k-photon decay rates from complex dilated floquet Hamiltonians

Complex dilation is known as an efficient tool for the extraction of total decay rates of atomic systems under strong external perturbations. This method is however believed to be unsuited to access partial decay rates into specific decay channels. We show that the latter indeed can be derived from the eigenstates of complex dilated Hamiltonians. As a specific example we demonstrate our novel approach to quantify the decay rates of periodically driven Rydberg systems into well defined k-photon ionisation channels.