Detailed analysis of spontaneous emission of an atom in front of a mirror*

The spontaneous emission rate of a two-level atom is proportional to the local density of states of the electromagnetic modes of the environment close to its transition frequency.
In Ref. [1], this was experimentally demonstrated for a 1D environment using a transmon qubit placed in a coplanar waveguide at a distance from its shorted end. The short acts as a mirror and thus modifies the local density of states. Here, we analyse in detail the atom dynamics when the distance is such that the density of states at the transition frequency is vanishing. We find that this indeed corresponds to a dark state of the system and discuss how this dark state is approached. We also discuss the emission dynamics as a function of the coupling strength and distance between the atom and the mirror.

[1] Probing the quantum vacuum with an artificial atom in front of a mirror, I.-C. Hoi et al., Nature Physics 11, 10451049 (2015)