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Non-Markovian quantum evolution of the electronic subsystem in a laser-drivenmolecule is characterized through the appearance of negative decoherence ratesin the canonical form of the electronic master equation. For a driven molecularsystem described in a bipartite Hilbert space H=Hel x Hvib of dimension 2 x Nv,we derive the canonical form of the electronic master equation, deducing thecanonical measures of non-Markovianity and the Bloch volume of accessiblestates. We find that one of the decoherence rates is always negative,accounting for the inherent non-Markovian character of the electronic evolutionin the vibrational environment. Enhanced non-Markovian behavior, characterizedby two negative decoherence rates, appears if there is a coupling between theelectronic states g, e, such that the evolution of the electronic populationsobeys d(PgPe)/dt > 0. Non-Markovianity of the electronic evolution is analyzedin relation to temporal behaviors of the electronic-vibrational entanglementand electronic coherence, showing that enhanced non-Markovian behavioraccompanies entanglement increase. Taking as an example the coupling of twoelectronic states by a laser pulse in the Cs2 molecule, we analyzenon-Markovian dynamics under laser pulses of various strengths, finding thatthe weaker pulse stimulates the bigger amount of non-Markovianity. We show thatincrease of the electronic-vibrational entanglement over a time interval iscorrelated to the growth of the total amount of non-Markovianity calculatedover the same interval using canonical measures and connected with the increaseof the Bloch volume. After the pulse, non-Markovian behavior is correlated toelectronic coherence, such that vibrational motion in the electronic potentialswhich diminishes the nuclear overlap, implicitly increasing the linear entropyof entanglement, brings a memory character to dynamics.

physical review. a/physical review, a

Non-Markovian dynamics of the electronic subsystem in a laser-driven  molecule: Characterization and connections with electronic-vibrational  entanglement and electronic coherence