which exhibits non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss the quantum dephasing dynamics of the system and the non-Markovian character exhibiting in the dynamical dephasing induced by non-Markovian random telegraph noise. We show that the dynamical dephasing of the quantum system does not always exhibit non-Markovian character which results from that the non-Markovian character in the dephasing dynamics depends both on the environmental non-Markovian character and the interaction between the system and environment. In addition, the dynamical dephasing of the quantum system can be modulated by the external modulation frequency of the environment. This result is significant to quantum information processing and helpful for further understanding non-Markovian dynamics of open quantum systems.

System susceptibility and bound-states in structured reservoirs

We propose a formulation to obtain the exact susceptibility for system arbitrary operators to the external fields by means of the whole-system Hamiltonian (system plus reservoir) diagonalization methods, where the dissipative effects directly reflect the nature of the structured non-Markovian reservoir. This treatment does not make the Born-Markovian approximation in structured non-Markovian reservoir. The relations between linear response function and bound-states for the system as well as structured reservoir are found, which shows the photon bound-states and continuous energy spectrum can be readout from the susceptibility, respectively. These results are then used to examine the validity of second-order Born-Markovian approximation, where we find interesting features (e.g., bound-states) are lost in the approximate treatments for open systems. We study the dependence of the response function on the type (spectrum density) of interaction between the system and structured reservoir. We also give the physical reasons behind the disappearance of the bound-states in the approximation method. Finally, these results are also extended to a more general quantum network involving an arbitrary number of coupled-bosonic system without rotating-wave approximation. The presented results might open a new door to understand the linear response and the energy spectrum for non-Markovian open systems with structured reservoirs.

Quantum Dynamics in a Fluctuating Environment

We theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master equations, respectively. We derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process, respectively. For the pure decoherence case with no tunneling coupling, the expressions of the decoherence factor we obtained are consistent with the well-known existing ones. The results are significant to quantum information processing and helpful for further understanding the quantum dynamics of open quantum systems.

Macroscopic entanglement in optomechanical system induced by non-Markovian environment

In this paper, the non-Markovian dynamics of an optomechanical system is analyzed by using the non-Markovian quantum state diffusion (NMQSD) method. An exact solution is obtained for the system composed of a Fabry-Pérot (F-P) cavity with two movable mirrors without the linearization of the Hamiltonian. Based on the solution, we find that the memory effect of the non-Markovian environment can be used to generate macroscopic entanglement between two mirrors. In order to achieve the maximum entanglement generation, the non-Markovian properties of the environment have to be chosen carefully depending on the properties of the system. Then, we also show that the coherence (superposition) in the initial state may produce entanglement in the evolution. At last, we show the entanglement sudden death and revival significantly depend on the strength of the memory effect, and the entanglement revival can be only observed in non-Markovian case. Our treatment, as an example, paves a way to exactly solve a large category of optomechanical systems without the linearization of the Hamiltonian.

Modelling the ultra-strongly coupled spin-boson model with unphysical modes

A quantum system weakly coupled to a zero-temperature environment will relax, via spontaneous emission, to its ground-state. However, when the coupling to the environment is ultra-strong the ground-state is expected to become dressed with virtual excitations. This regime is difficult to capture with some traditional methods because of the explosion in the number of Matsubara frequencies, i.e., exponential terms in the free-bath correlation function. To access this regime we generalize both the hierarchical equations of motion and pseudomode methods, taking into account this explosion using only a biexponential fitting function. We compare these methods to the reaction coordinate mapping, which helps show how these sometimes neglected Matsubara terms are important to regulate detailed balance and prevent the unphysical emission of virtual excitations. For the pseudomode method, we present a general proof of validity for the use of superficially unphysical Matsubara-modes, which mirror the mathematical essence of the Matsubara frequencies.

Retrieving Ideal Precision in Noisy Quantum Optical Metrology

Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometry. Here, we find that not only can the SNL be beaten, but also the ZL can be asymptotically recovered in a long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.

Optomechanical quadrature squeezing in the non-Markovian regime

Squeezing of quantum fluctuation plays an important role in fundamental quantum physics and has marked influence on ultrasensitive detection. We propose a scheme to generate and enhance the squeezing of mechanical mode by exposing the optomechanical system to a non-Markovian environment. It is shown that the effective parametric resonance term of mechanical mode can be induced due to interaction with the cavity and non-Markovian reservoir, thus resulting in quadrature squeezing of the mechanical resonator; jointing the two kinds of interactions can enhance the squeezing effect. Compared with the usual Markovian regime, we can obtain stronger squeezing, and, significantly, the squeezing can approach a low asymptotic stable value.

Universal Dissipationless Dynamics in Gaussian Continuous-Variable Open Systems

We investigate the universal dissipationless dynamics of Gaussian continuous-variable systems in the presence of a band-gapped bosonic environment. Our results show that environmental band gaps can induce localized modes, which give rise to the dissipationless dynamics where the system behaves as free oscillators instead of experiencing a full decay in the long-time limit. We present a complete characterization of localized modes and show the existence of the critical system-environment coupling. Beyond the critical values, localized modes can be produced, and the system dynamics become dissipationless. This novel dynamics can be utilized to overcome the environmental noises and protect the quantum resources in the continuous-variable quantum information.

Steepest entropy ascent for two-state systems with slowly varying Hamiltonians

The steepest entropy ascent approach is considered and applied to two-state systems. When the Hamiltonian of the system is time-dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact are given. In the limit of slowly varying Hamiltonians, which allows for the adiabatic approximation for the unitary part of the dynamics, the system exhibits significant robustness to the thermalization process. Specific examples such as a spin in a rotating field and a generic two-state system undergoing an avoided crossing are considered.

Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments-one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.

Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open-system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open-system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open-system dynamics as nonclassical. We give examples for open-system dynamics that are unital and classical, as well as unital and nonclassical.

Non-equilibrium quantum phase transition via entanglement decoherence dynamics

We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained.

Driven Liouville von Neumann Equation in Lindblad Form

The Driven Liouville von Neumann approach [J. Chem. Theory Comput. 2014, 10, 2927-2941] is a computationally efficient simulation method for modeling electron dynamics in molecular electronics junctions. Previous numerical simulations have shown that the method can reproduce the exact single-particle dynamics while avoiding density matrix positivity violation found in previous implementations. In this study we prove that in the limit of infinite lead models the underlying equation of motion can be cast in Lindblad form. This provides a formal justification for the numerically observed density matrix positivity conservation.

Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment

We investigate dynamics of an optomechanical system under the non-Markovian environment. In the weak optomechanical single-photon coupling regime, we provide an analytical approach fully taking into account the non-Markovian memory effects. When the cavity-bath coupling strength crosses a certain threshold, an oscillating memory state for the classical cavity field is formed. Due to the existence of the non-decay optical bound state, a nonequilibrium optomechanical thermal entanglement is preserved even without external driving laser. Our results provide a potential usage to generate and protect entanglement via non-Markovian environment.

Exact Closed Master Equation for Gaussian Non-Markovian Dynamics

Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows us to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schrödinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.

Quantum phase transition in a coupled two-level system embedded in anisotropic three-dimensional photonic crystals

The quantum phase transition (QPT) describes a sudden qualitative change of the macroscopic properties mapped from the eigenspectrum of a quantum many-body system. It has been studied intensively in quantum systems with the spin-boson model, but it has barely been explored for systems in coupled spin-boson models. In this paper, we study the QPT with coupled spin-boson models consisting of coupled two-level atoms embedded in three-dimensional anisotropic photonic crystals. The dynamics of the system is derived exactly by means of the Laplace transform method, which has been proven to be equivalent to the dissipationless non-Markovian dynamics. Drawing on methods for analyzing the ground state, we obtain the phase diagrams through two exact critical equations and two QPTs are found: one QPT is that from the phase without one bound state to the phase with one bound state and another is that from one phase with the bound state having one eigenvalue to another phase where the bound state has two eigenvalues. Our analytical results also suggest a way of control to overcome the effect of decoherence by engineering the spectrum of the reservoirs to approach the non-Markovian regime and to form the bound state of the whole system for quantum devices and quantum statistics.

Sustainability of Transient Kinetic Regimes and Origins of Death

It is generally recognized that a distinguishing feature of life is its peculiar capability to avoid equilibration. The origin of this capability and its evolution along the timeline of abiogenesis is not yet understood. We propose to study an analog of this phenomenon that could emerge in non-biological systems. To this end, we introduce the concept of sustainability of transient kinetic regimes. This concept is illustrated via investigation of cooperative effects in an extended system of compartmentalized chemical oscillators under batch and semi-batch conditions. The computational study of a model system shows robust enhancement of lifetimes of the decaying oscillations which translates into the evolution of the survival function of the transient non-equilibrium regime. This model does not rely on any form of replication. Rather, it explores the role of a structured effective environment as a contributor to the system-bath interactions that define non-equilibrium regimes. We implicate the noise produced by the effective environment of a compartmentalized oscillator as the cause of the lifetime extension.

General response formula and application to topological insulator in quantum open system

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

Role of initial system-bath correlation on coherence trapping

We study the coherence trapping of a qubit correlated initially with a non-Markovian bath in a pure dephasing channel. By considering the initial qubit-bath correlation and the bath spectral density, we find that the initial qubit-bath correlation can lead to a more efficient coherence trapping than that of the initially separable qubit-bath state. The stationary coherence in the long time limit can be maximized by optimizing the parameters of the initially correlated qubit-bath state and the bath spectral density. In addition, the effects of this initial correlation on the maximal evolution speed for the qubit trapped to its stationary coherence state are also explored.

Non-Markovian Complexity in the Quantum-to-Classical Transition

The quantum-to-classical transition is due to environment-induced decoherence, and it depicts how classical dynamics emerges from quantum systems. Previously, the quantum-to-classical transition has mainly been described with memory-less (Markovian) quantum processes. Here we study the complexity of the quantum-to-classical transition through general non-Markovian memory processes. That is, the influence of various reservoirs results in a given initial quantum state evolving into one of the following four scenarios: thermal state, thermal-like state, quantum steady state, or oscillating quantum nonstationary state. In the latter two scenarios, the system maintains partial or full quantum coherence due to the strong non-Markovian memory effect, so that in these cases, the quantum-to-classical transition never occurs. This unexpected new feature provides a new avenue for the development of future quantum technologies because the remaining quantum oscillations in steady states are decoherence-free.

Breakdown of Bose-Einstein distribution in photonic crystals

In the last two decades, considerable advances have been made in the investigation of nano-photonics in photonic crystals. Previous theoretical investigations of photon dynamics were carried out at zero temperature. Here, we investigate micro/nano cavity photonics in photonic crystals at finite temperature. Due to photonic-band-gap-induced localized long-lived photon dynamics, we discover that cavity photons in photonic crystals do not obey Bose-Einstein statistical distribution. Within the photonic band gap and in the vicinity of the band edge, cavity photons combine the long-lived non-Markovain dynamics with thermal fluctuations together to form photon states that memorize the initial cavity state information. As a result, Bose-Einstein distribution is completely broken down in these regimes, even if the thermal energy is larger or much larger than the cavity detuning energy. In this investigation, a crossover phenomenon from equilibrium to nonequilibrium steady states is also revealed.

Investigating Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment

Leggett-Garg inequalities (LGI) test the correlations of a single system measured at different times. Violation of LGI implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. We investigate the violation of the Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment. We discuss the non-Markovian dynamics of the violation of LGI at zero temperature and also at finite temperature for different structured environments. An enhanced quantum coherence is shown through the violation of Leggett-Garg inequality in the strong non-Markovian regime of the environment.

Canonical versus noncanonical equilibration dynamics of open quantum systems

In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator interacting with a reservoir, we evaluate microscopically the condition under which the equilibration to a canonical state is valid. It is revealed that the non-Markovian effect and the availability of a stationary state of the total system play a profound role in the equilibration. In the Markovian limit, the conventional canonical state can be recovered. In the non-Markovian regime, when the stationary state is absent, the system equilibrates to a generalized canonical state at an effective temperature; whenever the stationary state is present, the equilibrium state of the system cannot be described by any canonical state anymore. Our finding of the physical condition on such noncanonical equilibration might have significant impact on statistical physics. A physical scheme based on circuit QED is proposed to test our results.

Degree of non-Markovianity of quantum evolution

We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals the formal analogy between quantum evolution and the entanglement theory: Markovian evolution corresponds to a separable state and the non-Markovian one is further characterized by its degree. It enables one to introduce a non-Markovianity witness-an analog of an entanglement witness, and a family of measures-an analog of Schmidt coefficients, and finally to characterize maximally non-Markovian evolution being an analog of the maximally entangled state. Our approach allows us to classify the non-Markovianity measures introduced so far in a unified rigorous mathematical framework.

Quantum simulation of decoherence in optical waveguide lattices

We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.

Orthogonality catastrophe and decoherence in a trapped-fermion environment

The Fermi-edge singularity and the Anderson orthogonality catastrophe describe the universal physics which occurs when a Fermi sea is locally quenched by the sudden switching of a scattering potential, leading to a brutal disturbance of its ground state. We demonstrate that the effect can be seen in the controllable domain of ultracold trapped gases by providing an analytic description of the out-of-equilibrium response to an atomic impurity, both at zero and at finite temperature. Furthermore, we link the transient behavior of the gas to the decoherence of the impurity, and to the degree of the non-Markovian nature of its dynamics.

Precision control of charge coherence in parallel double dot systems through spin-orbit interaction

In terms of the exact quantum master equation solution for open electronic systems, the coherent dynamics of two charge states described by two parallel quantum dots with one fully polarized electron on either dot is investigated in the presence of spin-orbit interaction. We demonstrate that the double dot system can stay in a dynamically decoherence free space. The coherence between two double dot charge states can be precisely manipulated through a spin-orbit coupling. The effects of the temperature, the finite bandwidth of lead, and the energy deviations during the coherence manipulation are also explored.