Equilibrium Stationary Coherence In The Multilevel Spin-Boson Model

Interaction between a quantum system and its environment can induce stationary coherences-off-diagonal elements in the reduced system density matrix in the energy eigenstate basis-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 multilevel spin boson 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 (h) over bar, gives qualitatively correct behavior at ambient temperatures for all configurations examined.