Level shift and decay dynamics of a quantum emitter around a plasmonic nanostructure

We put forward a general approach for calculating the energy level shift of a quantum emitter (QE) in arbitrary-shaped nanostructure. It is expressed by the sum of the real part and a simple integral of the imaginary part of the scattered photon Green's function (GF) in a rather narrow real frequency range without a principal value. Compared with the method of direct evaluation of the principal value integral along the positive frequency axis or the method of transferring the principal value into an integration along the imaginary frequency axis, our method avoids the principal value integral and the evaluation of the scattered GF with imaginary frequency. It is numerically demonstrated for a QE located around a nanosphere and in a gap plasmonic nanocavity. The decay dynamics of an excited QE is calculated using the time-domain method through solving the Schrodinger equation in the form of a Volterra integral of the second kind, and using the frequency-domain method based on the Green's function expression for the evolution operator. It is found that the frequency domain method requires much narrower band information of the scattered GF. These findings are instructive in the field of coherent light-matter interactions.