System-environment Coupling Strength Research Articles

The role of initial system–environment correlations with a spin environment

Open quantum systems are a subject of immense interest as their understanding is crucial in the implementation of modern quantum technologies. In the study of their dynamics, the role of the initial system–environment correlations is commonly ignored. In this work, to gain insights into the role of these correlations, we solve an exactly solvable model of a single two-level system interacting with a spin environment, with the initial system state prepared by a suitable unitary operation. By solving the dynamics exactly for arbitrary system–environment coupling strength while taking into account the initial system–environment correlations, we show that the effect of the initial correlations is, in general, very significant and nontrivial. To further highlight the importance of the initial system–environment correlations, we also extend our study to investigate the dynamics of the entanglement between two two-level systems interacting with a common spin environment.

Individual versus simultaneous estimation of two parameters in a correlated noisy environment

Recently, the phase parametric estimation for a single qubit system driven by a phase noisy laser under non-Markovian dynamics has been reported [Annals of Physics 351, 952 (2014)]. We here generalize the single-parameter estimation to the two-parameter scenario where a two-qubit system is influenced by the classical correlated noisy laser, and compare the performances of two-parameter estimation in both individual and simultaneous strategies by using the quantum Fisher information and the quantum Fisher information matrix, respectively. Our results show the phase parametric estimation precision can be significantly improved due to the memory effect arising from successive applications of the noisy laser. With the memory coefficient μ increasing, the precision of parameter estimation becomes more accurate. Besides, the phase parameter estimation precision can be drastically enhanced by engineering the ratios of classical phase diffusion rate and system-environment coupling strength in both Markovian and non-Markovian regions. Remarkably, we find the simultaneous estimation of two-phase parameters is not always advantageous over the individual strategy.

On the practical truncation tier of fermionic hierarchical equations of motion.

The fermionic hierarchical equations of motion (HEOM) approach has found wide application in the exploration of open quantum systems, and extensive efforts have been committed to improving its efficiency and accuracy in practical calculations. In this work, by scrutinizing the stationary-state and dynamic properties of Kondo-correlated quantum impurity systems, we show that the strength of Kondo correlation induced by the system-environment entanglement primarily determines the converged hierarchical truncation tier of the HEOM method. This complements the rule of thumb regarding the positive correlation between the height of hierarchy and system-environment coupling strength. These insights will provide useful guidelines for developing a more sophisticated fermionic HEOM method for the investigation of many-body open quantum systems.

Non-Markovian Quantum Dynamics in a Squeezed Reservoir.

We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system–environment coupling strength and, thus, the strength of the dissipation.

Master equation incorporating the system-environment correlations present in the joint equilibrium state

We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.

Improving the estimation of environment parameters via initial probe-environment correlations

Small, controllable quantum systems, known as quantum probes, have been proposed to estimate various parameters characterizing complex systems such as the environments of quantum systems. These probes, prepared in some initial state, are allowed to interact with their environment, and subsequent measurements reveal information about different quantities characterizing the environment such as the system-environment coupling strength, the cutoff frequency, and the temperature. These estimates have generally been made by considering only the way that the probe undergoes decoherence. However, we show that information about the environment is also imprinted on the probe via the probe and environment correlations that exist before the probe state preparation. This information can then be used to improve our estimates for any environment. We apply this general result to the particular case of a two-level system probe undergoing pure dephasing, due to a harmonic oscillator environment, to show that a drastic increase in the quantum Fisher information, and hence the precision of our estimates, can indeed be obtained. We also consider applying periodic control pulses to the probe to show that with a combination of the two - the effect of the control pulses as well as the initial correlations - the quantum Fisher information can be increased by orders of magnitude.

Dynamics of local quantum uncertainty and local quantum fisher information for a two-qubit system driven by classical phase noisy laser

In this paper, the dynamics of quantum correlation quantified by local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) for two uncoupled qubits driven by classical phase noisy laser have been investigated. The results show that, both LQU and LQFI exhibit similar behaviours, either display exponential decay or oscillatory decay with revivals depending on the ratios of classical phase noisy laser rate and system-environment coupling strength. Beside, our results also confirm the amount of quantum correlation measured by LQU is strictly bounded by LQFI in an open system. Finally, we propose a scheme to protect quantum correlation against classical phase noisy laser with the technique of weak measurement and reversal.

Spin-Bath Dynamics in a Quantum Resonator-Qubit System: Effect of a Mechanical Resonator Coupled to a Central Qubit

In line with an experimentally feasible protocol was proposed by A. Asadian et al. [ PRL 112, 190402 (2014)], we introduce a pure dephasing model where the interaction of the central qubit with a nano-mechanical resonator is affected by a spin-bath to study the dynamics of resonator-qubit entangled states. We show that how system-bath coupling as well as the coupling among the bath’s spins, initial semi-classical states of the phonon as well as the initial states of the bath, modify the entanglement of the system using measures like concurrence. To gain insight into the effect of these correlations, we study the dynamics of the mentioned setup both with and without initial correlations for arbitrary system-environment coupling strengths. It is also shown that stable entanglement, which is dependent on correlated initial states of the system-bath, their coupling strength, and bath temperature, occurs even in the presence of decoherence.

Geometric phase corrected by initial system-environment correlations

We find the geometric phase of a two-level system undergoing pure dephasing via interaction with an arbitrary environment, taking into account the effect of the initial system-environment correlations. We use our formalism to calculate the geometric phase for the two-level system in the presence of both harmonic oscillator and spin environments, and we consider the initial state of the two-level system to be prepared by a projective measurement or a unitary operation. The geometric phase is evaluated for a variety of parameters such as the system-environment coupling strength to show that the initial correlations can affect the geometric phase very significantly even for weak and moderate system-environment coupling strengths. Moreover, the correction to the geometric phase due to the system-environment coupling generally becomes smaller (and can even be zero) if initial system-environment correlations are taken into account, thus implying that the system-environment correlations can increase the robustness of the geometric phase.

Generating Kerr nonlinearity with an engineered non-Markovian environment**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304503) and the National Natural Science Foundation of China (Grant Nos. 11835011, 11574353, 11734018, and 11674360).

Kerr nonlinearity is an important resource for creating squeezing and entanglement in quantum technology. Here we propose a scheme for generating Kerr nonlinearity originated from an engineered non-Markovian environment, which is different from the previous efforts using nonlinear media or quantum systems with special energy structures. In the present work, the generation of Kerr nonlinearity depends on the system–environment interaction time, the energy spectrum of the environment, and the system–environment coupling strength, regardless of the environmental initial state. The scheme can be realized in systems originally containing no Kerr interaction, such as superconducting circuit systems, optomechanical systems, and cavity arrays connected by transmission lines.

Effect of Environment on the Scattering of Electrons by a Junction of Different Topological Materials

AbstractThe studies of electron transport through a junction of topological materials in the literature so far ignore the coupling of a topological material to its surrounding environment. Here, the dynamics of an open system through a stochastic Hamiltonian are simulated to investigate the influence of the environment on the scattering of electrons by a junction of different topological materials, such as a Dirac–Weyl magnetic junction and a topological insulator. It is found that, although the detrimental effect of the environment is inevitable, the Landauer conductance can be enhanced via adjusting the system–environment coupling strength. This result supplies the possibilty of changing the transport feature of topological materials by modulating the surrounded environment. It is also demonstrated that a non‐Hermitian Hamiltonian can be used to replace the stochastic Hamiltonian for this study, when the system and the environment coupling are weak.

Environment-induced synchronization of two quantum oscillators

Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly coupled to a common bosonic quantum dissipative environment at zero temperature, in the absence of any driving mechanism. To do so, we compute the dynamics of the oscillators with an exact master equation obtained from a path integral formalism. Above some value of the system-environment coupling strength, we observe numerically a strongly reduced damping and a frequency locking in the dynamics of the oscillators. Beyond the synchronization mechanism, we also describe the rich phenomenology of the dynamics in the model and notably identify the additional emergence of a regime with long-lived oscillations.

Entanglement dynamics in a spin star system coupled weakly to a bosonic bath

In the broad realm of applications of quantum thermodynamics, a non-unitary formulation of theory is particularly well suited for describing the evolution of an open quantum system. The robust framework upon which this formulation is established enfolds the nature of system and its environment. Based on this frame, we use Born–Markov approximation to derive a master equation for the density operator of a spin star configuration. With the help of Markovian master equation, we analyze how the reservoir’s temperature and the value of system–environment coupling act on the behavior of entanglement. In the absence of an environment interaction, maximally entangled quantum W states are induced by the coherent evolution of the system. On the other hand, it is found that the environment can boost the entanglement between the second neighbors across the entanglement between the first neighbors at times when quantum W states were going to happen. At the same time instants, it is shown that the entanglement follows a power-law decay consistent with $$0.5-b\gamma ^\alpha $$ , where $$\gamma $$ is the system–environment coupling strength and the exponent lies in the range $$0.5<\alpha <0.6$$ . In addition, by comparing between the role of $$\gamma $$ and the environment’s temperature, it is revealed that the entanglement is not as sensitive to the bath’s temperature as the system–environment coupling coefficient. Our results can stimulate both experimental and theoretical interests in exploring the dissipative role of environment on spin star structures in realistic situations and can open new perspectives for this field.

Control of quantum dynamics of electron transfer in molecular loop structures: Spontaneous breaking of chiral symmetry under strong decoherence

Manipulation of quantum systems is the basis for many promising quantum technologies. However, how quantum mechanical principles can be used to manipulate the dynamics of quantum dissipative systems remains unanswered because of strong decoherence effects arising from interaction with the surrounding environment. In this work, we demonstrate that electron transfer dynamics in molecular loop structures can be manipulated with the use of Floquet engineering by applying a laser field. Despite strong dephasing, the system's dynamics spontaneously breaks the chiral symmetry of the loop in a controllable fashion, followed by the generation of a robust steady-state electronic current without an external voltage. An exponential scaling law that relates the magnitude of the current to the system-environment coupling strength is revealed numerically. The breaking of chiral symmetry and the consequent controllable unidirectional flow of electrons could be employed to construct functional molecular electronic circuits.

Effect of initial system–environment correlations with spin environments

Understanding the dynamics of open quantum systems is a highly important task for the implementation of emerging quantum technologies. To make the problem tractable theoretically, it is common to neglect initial system-environment correlations. However, this assumption is questionable in situations where the system is interacting strongly with the environment. In particular, the system state preparation can then influence the dynamics of the system via the system-environment correlations. To gain insight into the effect of these correlations, we solve an exactly solvable model of a quantum spin interacting with a spin environment both with and without initial correlations for arbitrary system-environment coupling strengths. We show that the effect of the system state preparation may or may not be significant in the strong system-environment coupling regime at low temperatures. We also study the dynamics of the entanglement between two spins interacting with a common spin environment with and without initial system-environment correlations to demonstrate that the correlations can play a significant role in the dynamics of two-qubit systems as well.

On the exact truncation tier of fermionic hierarchical equations of motion.

The hierarchical equations of motion (HEOM) theory is in principle exact for describing the dissipative dynamics of quantum systems linearly coupled to Gaussian environments. In practice, the hierarchy needs to be truncated at a finite tier. We demonstrate that, for general systems described by the fermionic HEOM, the (n+L̃)th-tier truncation with L̃=2NσNν yields the exact density operators up to the nth tier. Here, Nσ = 2 for fermionic systems and Nν is the system degrees of freedom. For noninteracting systems, L̃ is further reduced by half. Such an exact termination pattern originates from the Pauli exclusion principle for fermions, and it holds true regardless of the system-environment coupling strength, the number of coupling reservoirs, or the specific scheme employed to unravel the environment memory contents. The relatively small L̃ emphasizes the nonperturbative nature of the HEOM theory. We also propose a simplified HEOM approach to further reduce the memory cost for practical calculations.

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.

Multi-qubit non-Markovian dynamics in photonic crystal with infinite cavity-array structure

We study the exact non-Markovian dynamics of a multi-qubit system coupled to a photonic-crystal waveguide with infinite cavity-array structure. A general solution of the evolution state of the system is solved for a general initial state in the single-excitation subspace. With this solution, we find that the non-Markovian effect of the environment on the system could be enhanced not only by increasing the system-environment coupling strength but also by adding the qubit number in the system. The explicit non-Markovian dynamics are discussed under two initial states to see the non-Markovian effect on entanglement preservation and entanglement generation. We find that the non-Markovian effect tends to preserve the system in its initial state.

Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems

We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic and a fermionic environment at zero temperature are analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity no matter the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may inevitably reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.

The quantum Zeno and anti-Zeno effects with strong system-environment coupling

To date, studies of the quantum Zeno and anti-Zeno effects focus on quantum systems that are weakly interacting with their environment. In this paper, we investigate what happens to a quantum system under the action of repeated measurements if the quantum system is strongly interacting with its environment. We consider as the quantum system a single two-level system coupled strongly to a collection of harmonic oscillators. A so-called polaron transformation is then used to make the problem in the strong system-environment coupling regime tractable. We find that the strong coupling case exhibits quantitative and qualitative differences as compared with the weak coupling case. In particular, the effective decay rate does not depend linearly on the spectral density of the environment. This then means that, in the strong coupling regime that we investigate, increasing the system-environment coupling strength can actually decrease the effective decay rate. We also consider a collection of two-level atoms coupled strongly with a common environment. In this case, we find that there are further differences between the weak and strong coupling cases since the two-level atoms can now indirectly interact with one another due to the common environment.