Limits of Memory-Assisted Coherence in Cavity-Embedded Molecules

Strong light-matter coupling in optical cavities is being widely explored as a strategy for modifying molecular dynamics and enhancing coherence. At the same time, structured vibrational environments can exhibit non-Markovian memory that promotes information backflow and coherence revival. We investigate the competition between these effects in a vibronic molecular system strongly coupled to a lossy optical cavity. Using hierarchical equations of motion to treat structured vibrational baths, we quantify both system coherence and non-Markovianity via the l1 norm of coherence and the Breuer-Laine-Piilo measure, respectively. We find that cavity coupling enhances coherence in overdamped environments but can suppress memory-assisted coherence in resonant underdamped regimes, even in the absence of significant photon loss. This suppression arises from hybridization-induced modification of system-bath information flow. We demonstrate that cavity coupling does not universally protect coherence but establishes limits governed by the competition between vibrational recurrence time scales and polaritonic hybridization.