Long-Lived Quantum Coherence of the Non-Markovian Dynamics in Photosynthetic Complexes and the Measure of Non-Markovianity

Abstract

The long-lived quantum coherence in photosynthetic complexes existing in ambient temperature has been reported experimentally by two-dimensional photon echo (2DPE) technique and the origin of this phenomenon has attracted vigorous debates We propose an analytical non-Markovian dimer model without invoking any specific numerical implementation to simulate the dynamics of the photosynthetic complexes Our theory suggests that the non-Markovian coupling to the vibronic motion of the surrounding molecules plays an important role in sustaining the quantum coherence The mechanism is analogous to an externally driven Rabi-oscillations in quantum optics Sequentially we simplify the dimer model to a spin-boson model and apply two perturbative approaches to evaluate different master equations To understand how the two approximative equations deviate form the exact results we compare those with the hierarchy equations of motion (HEOM) method which is considered to be numerically exact We find out that both approximations perform well in the weak-coupling regime However when it goes to the intermediate-coupling regime the two approximations show different drawbacks The second-order time-convolution (TC2) model will over-estimate the quantum coherence whereas the second-order time-local (TL2) model over-estimates the decoherence rates and leads to a sluggish dynamics To quantify the effect of past memory in the above equations we briefly introduce several measures of non-Markovianity This topic has recently attracted great interests due to its fundamental importance in the theory of open quantum system We apply the RHP measure to quantify the non-Markovianity of our photosynthetic dimer model and find out the relations between the long-lived quantum coherence and non-Markovianity For further applications we compare the non-Markovianity of three approaches (TC2 TL2 and HEOM) and investigate its dependance on several parameters describing the system We find out a counter-intuitive increase of non-Markovianity with both temperature and with the coupling strength to the environment This suggests that the measure of non-Markovianity acts as a benchmark to quantify how well an approximative equations takes the memory effects into account To acquire a more fine-grained insight of non-Markovianity we further adopt the theory of $k$-positive maps to generalize a hierarchy of non-Markovianity We also develop a useful tool $k$-divisibility phase diagram to visualize the hierarchy of non-Markovianity This phase diagram provides a unified framework to study distinct measures of non-Markovianity and show correlations among them Comparison of those measures of non-Markovianity by means of $k$-divisibility phase diagram shows the origin of discrepancy and the circumstance under which these measures get reconciliation

Date of Award	2015 Jul 8
Original language	English
Supervisor	Yueh-Nan Chen (Supervisor)