Quantum resource-theoretical analysis of the role of vibrational structure in photoisomerization

Thermodynamical systems at the nanoscale, such as single molecules interacting with highly structured vibrational environments, typically undergo non-equilibrium physical processes that lack precise microscopic descriptions. Photoisomerization is such an example which has emerged as a platform on which to study single-molecule ultrafast photochemical processes from a quantum resource theoretic perspective. However, upper bounds on its efficiency have only been obtained under significant simplifications that make the mathematics of the resource-theoretical treatment manageable. Here we generalize previous models for the photoisomers, while retaining the full vibrational structure, and still get analytical bounds on the efficiency of hotoisomerization. We quantify the impact of such vibrational structure on the optimal photoisomerization quantum yield both when the vibrational coordinate has no dynamics of its own and when we take into account the vibrational dynamics. This work serves as an example of how to bridge the gap between the abstract language of quantum resource theories and the open system formulation of nanoscale processes.