Exact dynamics of first-order system-bath coherence in bilinear bosonic models

Abstract

We investigate the exact dynamics of first-order system--bath coherence induced by excitation exchange in bilinear bosonic models. By solving the linear Heisenberg equations, we obtain the exact evolution of system and bath operators and evaluate the first-order coherence between the system mode and the collective bath mode directly coupled to it. We analyze how this coherence depends on initial occupations, coupling strength, spectral width, and detuning, showing that its buildup and oscillatory behavior are closely related to excitation exchange and reservoir memory. We further examine controlled coherence dynamics under leakage-elimination-operator inspired modulation of the system frequency. The results show that random modulation can suppress excitation leakage and maintain finite and relatively stable coherence fluctuations at long times. These results clarify the evolution and control of first-order system--bath coherence in settings where a localized bosonic mode is coupled to a structured bosonic reservoir.