Electronic memory of vibrational dynamics: Non-Markovian evolution of electronic coherence from complex dynamical weak values
Phys. Rev. A 113, 012404 – Published 2 January, 2026
DOI: https://doi.org/10.1103/zvkl-s7hy
Abstract
We propose a non-Markovian perspective on the evolution of electronic coherence in a molecule prepared in a superposition of two electronic states entangled with their vibrational environment. We show that the non-Markovian evolution of electronic coherence is governed by dynamical generalized weak values, which are characteristic averages of the electronic energy difference within the vibrational environment. These complex generalized weak values characterize the dynamics of the vibrational environment and form the memory kernel in the evolution of electronic coherence. They reflect a property essential for the existence of complex electronic coherence: the set coherence of the preselected and postselected states in the vibrational Hilbert space. Anomalous weak values may emerge during the evolution when electronic coherence approaches zero. We numerically simulate several vibrational preparations of a cold diatomic molecule using chirped laser pulses to examine the evolution of electronic coherence in diverse vibrational environments. The complex dynamical weak value serves as a useful theoretical tool for differentiating types of coherence and understanding the evolution of the time-dependent phase of coherence. The occurrence of anomalous weak values in the evolution reveals the existence of sudden large fluctuations in the energy difference between the electronic states due to vibrational dynamics.
