Strong System-environment Coupling Research Articles

Spectral and steady-state properties of fermionic random quadratic Liouvillians

We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by MM random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, m=M/(2N_F)m=M/(2NF), we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for m=1/2m=1/2 and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below m=1/2m=1/2, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling.

Dissipative Topological Phase Transition with Strong System-Environment Coupling.

A primary motivation for studying topological matter regards the protection of topological order from its environment. In this work, we study a topological emitter array coupled to an electromagnetic environment. The photon-emitter coupling produces nonlocal interactions between emitters. Using periodic boundary conditions for all ranges of environment-induced interactions, the chiral symmetry inherent to the emitter array is preserved. This chiral symmetry protects the Hamiltonian and induces parity in the Lindblad operator. A topological phase transition occurs at a critical photon-emitter coupling related to the energy spectrum width of the emitter array. Interestingly, the critical point nontrivially changes the dissipation rates of edge states, yielding a dissipative topological phase transition. In the protected topological phase, edge states suffer from environment-induced dissipation for weak photon-emitter coupling. However, strong coupling leads to robust dissipationless edge states with a window at the emitter spacing. Our work shows the potential to manipulate topological quantum matter with electromagnetic environments.

Two-time correlation functions beyond quantum regression theorem: effect of external noise

We present the results of a study of the two-time correlation functions of a dichotomously driven two-level system in contact with a thermal bath by using corrections beyond the quantum regression theorem. In the strong system-environment coupling regime, it is found that the noise parameters could be tuned to control the magnitude of corrections at low environmental temperatures. The motional averaging and narrowing effect of the external noise was observed on the absorption and emission spectra of the two-state system. Furthermore, effects similar to the destruction of tunneling and noise enhancement of transport are observed in the dynamics of the two-time correlations.

Full-polaron master equation approach to dynamical steady states of a driven two-level system beyond the weak system-environment coupling

We apply a full-polaron master equation and a weak-coupling non-Markovian master equation to describe the steady-state time-averaged properties of a driven two-level system, an electron coherently tunneling between double quantum dots (DQDs), interacting with a bosonic phonon bath. Comparing the results obtained using these two master equations with those from a recent DQD experiment and its corresponding weak-coupling theoretical method, we find that the original parameter set used in the experiment and theoretical method is not in the weak-coupling parameter regime. By using the full-polaron master equation with a slight adjustment on only the value of the interdot separation in the original experimental parameter set, we find that a reasonable fit to the experimentally measured time-averaged steady-state population data can be achieved. The adjusted interdot separation is within the possible values allowed by the geometry of the surface gates that define the DQD in the experiment. Our full-polaron equation approach does not require the special renormalization scheme employed in their weak-coupling theoretical method, and can still describe the experimental results of driving-induced phonon-enhanced steplike shoulder behaviors in the experiment. This demonstrates that the full-polaron master equation approach is a correct and efficient tool to describe the steady-state properties of a driven spin-boson model in the case of strong system-environment coupling.

The quantum Zeno and anti-Zeno effects: from weak to strong system-environment coupling

By repeatedly measuring a quantum system, the evolution of the system can be slowed down (the quantum Zeno effect) or sped up (quantum anti-Zeno effect). We study these effects for a single two-level system coupled to a collection of harmonic oscillators. Previously, such systems have been studied in both the weak and the strong system-environment coupling regimes. In this paper, we apply a polaron transformation in a manner that allows us to study the quantum Zeno and anti-Zeno effects for a large variety of system-environment parameters. Using this approach, we reproduce previous results for the weak and strong system-environment coupling regimes. Moreover, as long as the environment is super-Ohmic, we show how our approach can be used to explore regimes such as the moderate system-environment coupling regime that could not be investigated before in a straightforward manner.

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.

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.

How Much Time Does a Measurement Take?

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.

Preferred States of Decoherence under Intermediate System-Environment Coupling

The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-envrionment interaction, the behavior of PS is well known. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging. The found PS can also continuously deform to expected limits for weak or strong system-environment coupling. Computational results are also qualitatively explained. The findings should be useful towards further understanding of decoherence and quantum thermalization processes.

Perturbative and nonperturbative master equations for open quantum systems

This paper develops perturbative and nonperturbative master equations for open quantum systems based on time-dependent variational functionals. The perturbative equations are more concise and suitable for dealing with cases of weak system-environment coupling for short evolution time scales. The nonperturbative equations are valid for all time and appropriate to treat cases of strong system-environment coupling. When a system contains an external control field, both the perturbative and nonperturbative master equations reveal the embedded control field dependence upon the system decoherence, which provides a basis for decoherence management.

Closed loop learning control to suppress the effects of quantum decoherence

This paper explores the use of laboratory closed loop learning control to suppress the effects of decoherence in quantum dynamics. Simulations of the process are performed in multilevel quantum systems strongly interacting with the environment. A genetic algorithm is used to find an optimal control field which seeks out transition pathways to achieve a minimum influence of decoherence upon the system at a target time. The simulations suggest that decoherence may be optimally managed in the laboratory through closed loop operations with a suitable cost that is sensitive to the coherence of the dynamics. The case studies of dimension N=4 and N=10 with strong system–environment coupling indicate that the additional complexity with increasing system dimension can make it more difficult to manage decoherence.