non-Markovian Reservoir Research Articles

Enhancing sideband cooling by initial photon-phonon correlation

We propose an optimized sideband cooling protocol for an optomechanical system coupled to a mechanical non-Markovian reservoir, considering the presence of initial system correlations. By incorporating the effect of initial correlations in the Heisenberg equations, we derive a more stringent dependence on the initial conditions and time-dependent evolution of the phonon numbers. Our findings demonstrate that considering the initial correlations can significantly reduce the number of phonons during the cooling process. Moreover, by adjusting the strength and phase of the initial correlation, the ground-state cooling process can be accelerated. We observe a characterization of this cooling optimization process that resembles the phenomenon of entanglement death and revival. This work provides a promising platform for effectively manipulating phonons and facilitating quantum information processing in optomechanical systems.

Magic behaviors in non-Markovian environment

Magic as an essential resource in fault-tolerant quantum computation may shed insight into quantum information processing of open quantum system. In this work, we study the dynamics of magic for atom system immersed in non-Markovian reservoir. It is found that magic decay process can be delayed and adjusted by the strength of classical driving field and non-Markovian memory effect. In addition, it is shown that the magic state is less susceptible to decay the process of system-environment coupling than stabilizer state, and for two atoms coupling to two independent reservoirs, magic can be generated. The results may be beneficial for theory and experiment of quantum computation and information in open quantum system.

Preservation and enhancement of quantum correlations under Stark effect

We analyse the dynamics of quantum correlations by obtaining the exact expression of Bures distance entanglement, trace distance discord, and local quantum uncertainty of two two-level atoms. Here, the atoms undergo two-photon transitions mediated through an intermediate virtual state where each atom is separately coupled to a dissipative reservoir at zero temperature in the presence of the Stark shift effect. We have investigated the dynamics of this atomic system for two different initial conditions of the environment. In the first case, we have assumed the environment's state to be in ground state and in the other case, we have assumed the state to be in the first excited state. The second initial condition is significant as it shows the role played by both the Stark shift parameters in contrast to only one of the Stark shift parameters for the first initial condition. Our results demonstrate that quantum correlations can be sustained for an extended period in the presence of Stark shift effect in the case of both Markovian and non-Markovian reservoirs. The effect in the non-Markovian reservoir is more prominent than the Markovian reservoir, even for a very small value of the Stark shift parameter. We observe that among the correlation measures considered, only local quantum uncertainty is accompanied by a sudden change phenomenon, i.e. an abrupt change in the decay rate of a correlation measure. Our findings are significant as preserving quantum correlations is one of the essential aspects in attaining optimum performance in quantum information tasks.

Quantum-memory-assisted entropic uncertainty and quantum correlation in structured reservoir

In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relation (EUR) and quantum correlation quantified by entropic discord and geometric discord within the Markovian reservoir and non-Markovian reservoir. Particularly, when the initial state is a pure sate or mixed state the EUR gradually increases during the evolution at first, but subsequently tends to stable in the long-time limit. On other hand, for the separable state the EUR almost keeps constant. In contrast, quantum discord decay asymptotically to zero for all types of initial states. As an application, we prove that both two quantum discords witnessed by the EUR are determined by the version of discord chosen, which regardless of the reservoir.

Quantum Correlation Dynamics of Three Qubits in Non-Markovian Environments

We investigate the quantum correlation dynamics of three independent qubits each locally interacting with a zero temperature non-Markovian reservoir by using the Geometric measure of quantum discord (GQD). The dependence of quantum correlation dynamicson amount of non-Markovian, the degree of initial quantum correlation and purity of the initial states are studied in detail. It is found that the quantum correlation of such three qubits system revives after instantaneous disappearance period when a proper amount of non-Markovian is present. A comparison to the pairwise quantum discord and entanglement dynamics in three qubits system is also made.

Quantum batteries in non-Markovian reservoirs.

In this Letter, we propose schemes to improve the performance of quantum batteries and provide a new, to the best of our knowledge, quantum source for a quantum battery without an external driving field. We show that the memory effect of the non-Markovian reservoir can play a significant role in improving the performance of quantum batteries, which originates from a backflow on the ergotropy in the non-Markovian regime, while there is no counterpart in Markovian approximation. We find that the peak for the maximum average storing power in the non-Markovian regime can be enhanced by manipulating the coupling strength between the charger and the battery. Finally, we find that the battery can also be charged by non-rotating wave terms without driving fields.

Dynamical heat engines with non-Markovian reservoirs

We discuss whether, and under which conditions, it is possible to realize a heat engine simply by dynamically modulating the couplings between the quantum working medium and thermal reservoirs. For that purpose, we consider the paradigmatic model of a quantum harmonic oscillator, exposed to a minimal modulation, that is, a monochromatic driving of the coupling to only one of the thermal baths. We demonstrate, at any order in the system/bath coupling strength, that in this setup non--Markovianity of the bath is a necessary condition to obtain a heat engine. In addition, we identify suitable structured environments for the engine to approach the ideal Carnot efficiency. Our results open up new possibilities for the use of non--Markovian open quantum systems for the construction and optimization of quantum thermal machines.

Nonlocal quantum correlations in a bipartite quantum system coupled to a bosonic non-Markovian reservoir

In this paper, we explore the dynamics of nonlocal correlations in a two-qubit system, that is, first prepared in a Gisin state and then interacts with a bosonic non-Markovian environment. We employ uncertainty-induced nonlocality (UIN) and the Horodecki measure (Bell function) to characterize the degree of nonclassical correlations and quantum nonlocality in the system, taking into account the influence of the non-Markovian reservoir. The dynamics of the UIN and the Bell nonlocality are next examined using the various parameters that define the non-Markovian reservoir and the initial Gisin state. Our results show that the amount of nonlocal correlations and the degree of violation of Bell’s inequality can be modulated by varying the physical parameters characterizing the non-Markovian reservoir and the initial Gisin state. We also show that in some specific cases, the system exhibits nonclassical correlations while the evolved Gisin state does not violate Bell’s inequality. Our results also confirm that UIN is robust than Bell’s nonlocality in the presence of decoherence induced by the interaction with the non-Markovian reservoir.

Switching of the information backflow between a helical spin system and non-Markovian bath

The dissipative dynamics of the spin chain coupled to the non-Markovian magnonic reservoir was studied. The chirality of the chain is formed due to the magnetoelectric coupling. We explored the sign of the trace distance derivative and found the alternating positive/negative periods in system’s time evolution. The negative sign is associated with the flow of information from the system to the bath and decrease in states distinguishability, while the positive sign is related to the flow of the information in the opposite direction and increase in distinguishability. We found the distinct effect of the applied electric and magnetic fields. While the Dzyaloshinskii–Moriya interaction and external electric field lead to reshuffling of the periods, the applied magnetic field leads to the swift positive–negative transitions. Thus, in the helical quantum rings coupled to the non-Markovian magnonic baths, it is possible to control the directions of information flow through the external fields.

Arbitrary-length XX spin chains boundary-driven by non-Markovian environments

In this work we provide a recursive method of calculating the wave function of an $XX$ spin chain coupled at both ends to non-Markovian reservoirs with arbitrary spectral density. The method is based on the appropriate handling of the time-dependent Schr\"odinger's equations of motion in Laplace space and leads to closed-form solutions of the transformed amplitudes for arbitrary chain lengths as well as arbitrary initial conditions within the single-excitation subspace. Results on the dynamical as well as state-transfer properties of the system for various combinations of parameters are also presented. In particular, detailed quantitative comparisons for Lorentzian and Ohmic reservoirs are illustrated.

Entanglement instability in the interaction of two qubits with a common non-Markovian environment

In this work we study the steady state entanglement between two qubits interacting asymetrically with a common non-Markovian environment. Depending on the initial two-qubit state, the asymmetry in the couplings between each qubit and the non-Markovian environment may lead to enhanced entanglement in the steady state of the system, measured in terms of the two-qubit concurrence. Our results indicate that, if a qubit-qubit interaction is also present, the two-qubit steady state concurrence is always favored by the symmetric or anti-symmetric coupling configuration. Although finite, the steady concurrence is predicted to be highly unstable in this regime as long as the interaction between the two qubits is larger than the couplings between each qubit and the non-Markovian reservoir.

Remote weak-signal measurement via bound states in optomechanical systems

A scheme for remote weak-signal sensors is proposed, in which a coupled-resonator optical waveguide (CROW), as a transmitter, couples to a hybrid optomechanical cavity and an observing cavity at its two ends. Non-Markovian theory is employed to study the weak-force sensor by treating the CROW as a non-Markovian reservoir of cavity fields. The dissipationless bound states in the non-Markovian regime are conducive to remotely transmitting a signal in the CROW. Our results show that a sensor with ultrahigh sensitivity can be achieved with the assistance of bound states under certain parameter regimes.

Freezing and revival of quantum coherence in decoherent reservoir

Quantum coherence (QC) as a crucial physical resource plays the vital role in recent researches of quantum information science, whereas the QC within an open system unavoidably deteriorates due to the system–environment interacting. In this paper, we analyze the dynamics of QC when the initial state is exposed to Markovian and non-Markovian reservoirs, respectively. We analytically derive the dynamical conditions under which the QC is frozen in the Markovian reservoir and explore the underlying physical mechanisms by investigating the trade-off relation between QC and mixedness of system. In the non-Markovian reservoir, we demonstrate the damped revivals of QC and show that these revivals can be effectively enhanced by increasing the memory degree of reservoir. These findings might provide an insightful physical interpretation for the dynamical phenomena of QC exhibiting in complex 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.

Multiple-scale perturbation method on integro-differential equations: Application to continuous-time quantum walks on regular networks in non-Markovian reservoirs

Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics schemes, especially the continuous-time quantum walk. Difficulty exists, however, in producing closed-form solutions with controllable accuracy against the complexity of memory kernels. Here, we introduce a new multiple-scale perturbation method that works on integro-differential equations for general study of memory effects in dynamical systems. We propose an open-system model in which a continuous-time quantum walk is enclosed in a non-Markovian reservoir, that naturally corresponds to an error correction algorithm scheme. By applying the multiple-scale method we show how emergence of different time scales is related to transition of system dynamics into the non-Markovian regime. We find that up to two long-term modes and two short-term modes exist in regular networks, limited by their intrinsic symmetries. In addition to the effective approximation by our perturbation method on general forms of reservoirs, the speed-up of quantum walks assisted by non-Markovianity is also confirmed, revealing the advantage of reservoir engineering in designing time-sensitive quantum algorithms.

Entanglement Protection of Two‐Qubit System in Non‐Markovian Reservoir via Weak Measurement and Weak Measurement Reversal

The protection schemes of the entanglement in the system of two entangled atoms from nonMarkovian reservoirs via previous Weak measurement (pre-WM) and posterior Weak measurement reversal (post-WMR) are investigated. We firstly compare the effects of combination applying of pre-WM and post-WMR (scheme 1) and twice Weak measurements (WMs) (scheme 2) in the condition of different initial entangled states. The analysis indicates that the protection performance of scheme 1 is much better than that of scheme 2. The scheme 1 was utilized when the system of two entangled atoms suffers from the independent reservoirs. The numerical results show that the combination of pre-WM and post-WMR can effectively enhance entanglement and shorten the time of Entanglement sudden death (ESD) in non-Makovain environment. We have found the optimum of WM strengthens is drastically related to the initial entangled state.

Dynamics of two levitated nanospheres nonlinearly coupling with non-Markovian environment**Project supported by the National Natural Science Foundation of China (Grant Nos. 11874099, 11605022, 11775040, 11747317, and 11474044).

The dynamics of two nanospheres nonlinearly coupling with non-Markovian reservoir is investigated. A master equation of the two nanospheres is derived by employing quantum state diffusion method. It is shown that the nonlinear coupling can improve the non-Markovianity. Due to the sharing of the common non-Markovian environment, the state transfer between the two nanospheres can be realized. The entanglement and the squeezing of the individual mode, as well as the jointed two-mode are analyzed. The present system can be realized by trapping two nanospheres in a wideband cavity, which might provide a method to study adjustable non-Markovian dynamics of mechanical motion.

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.

Path-integral approach for nonequilibrium multitime correlation functions of open quantum systems coupled to Markovian and non-Markovian environments

Using a real-time path integral approach we develop an algorithm to calculate multi-time correlation functions of open few-level quantum systems that is applicable to highly nonequilibrium dynamics. The calculational scheme fully keeps the non-Markovian memory introduced by the pure-dephasing type coupling to a continuum of oscillators. Furthermore, we discuss how to deal consistently with the simultaneous presence of non-Markovian and Markovian system reservoir interactions. We apply the method to a crucial test case, namely the evaluation of emission spectra of a laser-driven two-level quantum dot coupled to a continuum of longitudinal acoustic phonons, which give rise to non-Markovian dynamics. Here, we also account for the coupling to a photonic environment, which models radiative decay and can be treated as a Markovian bath. The phonon side bands are found on the correct side of the zero phonon line in our calculation, in contrast to known results where the quantum regression theorem is applied naively to non-Markovian dynamics. Combining our algorithm with a recently improved iteration scheme for performing the required sum over paths we demonstrate the numerical feasibility of our approach to systems with more than two levels. Results are shown for the second-order photonic two-time correlation function of a quantum dot-cavity system with seven states on the Jaynes-Cummings ladder taken into account.

Floquet stroboscopic divisibility in non-Markovian dynamics

We provide a general description of a time-local master equation for a system coupled to a non-Markovian reservoir based on Floquet theory. This allows us to have a divisible dynamical map at discrete times, which we refer to as Floquet stroboscopic divisibility. We illustrate the theory by considering a harmonic oscillator coupled to both non-Markovian and Markovian baths. Our findings provide us with a theory for the exact calculation of spectral properties of time-local non-Markovian Liouvillian operators, and might shed light on the nature and existence of the steady state in non-Markovian dynamics.