Light-matter decoupling and A(2) term detection in superconducting circuits

The spontaneous and stimulated emission of a superconducting qubit in the presence of propagating microwaves originates from an effective light-matter interaction that, similarly to the case of the atomic case, can contain a diamagnetic term proportional to the square vector potential A(2). In the present work we prove that an increase in the strength of the diamagnetic term leads to an effective decoupling of the qubit from the electromagnetic field, and that this effect is observable at any range of qubit-photon coupling. To measure this effect we propose to use a transmon suspended over a transmission line, where the relative strength of the A(2) term is controlled by the qubit-line separation. We show that the spontaneous emission rate of the suspended transmon onto the line can, at short distances, increase with such a separation, instead of decreasing.