Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

Abstract

a b s t r a c tThe non-Markovianity of the electron transfer in an oligothiophene-fullerene heterojunction described by a spin-boson model is analyzed using the time dependent decoherence canonical rates and the volume of accessible states in the Bloch sphere. The dynamical map of the reduced electronic system is computed by the hierarchical equations of motion methodology (HEOM) providing an exact dynamics. Transitory witness of non-Markovianity is linked to the bath dynamics analyzed from the HEOM auxiliary matrices. The signature of the collective bath mode detected from HEOM in each electronic state is compared with predictions of the effective mode extracted from the spectral density. We show that including this main reaction coordinate in a one-dimensional vibronic system coupled to a residual bath satisfactorily describes the electron transfer by a simple Markovian Redfield equation. Non-Markovianity is computed for three inter fragment distances and compared with a priori criterion based on the system and bath characteristic timescales.

Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion

“…As mid-term perspectives, future works should deal with exerting control directly on bath dynamics, in such a way to decrease decoherence of the sub-system, or in other words, achieve appropriate control of non-Markovianity to better protect sub-system characteristics. To that end, different strategies can be proposed: (i) additional control of the environment through the introduction of a transition dipole among bath normal modes; (ii) extraction of a collective mode from the bath so as to deal with a control involving an augmented active system, as has already been done in field-free heterojunction [38] or in a SQUID model [24]. We are actively pursuing research of these topics.…”

“…Analytical expressions for the α k and γ k parameters can be derived when the spectral density is fitted by a sum of two-poles [67] or four-pole Lorentzian functions leading to an Ohmic or super Ohmic behavior at low frequencies [38]. The complex conjugate of the correlation function can be expressed by keeping the same coefficients γ k in the exponential functions but using modified coefficients ã k according to:…”

“…The field-free energy gap is 0.33 eV and the optimal fields induce different Stark shifts in a range of about 0.25-0.65 eV, so that the instantaneous resonance frequency ω 0 (t) moves with respect to the spectral density peaks, with its expected consequences on non-Markovianity [29,30]. Obviously, different initial states, with different field-free energy gaps (characterizing heterojunction models with different inner-fragment distances [38]) will result into different control parameters, but still with transposable strategies and generic enough results. The fluctuations of the eigenenergy gap of the field-dressed system Hamiltonian are shown in panels (g)-(i) of figure 2.…”

“…However the results contain most of the physics we want to exhibit: (1) the non-Markovian witnesses qualitatively behave as during the short control. The studied system is strongly non-Markovian as can be seen in the field-free case from the transitory negative sum of the canonical rates well after the bath correlation time as shown in [38]. (2) The field driven dynamics exploits the non-Markovian character of the bath well beyond the bath correlation time.…”

“…The interaction of the two-level system with the bath is described by the standard SB Hamiltonian which can be used in many different situations ranging from qubit in quantum dots to exciton or charge transfer. In the present work, it is built and calibrated to simulate a charge transfer between donor and acceptor electronic states in a heterojunction [36][37][38]. The model addresses ultra-short control of electronic dynamics in a complex system strongly coupled to the nuclear vibrational motion [5].…”