Non-Markovian quantum jumps in excitonic energy transfer

Rebentrost, Patrick; Chakraborty, Rupak; Aspuru‐Guzik, Alán

doi:10.1063/1.3259838

Cited by 130 publications

(173 citation statements)

References 47 publications

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“…Our approach is related in spirit to treatments of excitation energy transfer in photosynthetic pigment protein complexes, where reduced density matrix simulations similar to those proposed here have enjoyed great success in understanding quantum effects in complex, multi-state biological systems. [29][30][31] The second and third articles of this series will make clear the utility of this formalism as we investigate singlet fission in dimers and crystals, respectively.…”

Section: Introductionmentioning

confidence: 99%

Microscopic theory of singlet exciton fission. I. General formulation

Berkelbach¹,

Hybertsen²,

Reichman³

2013

The Journal of Chemical Physics

254

415

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Singlet fission, a spin-allowed energy transfer process generating two triplet excitons from one singlet exciton, has the potential to dramatically increase the efficiency of organic solar cells. However, the dynamical mechanism of this phenomenon is not fully understood and a complete, microscopic theory of singlet fission is lacking. In this work, we assemble the components of a comprehensive microscopic theory of singlet fission that connects excited state quantum chemistry calculations with finite-temperature quantum relaxation theory. We elaborate on the distinction between localized diabatic and delocalized adiabatic bases for the interpretation of singlet fission experiments in both the time and frequency domains. We discuss various approximations to the exact density matrix dynamics and propose Redfield theory as an ideal compromise between speed and accuracy for the detailed investigation of singlet fission in dimers, clusters, and crystals. Investigations of small model systems based on parameters typical of singlet fission demonstrate the numerical accuracy and practical utility of this approach.

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Section: Introductionmentioning

confidence: 99%

Microscopic theory of singlet exciton fission. I. General formulation

Berkelbach¹,

Hybertsen²,

Reichman³

2013

The Journal of Chemical Physics

254

415

View full text Add to dashboard Cite

show abstract

“…To overcome these problems inherent in the nonMarkovian dynamics, different strategies can be used, such as the correlated projector method [51], the time-dependent projection-operator approach [52], the effective-mode representation [53] and the quantum jumps approach [54]. Here, we use the operatorial formulation of the perturbation theory (PT) [55] recently introduced for studying the dynamics of the excitonic coherences [56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Energy transfer in finite-size exciton-phonon systems: Confinement-enhanced quantum decoherence

Pouthier

2012

The Journal of Chemical Physics

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Based on the operatorial formulation of the perturbation theory, the exciton-phonon problem is revisited for investigating exciton-mediated energy flow in a finite-size lattice. Within this method, the exciton-phonon entanglement is taken into account through a dual dressing mechanism so that exciton and phonons are treated on an equal footing. In a marked contrast with what happens in an infinite lattice, it is shown that the dynamics of the exciton density is governed by several time scales. The density evolves coherently in the short-time limit whereas a relaxation mechanism occurs over intermediated time scales. Consequently, in the long-time limit, the density converges toward a nearly uniform distributed equilibrium distribution. Such a behavior results from quantum decoherence that originates in the fact that the phonons evolve differently depending on the path followed by the exciton to tunnel along the lattice. Although the relaxation rate increases with the temperature and with the coupling, it decreases with the lattice size, suggesting that the decoherence is inherent to the confinement.

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“…In addition to their importance in addressing fundamental questions [12], this is mainly due to the applications non-Markovian systems find in many branches of physics. Non-Markovian processes appear in quantum optics [1,13,14], solid state physics [15], quantum chemistry [16], quantum information processing [17], and even in the description of biological systems [18].…”

Section: Introductionmentioning

confidence: 99%

Phenomenological memory-kernel master equations and time-dependent Markovian processes

et al. 2010

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Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological integrodifferential master equations describing the dynamics of a spin 1/2 in a thermal bath. By using a recently introduced measure to quantify non-Markovianity [H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that as far as the equations retain their physical sense, the key feature of non-Markovian behavior does not appear in the considered memory kernel master equations. Namely, there is no reverse flow of information from the environment to the open system. Therefore, the assumption that the integration over a memory kernel always leads to a non-Markovian dynamics turns out to be vulnerable to phenomenological approximations. Instead, the considered phenomenological equations are able to describe time-dependent and uni-directional information flow from the system to the reservoir associated to time-dependent Markovian processes.

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Non-Markovian quantum jumps in excitonic energy transfer

Cited by 130 publications

References 47 publications

Microscopic theory of singlet exciton fission. I. General formulation

Microscopic theory of singlet exciton fission. I. General formulation

Energy transfer in finite-size exciton-phonon systems: Confinement-enhanced quantum decoherence

Phenomenological memory-kernel master equations and time-dependent Markovian processes

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