We propose an analytical procedure to fully solve a two-level system coupled to phonons. Instead of using the common formulation in terms of linear and quadratic system-phonon couplings, we introduce different phonons depending on the system electronic level. We use this approach to recover known results for the linear-coupling limit in a simple way. More importantly, we derive results for the quadratic coupling induced by a phonon frequency change, a problem considered up to now as not analytically solvable.
@article{arxiv.1812.09043,
title = {Two-level System coupled to Phonons: Full Analytical Solution},
author = {Aurélia Chenu and Shiue-Yuan Shiau and Monique Combescot},
journal= {arXiv preprint arXiv:1812.09043},
year = {2019}
}