Light-matter decoupling and $A^2$ term detection in superconducting circuits

We study the spontaneous emission of a qubit interacting with a one-dimensional waveguide through a realistic minimal-coupling interaction. We show that the diamagnetic term $A^2$ leads to an effective decoupling of a single qubit from the electromagnetic field. This effect is observable at any range of qubit-photon couplings. For this we study a setup consisting of a transmon that is suspended over a transmission line. Assuming a standard model of qubit-line interaction, we prove that the relative strength of the $A^2$ term is controlled with the qubit-line separation and show that, as a consequence, the spontaneous emission rate of the suspended transmon onto the line can increase with such separation, instead of decreasing.\footnote{Light-matter decoupling and $A^2$ term detection in superconducting circuits, J. J. Garcia-Ripoll, B. Peropadre, S. De Liberato, arXiv:1410.7785}