Semi-empirical quantum optics for mid-infrared molecular nanophotonics

Nanoscale infrared (IR) resonators with sub-diffraction limited mode volumes and open geometries have emerged as new platforms for implementing cavity quantum electrodynamics at room temperature. The use of IR nanoantennas and tip nanoprobes to study strong light-matter coupling of molecular vibrations with the vacuum field can be exploited for IR quantum control with nanometer spatial and femtosecond temporal resolution. In order to advance the development of molecule-based quantum nanophotonics in the mid-IR, we propose a generally applicable semi-empirical methodology based on quantum optics to describe light-matter interaction in systems driven by mid-IR femtosecond laser pulses. The theory is shown to reproduce recent experiments on the acceleration of the vibrational relaxation rate in infrared nanostructures. It also provides physical insights on the implementation of coherent phase rotations of the near-field using broadband nanotips. We then apply the quantum framework to develop general tip-design rules for the experimental manipulation of vibrational strong coupling and Fano interference effects in open infrared resonators. We finally propose the possibility of transferring the natural anharmonicity of molecular vibrational levels to the resonator near-field in the weak coupling regime to implement intensity-dependent phase shifts of the coupled system response with strong pulses and develop a vibrational chirping model to understand the effect. The semi-empirical quantum theory is equivalent to first-principles techniques based on Maxwell's equations, but its lower computational cost suggests its use as a rapid design tool for the development of strongly coupled infrared nanophotonic hardware for applications ranging from quantum control of materials to quantum information processing.