Equilibrium Coherence in the Multi-level Spin-boson Model

Interaction between a quantum system and its environment can induce stationary coherences -- off-diagonal elements in the reduced system density matrix -- even at equilibrium. This work investigates the ``quantumness'' of such phenomena by examining the ability of classical and semiclassical models to describe equilibrium stationary coherence in the multi-level spin boson (MLSB) model, a common model for light-harvesting systems. A well justified classical harmonic oscillator model is found to fail to capture equilibrium coherence. This failure is attributed to the effective weakness of classical system-bath interactions due to the absence of a discrete system energy spectrum and, consequently, of quantized shifts in oscillator coordinates. Semiclassical coherences also vanish for a dimeric model with parameters typical of biological light-harvesting, i.e., where both system sites couple to the bath with the same reorganization energy. In contrast, equilibrium coherence persists in a fully quantum description of the same system, suggesting a uniquely quantum-mechanical origin for equilibrium stationary coherence in, e.g., photosynthetic systems. Finally, as a computational tool, a perturbative expansion is introduced that, at third order in $\hbar$, gives qualitatively correct behavior at ambient temperatures for all configurations examined.