The role of the multiple excitation manifold in a driven quantum simulator of an antenna complex

Biomolecular light-harvesting antennas operate as nanoscale devices in a regime where the coherent interactions of individual light, matter and vibrational quanta are non-perturbatively strong. The complex behaviour arising from this could, if fully understood, be exploited for myriad energy applications. However, non-perturbative dynamics are computationally challenging to simulate, and experiments on biomaterials explore very limited regions of the non-perturbative parameter space. So-called `quantum simulators' of light-harvesting models could provide a solution to this problem, and here we employ the hierarchical equations of motion technique to investigate recent superconducting experiments of Poto{č}nik it{et} it{al.} (Nat. Com. 9, 904 (2018)) used to explore excitonic energy capture. By explicitly including the role of optical driving fields, non-perturbative dephasing noise and the full multi-excitation Hilbert space of a three-qubit quantum circuit, we predict the measureable impact of these factors on transfer efficiency. By analysis of the eigenspectrum of the network, we uncover a structure of energy levels that allows the network to exploit optical `dark' states and excited state absorption for energy transfer. We also confirm that time-resolvable coherent oscillations could be experimentally observed, even under strong, non-additive action of the driving and optical fields.