non-Markovian Open Quantum Systems Research Articles

Memory effects and quantum speedup for a quantum emitter near a molybdenum disulfide nanodisk

We study memory effects (non-Markovian evolution) in the spontaneous emission dynamics of a quantum emitter near a molybdenum disulfide nanodisk by going beyond the analysis of the reversible population dynamics of the excited state and considering the dynamics of the non-Markovian open system. Specifically, we quantify the non-Markovian spontaneous emission dynamics using different non-Markovianity measures and also investigate the potential quantum speed up of the dynamics in relation to its non-Markovian features. We find that the values of the non-Markovianity measures and of the potential quantum speed up are large under strong coupling conditions, while in both cases the non-Markovianity measures and the quantum speed up decreases as the coupling between the emitter and the nanodisk becomes weaker. A comparison of the different non-Markovianity measures is also presented for the system under study. • Memory effects in the photon emission of a quantum emitter next to a MoS 2 nanodisk are analyzed. • The system is treated as a non-Markovian open quantum system . • For obtaining the results, we use a combination of quantum dynamics calculations with electromagnetic calculations. • Results for different non-Markovianity measures are presented. • The quantum speed limit of the quantum emitter next to the MoS 2 nanodisk is also calculated.

Frame-Based Filter-Function Formalism for Quantum Characterization and Control

We introduce a theoretical framework for resource-efficient characterization and control of non-Markovian open quantum systems, which naturally allows for the integration of given, experimentally motivated, control capabilities and constraints. This is achieved by developing a transfer filter-function formalism based on the general notion of a frame and by appropriately tying the choice of frame to the available control. While recovering the standard frequency-based filter-function formalism as a special instance, this control-adapted generalization affords intrinsic flexibility and, crucially, it permits an efficient representation of the relevant control matrix elements and dynamical integrals if an appropriate finite-size frame condition is obeyed. Our frame-based formulation overcomes important limitations of existing approaches. In particular, we show how to implement quantum noise spectroscopy in the presence of nonstationary noise sources, and how to effectively achieve control-driven model reduction for noise-optimized prediction and quantum gate design.

Erratum: Subspace stabilization analysis for a class of non-Markovian open quantum systems [Phys. Rev. A 101 , 042327 (2020)

Erratum: Subspace stabilization analysis for a class of non-Markovian open quantum systems [Phys. Rev. A <b>101</b> , 042327 (2020)

Quantum Heat Statistics with Time-Evolving Matrix Product Operators

We present a numerically exact method to compute the full counting statistics of heat transfer in non-Markovian open quantum systems, which is based on the time-evolving matrix product operator (TEMPO) algorithm. This approach is applied to the paradigmatic spin-boson model in order to calculate the mean and fluctuations of the heat transferred to the environment during thermal equilibration. We show that system-reservoir correlations make a significant contribution to the heat statistics at low temperature and present a variational theory that quantitatively explains our numerical results. We also demonstrate a fluctuation-dissipation relation connecting the mean and variance of the heat distribution at high temperature. Our results reveal that system-bath interactions make a significant contribution to heat transfer even when the dynamics of the open system is effectively Markovian. The method presented here provides a flexible and general tool to predict the fluctuations of heat transfer in open quantum systems in non-perturbative regimes.

Stochastic Schr\xf6dinger equation derivation of non-Markovian two-time correlation functions

We derive the evolution equations for two-time correlation functions of a generalized non-Markovian open quantum system based on a modified stochastic Schrödinger equation approach. We find that the two-time reduced propagator, an object that used to be characterized by two independent stochastic processes in the Hilbert space of the system, can be simplified and obtained by taking ensemble average over one single noise. This discovery can save the cost of computation, and accelerate the converging process when taking the average over noisy trajectories. As a result, our method can be widely applied to many open quantum models, especially large-scale systems and extend the quantum regression theory to the non-Markovian case. In the short-time simulations, it is observed a significant difference between Markovian and non-Markovian cases, which can be applied to realize the environmental spectrum detection and enhance the measurement sensitivity in varying open quantum systems.

Efficient Exploration of Hamiltonian Parameter Space for Optimal Control of Non-Markovian Open Quantum Systems.

We present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems, and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in a specific state. The optimization of control procedures for quantum systems with strong coupling to structured environments-where time-local descriptions fail-is a computationally challenging task. Wemodify the numerically exact time evolving matrix product operator (TEMPO) method, such that it allows the repeated computation of the time evolution of the reduced system density matrix for various sets of control parameters at very low computational cost. This method is potentially useful for studying numerous optimal control problems, in particular in solid state quantum devices where the coupling to vibrational modes is typically strong.

Hidden non-Markovianity in open quantum systems

We show that non-Markovian open quantum systems can exhibit exact Markovian dynamics up to an arbitrarily long time; the non-Markovianity of such systems is thus perfectly "hidden", i.e. not experimentally detectable by looking at the reduced dynamics alone. This shows that non-Markovianity is physically undecidable and extremely counterintuitive, since its features can change at any time, without precursors. Some interesting examples are discussed.

Experimental realization of high-fidelity teleportation via a non-Markovian open quantum system

Open quantum systems and study of decoherence are important for our fundamental understanding of quantum physical phenomena. For practical purposes, there exists a large number of quantum protocols exploiting quantum resources, e.g. entanglement, which allows to go beyond what is possible to achieve by classical means. We combine concepts from open quantum systems and quantum information science, and give a proof-of-principle experimental demonstration -- with teleportation -- that it is possible to implement efficiently a quantum protocol via non-Markovian open system. The results show that, at the time of implementation of the protocol, it is not necessary to have the quantum resource in the degree of freedom used for the basic protocol -- as long as there exists some other degree of freedom, or environment of an open system, which contains useful resources. The experiment is based on a pair of photons, where their polarizations act as open system qubits and frequencies as their environments -- while the path degree of freedom of one of the photons represents the state of Alice's qubit to be teleported to Bob's polarization qubit.

Controllable non-Markovianity in phase relaxation

Recently remarkable progress in quantum technology has been witnessed. In view of this it is important to investigate an open quantum system as a model of such quantum devices. Quantum devices often require extreme conditions for the devices to operate: dynamics can be non-Markovian here. This observation necessitates us to investigate a non-Markovian open quantum system, both theoretically and experimentally. In this paper, we report two important results: (1) exact solution of a simple but non-trivial theoretical model and (2) demonstration of this model by NMR experiments, where non-Markovianity is continuously controllable. We observe qualitative agreement between theory and experiment.

Subspace stabilization analysis for a class of non-Markovian open quantum systems

Studied in this article is non-Markovian open quantum systems parametrized by Hamiltonian H, coupling operator L, and memory kernel function {\gamma}, which is a proper candidate for describing the dynamics of various solid-state quantum information processing devices. We look into the subspace stabilization problem of the system from the perspective of dynamical systems and control. The problem translates itself into finding analytic conditions that characterize invariant and attractive subspaces. Necessary and sufficient conditions are found for subspace invariance based on algebraic computations, and sufficient conditions are derived for subspace attractivity by applying a double integral Lyapunov functional. Mathematical proof is given for those conditions and a numerical example is provided to illustrate the theoretical result.

Correlation measure detecting almost all non-Markovian evolutions

We investigate the ability of correlation measures to witness non-Markovian open quantum system dynamics. It is shown that the mutual information and any entanglement measure between the system and an ancilla do not witness all non-Markovian dynamics. A correlation measure is introduced, and it is proven that, in an enlarged setting with two ancillary systems, this measure detects almost all non-Markovian dynamics, except possibly a zero-measure set of dynamics that is non-bijective in finite time-intervals. Our proof is constructive and provides different initial states detecting the non-Markovian evolutions. These states are all separable and some are arbitrarily close to a product state.

Quantum correlations in non-Markovian open quantum systems at different ranges of temperature

In this paper, we numerically explore the quantum correlations in a system consisting of two identical qubits, each of them locally interacting with a bosonic reservoir under non-Markovian regime, dissipative quantum system. The influences of Ohmic reservoir with Lorentz–Drude regularization on the quantum discord and entanglement are studied. We analyze the quantum correlations rate in high temperature, intermediate temperature, and low temperature reservoirs, respectively. The dependence of the quantum correlations on the ratio r of the reservoir cutoff frequency and the system oscillator frequency, and temperature kBT shows that the decreasing of the frequency ratio r enhances the amount of quantum correlations between the two qubits, while the increasing of the temperature damages the amount of correlations. More precisely, we find a sudden death of quantum entanglement, that is, the entanglement vanishes as time becomes large for different temperatures. On the other hand, we show in contrast to what happens to entanglement, the quantum discord does not vanish even at high temperatures.

Emergent phases and critical behavior in a non-Markovian open quantum system

Open quantum systems exhibit a range of novel out-of-equilibrium behavior due to the interplay between coherent quantum dynamics and dissipation. Of particular interest in these systems are driven, dissipative transitions, the emergence of dynamical phases with novel broken symmetries, and critical behavior that lies beyond the conventional paradigms of Landau-Ginzburg phenomenology. Here, we consider a parametrically driven two-mode system in the presence of non-Markovian system-reservoir interactions. We show that non-Markovianity modifies the phase diagram of this system resulting in the emergence of a novel broken symmetry phase in a new universality class that has no counterpart in a Markovian or equilibrium system. Such reservoir-engineered dynamical phases can potentially shed light on universal aspects of dynamical phase transitions in a wide range of non-equilibrium systems, and aid in the development of techniques for the robust generation of entanglement and quantum correlations at finite temperatures with potential applications to quantum metrology.

Pseudothermalization in driven-dissipative non-Markovian open quantum systems

We investigate a `pseudo thermalization' effect, where an open quantum system coupled to several non-Markovian reservoirs presents an emergent thermal behaviour in spite of its coupling to a non-equilibrated environment. The thermal behaviour is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a microscopical quantum optics model. For generic non-Markovian reservoirs, we demonstrate that the emergence of thermal properties occurs in the range of frequencies corresponding to low-energy excitations. For the specific case of non-Markovian baths verifying the Kennard-Stepanov relation, we show that pseudo-thermalization can instead occur at all energy scales. The possible implications regarding the interpretation of thermal laws in exciton-polariton low temperature experiments are discussed. We finally show that the presence of either a saturable pumping or a dispersive environment leads to a breakdown of the pseudo-thermalization effect.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Quantum critical probing and simulation of colored quantum noise

We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol the environment spatial correlations are mapped into the time correlations of a noise that drives the dynamics of the open system. Considering the weak coupling limit the open system can also be considered as a probe of the environment properties. In this regard, when preparing the environment in its ground state, a measurement of the dynamics of the open system allows to determine the length of the environment spatial correlations and therefore its critical properties. To illustrate our proposal we simulate the full system dynamics with matrix-product-states and compare this with the reduced dynamics obtained with an approximated variational master equation.

Effect of Time-Delayed Feedback on the Interaction of a Dimer System with its Environment

In this work, we report modeling of non-Markovian open quantum systems, consisting of an excitonic dimer that displays memory effect due to time delayed interaction with its environment. We, indeed investigate the effect of these time delays on quantum coherence and excitation dynamical behavior in the time domain generally considered for photosynthetic experiments (few hundred femtoseconds). In particular, we show that the coherence is maintained for periods proportional to time delays. Additionally, if delay is taken into account, coupling to the environment can be tuned to lower values, unlike in previous studies. This kind of intriguing effect can, therefore, when generalized to complete systems, permit more control on the experimental parameters, which may lead to more accurate description of the photosynthetic energy transfer functioning and subsequent applications in artificial photovoltaic research.

Dynamics of non-Markovian open quantum systems

Open quantum systems (OQSs) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. An overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation. Some of these techniques, such as master equations, Heisenberg equations, and stochastic methods, are based on solving the reduced OQS dynamics, while others, such as path integral Monte Carlo or chain mapping approaches, are based on solving the dynamics of the full system. The physical interpretation and derivation of the various approaches are emphasized, how they are connected is explored, and how different methods may be suitable for solving different problems is examined.

Problem of coherent control in non-Markovian open quantum systems

We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a serious pitfall causing insurmountable difficulties in the effective modelling of the controlled system. We show that the only way to avoid these problems is a full microscopic description of the controlled system in presence of noise. We illustrate our findings with a paradigmatic example.

Digital quantum simulation of many-body non-Markovian dynamics

We present an algorithmic method for the digital quantum simulation of many-body locally indivisible non-Markovian open quantum systems. It consists of two parts: firstly, a Suzuki-Lie-Trotter decomposition of the global system propagator into the product of subsystem propagators, which may not be quantum channels, and secondly, an algorithmic procedure for the implementation of the subsystem propagators through unitary operations and measurements on a dilated space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter decomposition, we are able to analyze the efficiency of the method, and connect it with an appropriate measure of the local indivisibility of the system. In light of our analysis, the proposed method is expected to be experimentally achievable for a variety of interesting cases.