System-environment Interaction Research Articles

System-environment correlations and Markovian embedding of quantum non-Markovian dynamics

We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e. the open dynamics is modelled through sequences of unitary interactions between the system and the individual constituents of the environment, termed "ancillas", which are subsequently traced out. In this setting non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of "memory depth" where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a non-monotonic time behaviour of the heat flux serves as an indicator of non-Markovian behaviour.

How Biochemical Environments Fine-Tune a Redox Process: From Theoretical Models to Practical Applications.

In this study, we give a new physical insight into how enzymatic environments influence a redox process. This is particularly important in a biochemical context, in which oxidoreductase enzymes and low-molecular-weight cofactors create a microenvironment, fine-tuning their specific redox potential. We present a new theoretical model, quantitatively backed up by quantum chemically calculated data obtained for key biological sulfur-based model reactions involved in preserving the cellular redox homeostasis during oxidative stress. We show that environmental effects can be quantitatively predicted from the thermodynamic cycle linking ΔΔ G(OX/RED)ref-ligand values to the differential interaction energy ΔΔ Gint of the reduced and oxidized species with the environment. Our obtained data can be linked to hydrogen-bond patterns found in protein active sites. The thermodynamic model is further understood in the framework of molecular orbital theory. The key insight of this work is that the intrinsic properties of neither a redox couple nor the interacting environment (e.g., ligand) are enough by themselves to uniquely predict reduction potentials. Instead, system-environment interactions need to be considered. This study is of general interest as redox processes are pivotal to empower, protect, or damage organisms. Our presented thermodynamic model allows a pragmatically evaluation on the expected influence of a particular environment on a redox process, necessary to fully understand how redox processes take place in living organisms.

Generation of Human-Like Movement from Symbolized Information.

An important function missing from current robotic systems is a human-like method for creating behavior from symbolized information. This function could be used to assess the extent to which robotic behavior is human-like because it distinguishes human motion from that of human-made machines created using currently available techniques. The purpose of this research is to clarify the mechanisms that generate automatic motor commands to achieve symbolized behavior. We design a controller with a learning method called tacit learning, which considers system–environment interactions, and a transfer method called mechanical resonance mode, which transfers the control signals into a mechanical resonance mode space (MRM-space). We conduct simulations and experiments that involve standing balance control against disturbances with a two-degree-of-freedom inverted pendulum and bipedal walking control with humanoid robots. In the simulations and experiments on standing balance control, the pendulum can become upright after a disturbance by adjusting a few signals in MRM-space with tacit learning. In the simulations and experiments on bipedal walking control, the robots realize a wide variety of walking by manually adjusting a few signals in MRM-space. The results show that transferring the signals to an appropriate control space is the key process for reducing the complexity of the signals from the environment and achieving diverse behavior.

Adding dynamical generators in quantum master equations

The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact and versatile description. However, care needs to be taken when several noise processes act simultaneously or the Hamiltonian evolution of the system is modified. Here, we show that generators can be added at the master equation level without compromising physicality only under restrictive conditions. Moreover, even when adding generators results in legitimate dynamics, this does not generally correspond to the true evolution of the system. We establish a general condition under which direct addition of dynamical generators is justified, showing that it is ensured under weak coupling and for settings where the free system Hamiltonian and all system-environment interactions commute. In all other cases, we demonstrate by counterexamples that the exact evolution derived microscopically cannot be guaranteed to coincide with the dynamics naively obtained by adding the generators.

Non-Markovianity in the collision model with environmental block

We present an extended collision model to simulate the dynamics of an open quantum system. In our model, the unit to represent the environment is, instead of a single particle, a block which consists of a number of environment particles. The introduced blocks enable us to study the effects of different strategies of system–environment interactions and states of the blocks on the non-Markovianities. We demonstrate our idea in the Gaussian channels of an all-optical system and derive a necessary and sufficient condition of non-Markovianity for such channels. Moreover, we show the equivalence of our criterion to the non-Markovian quantum jump in the simulation of the pure damping process of a single-mode field. We also show that the non-Markovianity of the channel working in the strategy that the system collides with environmental particles in each block in a certain order will be affected by the size of the block and the embedded entanglement and the effects of heating and squeezing the vacuum environmental state will quantitatively enhance the non-Markovianity.

Dynamics of tripartite quantum correlations and decoherence in flux qubit systems under local and non-local static noise

We investigate the dynamics of entanglement, decoherence and quantum discord in a system of three non-interacting superconducting flux qubits (fqubits) initially prepared in a Greenberger–Horne–Zeilinger (GHZ) state and subject to static noise in different, bipartite and common environments, since it is recognized that different noise configurations generally lead to completely different dynamical behavior of physical systems. The noise is modeled by randomizing the single fqubit transition amplitude. Decoherence and quantum correlations dynamics are strongly affected by the purity of the initial state, type of system–environment interaction and the system–environment coupling strength. Specifically, quantum correlations can persist when the fqubits are commonly coupled to a noise source, and reaches a saturation value respective to the purity of the initial state. As the number of decoherence channels increases (bipartite and different environments), decoherence becomes stronger against quantum correlations that decay faster, exhibiting sudden death and revival phenomena. The residual entanglement can be successfully detected by means of suitable entanglement witness, and we derive a necessary condition for entanglement detection related to the tunable and non-degenerated energy levels of fqubits. In accordance with the current literature, our results further suggest the efficiency of fqubits over ordinary ones, as far as the preservation of quantum correlations needed for quantum processing purposes is concerned.

On One Possible Generalization of the Regression Theorem

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.

Leggett-Garg Inequality for a Two-Level System under Decoherence

We consider a macroscopic quantum system subjected to an asymmetric double-well potential in a harmonic environment. By using a time-dependent approach, we calculate tunnelling probabilities for the system which contain oscillation effects. To show how one can decide between quantum mechanics and the implications of macrorealism assumptions, a given form of Leggett-Garg inequality is considered. The violation of this inequality occurs for a broader range of the system-environment interactions, compared to previous results obtained for two-level systems. Assuming that the coupling strength between the system and the environment can be controlled with time, one can see the violation even for strong decoherence effects. We also investigate the variation of the tilt/tunnelling parameters on the violation of Leggett-Garg inequality.

Ultra-fast relaxation, decoherence, and localization of photoexcited states in π-conjugated polymers.

The exciton relaxation dynamics of photoexcited electronic states in poly(p-phenylenevinylene) are theoretically investigated within a coarse-grained model, in which both the exciton and nuclear degrees of freedom are treated quantum mechanically. The Frenkel-Holstein Hamiltonian is used to describe the strong exciton-phonon coupling present in the system, while external damping of the internal nuclear degrees of freedom is accounted for by a Lindblad master equation. Numerically, the dynamics are computed using the time evolving block decimation and quantum jump trajectory techniques. The values of the model parameters physically relevant to polymer systems naturally lead to a separation of time scales, with the ultra-fast dynamics corresponding to energy transfer from the exciton to the internal phonon modes (i.e., the C-C bond oscillations), while the longer time dynamics correspond to damping of these phonon modes by the external dissipation. Associated with these time scales, we investigate the following processes that are indicative of the system relaxing onto the emissive chromophores of the polymer: (1) Exciton-polaron formation occurs on an ultra-fast time scale, with the associated exciton-phonon correlations present within half a vibrational time period of the C-C bond oscillations. (2) Exciton decoherence is driven by the decay in the vibrational overlaps associated with exciton-polaron formation, occurring on the same time scale. (3) Exciton density localization is driven by the external dissipation, arising from "wavefunction collapse" occurring as a result of the system-environment interactions. Finally, we show how fluorescence anisotropy measurements can be used to investigate the exciton decoherence process during the relaxation dynamics.

Engineering thermal reservoirs for ultracold dipole–dipole-interacting Rydberg atoms

We consider an open quantum system of ultracold Rydberg atoms. The system part consists of resonant dipole–dipole-interacting Rydberg states. The environment part is formed by ‘three-level atoms’: each atom has a ground state, a short-lived excited state, and a Rydberg state that interacts with the system states. The two transitions in the environment atoms are optically driven, and provide control over the environment dynamics. Appropriate choice of the laser parameters allows us to prepare a Boltzmann distribution of the system’s eigenstates. By tuning the laser parameters and system-environment interaction, we can change the temperature associated with this Boltzmann distribution, and also the thermalization dynamics. Our method provides novel opportunities for quantum simulation of thermalization dynamics using ultracold Rydberg atoms.

New construction of quantum error-avoiding codes via group representation of quantum stabilizer codes

In quantum computing, nice error bases as generalization of the Pauli basis were introduced by Knill. These bases are known to be projective representations of finite groups. In this paper, we propose a group representation approach to the study of quantum stabilizer codes. We utilize this approach to define decoherence-free subspaces (DFSs). Unlike previous studies of DFSs, this type of DFSs does not involve any spatial symmetry assumptions on the system-environment interaction. Thus, it can be used to construct quantum error-avoiding codes (QEACs) that are fault tolerant automatically. We also propose a new simple construction of QEACs and subsequently develop several classes of QEACs. Finally, we present numerical simulation results encoding the logical error rate over physical error rate on the fidelity performance of these QEACs. Our study demonstrates that DFSs-based QEACs are capable of providing a generalized and unified framework for error-avoiding methods.

Implementation and Application of the Frozen Density Embedding Theory with the Algebraic Diagrammatic Construction Scheme for the Polarization Propagator up to Third Order.

Implementation, benchmarking, and representative applications of the new FDE-ADC(3) method for describing environmental effects on excited states as a combination of frozen density embedding (FDE) and the algebraic-diagrammatic construction scheme for the polarization propagator of third order (ADC(3)) are presented. Results of FDE-ADC(3) calculations are validated with respect to supersystem calculations on test systems with varying molecule-environment interaction strengths from dispersion up to multiple hydrogen bonds. The overall deviation compared to the supersystem calculations is as small as 0.029 eV for excitation energies, which is even smaller than the intrinsic error of ADC(3). The dependence of the accuracy on the choice of method and functional for the calculation of the environment and the nonelectrostatic part of the system-environment interaction is evaluated. In three representative examples, the FDE-ADC method is applied to investigate larger systems and to analyze excited state properties using visualization of embedded densities and orbitals.

Dark state with counter-rotating dissipative channels

Dark state as a consequence of interference between different quantum states has great importance in the fields of chip-scale atomic clock and quantum information. For the Λ-type three-level system, this dark state is generally regarded as being dissipation-free because it is a superposition of two lowest states without dipole transition between them. However, previous studies are based on the rotating-wave approximation (RWA) by neglecting the counter-rotating terms in the system-environment interaction. In this work, we study non-Markovian quantum dynamics of the dark state in a Λ-type three-level system coupled to two bosonic baths and reveal the effect of counter-rotating terms on the dark state. In contrast to the dark state within the RWA, leakage of the dark state occurs even at zero temperature, as a result of these counter-rotating terms. Also, we present a method to restore the quantum coherence of the dark state by applying a leakage elimination operator to the system.

Quantum Zeno Effects from Measurement Controlled Qubit-Bath Interactions.

The Zeno and anti-Zeno effects are features of measurement-driven quantum evolution where frequent measurement inhibits or accelerates the decay of a quantum state. Either type of evolution can emerge depending on the system-environment interaction and measurement method. In this experiment, we use a superconducting qubit to map out both types of Zeno effect in the presence of structured noise baths and variable measurement rates. We observe both the suppression and acceleration of qubit decay as repeated measurements are used to modulate the qubit spectrum causing the qubit to sample different portions of the bath. We compare the Zeno effects arising from dispersive energy measurements and purely dephasing "quasimeasurements," showing energy measurements are not necessary to accelerate or suppress the decay process.

Evolutionary Developmental Robotics: Improving Morphology and Control of Physical Robots.

Evolutionary algorithms have previously been applied to the design of morphology and control of robots. The design space for such tasks can be very complex, which can prevent evolution from efficiently discovering fit solutions. In this article we introduce an evolutionary-developmental (evo-devo) experiment with real-world robots. It allows robots to grow their leg size to simulate ontogenetic morphological changes, and this is the first time that such an experiment has been performed in the physical world. To test diverse robot morphologies, robot legs of variable shapes were generated during the evolutionary process and autonomously built using additive fabrication. We present two cases with evo-devo experiments and one with evolution, and we hypothesize that the addition of a developmental stage can be used within robotics to improve performance. Moreover, our results show that a nonlinear system-environment interaction exists, which explains the nontrivial locomotion patterns observed. In the future, robots will be present in our daily lives, and this work introduces for the first time physical robots that evolve and grow while interacting with the environment.

Effects of static noise on the dynamics of quantum correlations for a system of three qubits

Correlations in open quantum systems exhibit peculiar phenomena under the effect of various sources of noise. Here, we investigate the dynamics of entanglement and quantum discord (QD) for three noninteracting qubits coupled with a classical environmental static noise characterized by an external random field. Two initial entangled states of the system are examined, namely, the GHZ- and [Formula: see text]-type states. The system-environment interaction is here analyzed in three different configurations, namely, independent, mixed and common environments. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the purity of the initial entangled state. Indeed, depending on the type of interaction and the value of the purity of the initial state, peculiar phenomena such as sudden death, revivals and long-time survival of quantum correlations are observed. On the other hand, our results clearly show that quantum correlations initially present in the [Formula: see text]-type states are less robust than those of the GHZ-type states. Furthermore, we find that the long-time survival of entanglement can be detected by means of the suitable entanglement witnesses.

Tuning quantum measurements to control chaos

Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.

Dynamical decoupling and homogenization of continuous variable systems

For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.

Hierarchical equations of motion method applied to nonequilibrium heat transport in model molecular junctions: Transient heat current and high-order moments of the current operator

We present a theoretical approach to study nonequilibrium quantum heat transport in molecular junctions described by a spin-boson type model. Based on the Feynman-Vernon path integral influence functional formalism, expressions for the average value and high-order moments of the heat current operators are derived, which are further obtained directly from the auxiliary density operators (ADOs) in the hierarchical equations of motion (HEOM) method. Distribution of the heat current is then derived from the high-order moments. As the HEOM method is nonperturbative and capable of treating non-Markovian system-environment interactions, the method can be applied to various problems of nonequilibrium quantum heat transport beyond the weak coupling regime.

Dynamics of tripartite quantum entanglement and discord under a classical dephasing random telegraph noise

We address the dynamics of quantum correlations, including entanglement and quantum discord of a three-qubit system interacting with a classical pure dephasing random telegraph noise (RTN) in three different physical environmental situations (independent, mixed and common environments). Two initial entangled states of the system are examined, namely the Greenberger-Horne-Zeilinger (GHZ)- and Werner (W)-type states. The classical noise is introduced as a stochastic process affecting the energy splitting of the qubits. With the help of suitable measures of tripartite entanglement (entanglement witnesses and lower bound of concurrence) and quantum discord (global quantum discord and quantum dissension), we show that the evolution of quantum correlations is not only affected by the type of the system-environment interaction but also by the input configuration of the qubits and the memory properties of the environmental noise. Indeed, depending on the memory properties of the environmental noise and the initial state considered, we find that independent, common and mixed environments can play opposite roles in preserving quantum correlations, and that the sudden death and revival phenomena or the survival of quantum correlations may occur. On the other hand, we also show that the W-type state has strong dynamics under this noise than the GHZ-type ones.