Essential vs Removable Bath Anharmonicity: Path Integral Results with Model Electronic-Vibrational Baths

Fully quantum mechanical real-time path integral calculations on a two-level system (TLS) interacting with a simple or composite anharmonic bath are presented. The bath consists of a few or many units, each comprising two or three electronic states coupled to secondary harmonic vibrational baths. The primitive harmonic bath approximation leads to qualitatively wrong system dynamics at high temperatures, while the effective harmonic bath mapping becomes exact in the macroscopic bath limit. Significant deviations are observed when the number of bath units is small, including skewing and blue shifts in the population oscillations and enhanced or suppressed coherence. These effects reflect the essential anharmonic character of the bath and cannot be captured by harmonic bath treatments.