Fig. 2: Bosonic mapping of molecular polaritons.
From: Radiative pumping vs vibrational relaxation of molecular polaritons: a bosonic mapping approach
A permutationally symmetric wavefunction of the entire molecular ensemble and cavity remains in the permutationally symmetric subspace throughout its evolution generated by \(\hat{H}\). Hence, a dramatic simplification of the simulation can be afforded by working in the bosonic subspace. In this bosonic representation, the vibronic states \(| g,{\varphi }_{i}^{(g)}\left.\right\rangle\) and \(| e,{\varphi }_{i}^{(g)}\left.\right\rangle\) are mapped to the harmonic oscillators \({\hat{b}}_{i}\) and \({\hat{B}}_{i}\) carrying a number of excitations equal to the number of molecules in such states. Similarly, the vibronic coupling \({V}_{eg,ij}=\langle {\varphi }_{i}^{(g)}| {\hat{V}}_{eg}| {\varphi }_{j}^{(g)}\rangle\) between excited vibronic states now couples vibronic modes.
