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

Abstract

Non-Markovian quantum evolution of the electronic subsystem in a laser-driven molecule is characterized through the appearance of negative decoherence rates in the canonical form of the electronic master equation. For a driven molecular system described in a bipartite Hilbert space $\mathcal{H}={\mathcal{H}}_{el}⨂{\mathcal{H}}_{\mathrm{vib}}$ of dimension $2\ifmmode\times\else\texttimes\fi{}{N}_{v}$, we derive the canonical form of the electronic master equation, deducing the canonical measures of non-Markovianity and the Bloch volume of accessible states. We find that one of the decoherence rates is always negative, accounting for the inherent non-Markovian character of the electronic evolution in the vibrational environment. Enhanced non-Markovian behavior, characterized by two negative decoherence rates, appears if there is a coupling between the electronic states $g,\phantom{\rule{0.16em}{0ex}}e$, such that the evolution of the electronic populations obeys $d({P}_{g}{P}_{e})/dt>0$. Non-Markovianity of the electronic evolution is analyzed in relation to temporal behaviors of the electronic-vibrational entanglement and electronic coherence, showing that enhanced non-Markovian behavior accompanies entanglement increase. Taking as an example the coupling of two electronic states by a laser pulse in the ${\mathrm{Cs}}_{2}$ molecule, we analyze non-Markovian dynamics under laser pulses of various strengths, finding that the weaker pulse stimulates the bigger amount of non-Markovianity. Our results show that increase of the electronic-vibrational entanglement over a time interval is correlated to the growth of the total amount of non-Markovianity calculated over the same interval using canonical measures and connected with the increase of the Bloch volume. After the pulse, non-Markovian behavior is correlated to electronic coherence, such that vibrational motion in the electronic potentials which diminishes the nuclear overlap, implicitly increasing the linear entropy of entanglement, brings a memory character to dynamics.