We introduce an approach to studying a driven qubit-oscillator system in the ultrastrong coupling regime, where the ratio g/Ω between coupling strength and oscillator frequency approaches unity or goes beyond, and simultaneously for driving strengths much bigger than the qubit energy splitting (extreme driving). Both qubit-oscillator coupling and external driving lead to a dressing of the qubit tunneling matrix element of different nature: the former can be used to suppress selectively certain oscillator modes in the spectrum, while the latter can bring the qubit's dynamics to a standstill at short times (coherent destruction of tunneling) even in the case of ultrastrong coupling.
@article{arxiv.1009.1485,
title = {Qubit-oscillator system under ultrastrong coupling and extreme driving},
author = {Johannes Hausinger and Milena Grifoni},
journal= {arXiv preprint arXiv:1009.1485},
year = {2011}
}