System-environment Coupling Strength Research Articles

Landau-Zener transitions in an open multilevel quantum system

We consider the Landau-Zener problem for a multilevel quantum system that is coupled to an external environment. In particular, we consider a number of cases of three-level systems coupled to a harmonic oscillator that represents the external environment. We find that, similar to the case of the Landau-Zener problem with a two-level system, when the quantum system and the environment are both initially in their ground states the probability that the system remains in the same quantum state is not affected by the coupling to the environment. The final occupation probabilities of the other states are well described by a common general principle: the coupling to the environment turns each Landau-Zener transition process in the closed system into a sequence of smaller transitions in the combined Hilbert space of the system and environment, and this sequence of transitions lasts a total duration that increases with increasing system-environment coupling strength. These results provide an intuitive understanding of Landau-Zener transitions in open multilevel quantum systems.

Non-equilibrium quantum phase transition via entanglement decoherence dynamics.

We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained.

Quantum Fisher information of the GHZ state due to classical phase noise lasers under non-Markovian environment

The dynamics of N-qubit GHZ state quantum Fisher information (QFI) under phase noise lasers (PNLs) driving is investigated in terms of non-Markovian master equation. We first investigate the non-Markovian dynamics of the QFI of N-qubit GHZ state and show that when the ratio of the PNL rate and the system–environment coupling strength is very small, the oscillations of the QFIs decay slower which corresponds to the non-Markovian region; yet when it becomes large, the QFIs monotonously decay which corresponds to the Markovian region. When the atom number N increases, QFIs in both regions decay faster. We further find that the QFI flow disappears suddenly followed by a sudden birth depending on the ratio of the PNL rate and the system–environment coupling strength and the atom number N, which unveil a fundamental connection between the non-Markovian behaviors and the parameters of system–environment couplings. We discuss two optimal positive operator-valued measures (POVMs) for two different strategies of our model and find the condition of the optimal measurement. At last, we consider the QFI of two atoms with qubit–qubit interaction under random telegraph noises (RTNs).

Excess energy and decoherence factor of a qubit coupled to a one-dimensional periodically driven spin chain.

We take a central spin model (CSM), consisting of a one-dimensional environmental Ising spin chain and a single qubit connected globally to all the spins of the environment, to study the excess energy (EE) of the environment and the logarithm of decoherence factor namely, generalized fidelity susceptibility per site (GFSS), associated with the qubit under a periodic driving of the transverse field term of environment across its critical point using the Floquet theory. The coupling to the qubit, prepared in a pure state, with the transverse field of the spin chain yields two sets of EE corresponding to the two species of Floquet operators. In the limit of weak coupling, we derive an approximated expression of GFSS after an infinite number of driving period which can successfully estimate the low- and intermediate-frequency behavior of GFSS obtained numerically with a large number of time periods. Our main focus is to analytically investigate the effect of system-environment coupling strength on the EEs and GFSS and relate the behavior of GFSS to EEs as a function of frequency by plausible analytical arguments. We explicitly show that the low-frequency beatinglike pattern of GFSS is an outcome of two frequencies, causing the oscillations in the two branches of EEs, that are dependent on the coupling strength. In the intermediate frequency regime, dip structure observed in GFSS can be justified by the resonance peaks of EEs at those coupling parameter-dependent frequencies; high-frequency saturation behavior of EEs and GFSS are controlled by the same static Hamiltonian and the associated saturation values are related to the coupling strength.

Quantum decoherence and thermalization at finite temperature within the canonical-thermal-state ensemble

We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The entirety $S+E$ is prepared in a canonical-thermal state at a finite temperature; that is, the entirety is in a steady state. Both our numerical results and theoretical predictions show that measures of the decoherence and the thermalization of $S$ are generally finite, even in the thermodynamic limit, when the entirety $S+E$ is at finite temperature. Notably, applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider $S$ uncoupled from $E$, but entangled with $E$, to predict decoherence and thermalization measures of $S$. This decoupling allows closed-form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of $S$ and of $E$. Large-scale numerical results for both coupled and uncoupled entireties with up to 40 quantum spins support these findings.

Non-Markovianity measure using two-time correlation functions

We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov limit. Such non-Markovianity measure can easily be measured in experiments. We found that the non-Markovianity dynamics in different time scale crucially depends on the system-environment coupling strength and other physical parameters such as the initial temperature of the environment and the initial state of the system. In particular, we obtain the short-time and long-time behaviors of non-Markovianity for different spectral densities. We also find that the thermal fluctuation always reduce the non-Markovian memory effect. Also, the non-Markovianity measure shows non-trivial initial state dependence in different time scales.

Dissipative dynamics in a quantum bistable system: crossover from weak to strong damping.

The dissipative dynamics of a quantum bistable system coupled to a Ohmic heat bath is investigated beyond the spin-boson approximation. Within the path-integral approach to quantum dissipation, we propose an approximation scheme which exploits the separation of time scales between intra- and interwell (tunneling) dynamics. The resulting generalized master equation for the populations in a space localized basis enables us to investigate a wide range of temperatures and system-environment coupling strengths. A phase diagram in the coupling-temperature space is provided to give a comprehensive account of the different dynamical regimes.

Non-Markovianity for a qubit system driven by a classical phase noisy laser

In this paper, the degree of non-Markovian behaviour for a qubit system driven by a classical phase noisy laser (CPNL) is investigated. We analyse the dynamics of the rate of change of the trace distance in two different dynamical regimes in relation to the values of the system parmeters. The results show that the behaviour of the non-Markovianity depends on the ratio of the CPNL rate and the system-environment coupling strength. In the non-Markovian classical noise region, the non-Markovian character becomes less evident when the ratio of the CPNL rate and the system-environment coupling increases.

Dynamics and Protection of Quantum Discord for Two Uncoupled Qubits Driven by Classical Phase Noisy Laser

In this paper, the dynamics and protection of quantum discord for two uncoupled qubits driven by classical phase noisy laser(CPNL) is investigated. The results show that, the dynamics of quantum discord depends on the ratio of CPNL rate and the system-environment coupling strength. The quantum discord can be well protected by increasing the ratio in the Markovian classical noise region or by decreasing the ratio in the non-Markovian classical noise region. Besides, we explain the revivals of the quantum discord by means of the increase of parameter used to quantify non-Markovianty of the single qubit dynamics in the non-Markovian classical noise region.

Zeno and anti-Zeno effects on dephasing

Quantum Zeno and anti-Zeno effects on pure dephasing are studied using exactly solvable microscopic models. The crossover between these two opposite effects is investigated. The case of a single two-level system undergoing dephasing is already different from the previously studied population decay problem, even without taking into account any back action from the environment. For many two-level systems interacting with a common environment, multiple transitions between Zeno and anti-Zeno regimes are predicted. Finally, if the system-environment coupling strength is not weak, we show that the nontrivial evolution of the environment between measurements can considerably alter the quantum Zeno and anti-Zeno effects.

Effect of Decoherence Induced by a Spin Environment on Quantum Channel Capacity

We investigate the effect of decoherence from a spin environment on the quantum channel capacity. Our results imply that the time evolution of the quantum channel capacity depends on the number of freedom degrees of the environment, the tunneling element, the initial state of the environment, and the system-environment coupling strength. From the analysis, we find that the strong tunneling elements and the weak coupling strength can enhance the quantum channel capacity while the environment with a large number of freedom degrees and the strong coupling strength will shrink it.

Consistent treatment of coherent and incoherent energy transfer dynamics using a variational master equation

We investigate the energy transfer dynamics in a donor-acceptor model by developing a time-local master equation technique based on a variational transformation of the underlying Hamiltonian. The variational transformation allows a minimisation of the Hamiltonian perturbation term dependent on the system parameters, and consequently results in a versatile master equation valid over a range of system-bath coupling strengths, temperatures, and environmental spectral densities. While our formalism reduces to the well-known Redfield, Förster and polaron forms in the appropriate limits, in general it is not equivalent to perturbing in either the system-environment or donor-acceptor coupling strengths, and hence can provide reliable results between these limits as well. Moreover, we show how to include the effects of both environmental correlations and non-equilibrium preparations within the formalism.

High Fidelity Quantum Gates via Dynamical Decoupling

Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of magnitude improvement in the fidelities of a universal set of quantum gates, relative to unprotected evolution, is achieved over a broad range of system-environment coupling strengths, using recursively constructed (concatenated) dynamical decoupling pulse sequences.

Universal decoherence induced by an environmental quantum phase transition

Decoherence induced by coupling a system with an environment may display universal features. We demonstrate that when the coupling to the system drives a quantum phase transition in the environment, the decay of quantum coherences in the system is Gaussian with a width independent of the system-environment coupling strength. We obtain analytical results for a class of solvable models, and present numerical evidence supporting the validity of our results in more general cases. This effect opens the way for a quantum simulation algorithm, where a single qubit is used to detect a quantum phase transition. We discuss possible implementations of such an algorithm and relate our results to available data on universal decoherence in NMR echo experiments.

Decoherence induced by interacting quantum spin baths

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, $XY$, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the $XY$ models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.

Decoherence of tripartite states—a trapped ion coupled to an optical cavity

We investigate the decoherence process of a three-qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Interaction of the ion with a resonant laser and the cavity field tuned to red sideband of ionic vibrational motion generates tripartite entanglement of the internal state of the ion, vibrational state of ionic centre of mass motion and the cavity-field state. Non-dissipative decoherence occurs due to entanglement of the system with the environment, modelled as a set of non-interacting harmonic oscillators. Analytic expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state and the population inversion have been obtained. Coupling to environment results in exponential decay of off-diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different values of system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence sources has been analysed. The maximum tripartite entanglement is found to decrease with increase in the strength of system–environment coupling. The negativity as well as the linear entropy as entanglement measures gives qualitatively similar results, uniquely identifying maximally entangled and separable states of the system. For large values of system–environment coupling strength, the mixed states of the composite system lying at the boundary of an entangled–separable region are reached. For these states, whereas the negativity measures only quantum correlations, the linear entropy measures classical correlations as well.

Decoherence in a classically chaotic quantum system: entropy production and quantum-classical correspondence.

We study the decoherence process for an open quantum system that is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators). We carefully analyze the time dependence of the rate of entropy production showing that it has two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength); for longer times (but before equilibration) it is fixed by dynamical properties of the system (and is related to the Lyapunov exponent). The nature of the transition time between both regimes is investigated and the issue of quantum to classical correspondence is addressed. Finally, the impact of the interaction with the environment on coherent tunneling is analyzed.

Decoherence and the rate of entropy production in chaotic quantum systems

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength). For longer times (but before equilibration) there is a regime where the entropy production rate is fixed by the Lyapunov exponent. The nature of the transition time between both regimes is investigated.

Laser control of intramolecular hydrogen transfer reactions: A real-time path integral approach

Different pulse shapes realizing photo isomerization via laser driven tunnelling or vibrational transitions are studied here. Particular attention is paid to the investigation of their robustness with respect to the influence of dissipative processes introduced by the interaction with an environment. An iterative scheme for propagation of the reduced density matrix in the path integral representation is used to take into account arbitrary system-environment coupling strengths as well as the effect of non-Markovian dynamics.