The coupled quantum dynamics of excitonic and vibrational degrees of freedom is investigated for high-dimensional models of the Fenna-Matthews-Olson complex. This includes a seven- and an eight-site model with 518 and 592 harmonic vibrational modes, respectively. The coupling between local electronic transitions and vibrations is described within the Huang-Rhys model using parameters that are obtained by discretization of an experimental spectral density. Different pathways of excitation energy flow are analyzed in terms of the reduced one-exciton density matrix, focussing on the role of vibrational and vibronic excitations. Distinct features due to both competing time scales of vibrational and exciton motion and vibronically assisted transfer are observed. The question of the effect of initial state preparation is addressed by comparing the case of an instantaneous Franck-Condon excitation at a single site with that of a laser field excitation.

Multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach to the correlated exciton-vibrational dynamics in the FMO complex.

The coupled quantum dynamics of excitonic and vibrational degrees of freedom is investigated for high-dimensional models of the Fenna-Matthews-Olson (FMO) complex. This includes a seven and an eight-site model with 518 and 592 harmonic vibrational modes, respectively. The coupling between local electronic transitions and vibrations is described within the Huang-Rhys model using parameters that are obtained by discretization of an experimental spectral density. Different pathways of excitation energy flow are analyzed in terms of the reduced one-exciton density matrix, focussing on the role of vibrational and vibronic excitation. Distinct features due to both competing time scales of vibrational and exciton motion and vibronically-assisted transfer are observed. The question of the effect of initial state preparation is addressed by comparing the case of an instantaneous Franck-Condon excitation at a single site with that of a laser field excitation.

Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) Approach to the Correlated Exciton-Vibrational Dynamics in the FMO Complex

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble (“bundle”) of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar ...

On the non-stationary generalized Langevin equation

Density matrix theory and computational aspects of quantum dynamics in active medium

Over the past few years, the exploration of mesoscopic quantum systems progressed drastically with experiments one could not imagine twenty years ago. New measurements, such as the detection of entanglement in large-scale quantum systems, require novel modeling tools. The open quantum system formalism, which took off in the 70s but was popularized at the turn of the century, played a central role in the analysis of these data. The existence of so-called non-trivial quantum effects got increasingly manifest with the measurement of quantum coherence at room temperature in bacterial light-harvesting complexes and two-dimensional nanostructures. There exists actually a plethora of techniques to discuss such kind of effects. However, since open systems are out-of-equilibrium it is crucial to ensure their thermodynamical consistency. To produce tractable models, we have decided in this work to rely on the modular dynamical semigroup approach. This framework permits to postulate Markovian equations leading to a time-evolution preserving the positivity of the density matrix. Moreover, it ensures that the second law of thermodynamics and the convergence to the correct steady-state hold. In order to compare these equations with experiments, we adapt the fluctuation dissipation theorem and the Green-Kubo formula to open quantum system. Thereby, we examine the linear response of a single qubit connected to a heat reservoir and find that the decay of the coherence depends on the initial state’s phase in presence of non-secular terms. Besides, we show the emergence of a biexponential decay of the coherence, associated to two distinct decoherence times and non-Lorentzian susceptibility profiles. Both phenomena were measured in numerous setups; they could be exploited to shorten or prolong the coherence time to contribute, for example, to fulfill one of DiVincenzo’s criteria for quantum computing. These findings remain true for two qubits, either connected to independent reservoirs or to a single common reservoir, allowing to accelerate or refrain the decay of entanglement. In the same vein, we explain how to create coherence and entanglement in a transitory or steady manner through the action of a common reservoir. On the other hand, we prove that one can fix the problem of the artificial position diffusion taking place in quantum Brownian motion within the presented framework. Furthermore, we provide a scheme for the nonlinear response going beyond Mukamel’s formulation. Taken altogether, our results support the idea that the postulated master equations can be substituted to the derived ones to fix their drawbacks. Finally, we explain how coherence can be used to tune the energy transfer in light-harvesting complexes, near and far-away from equilibrium, by manipulating the system Hamiltonian as well as the interaction with the environment.

Thermodynamics of Mesoscopic Quantum Systems: from a single qubit to light harvesting complexes

The time-dependent projection operator technique according to Willis and Picard (Phys. Rev. A 9 (1974) 1343) offers a unique quantum statistical description of two interacting subsystems. The technique is used here to go beyond the standard quantum master equation (QME) for a small system coupled to a reservoir. Applying the time-dependent projection operator approach, one is able to overcome a perturbational treatment of the system–reservoir coupling and can incorporate, (i) how the dynamics of the system may drive the reservoir out of the equilibrium, and (ii) how this nonequilibrium state reacts back on the system dynamics. The case of a reservoir of harmonic oscillators coupled linearly by its coordinates to the small system is studied in detail. The derivation of a closed nonlinear equation of motion for the reduced statistical operator of the small system is demonstrated. The method is used to describe the motion of a quantum particle in a molecular system, e.g. a tunneling electron or an exciton, which interacts strongly with its environment.

O. Linden

Papers

Application of the time-dependent projection operator technique: The nonlinear quantum master equation