Abstract
A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time. We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics. We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists. A general criterion for identifying the existence of a bound state is presented. The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity. Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value. In addition, it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface, but nearly independent on the size of the nanosphere or the rod. Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.
Highlights
Coherent interaction between a quantum emitter (QE), such as atom, molecule or quantum dot, and the quantized electromagnetic field lies at the heart of quantum optics [1,2,3,4,5,6,7,8]
We have found that the critical dipole strength dc is heavily dependent on the dipole-sphere distance h but much less dependent on the sphere-radius a for the QE located around a nanosphere
For the QE at the center of a plasmonic nanocavity composed of two nanorods, we have found that dc is nearly independent of the radius and height of the rod
Summary
Coherent interaction between a quantum emitter (QE), such as atom, molecule or quantum dot, and the quantized electromagnetic field lies at the heart of quantum optics [1,2,3,4,5,6,7,8]. We have proposed a general numerical method for calculating the energy level shift of a QE in an arbitrary nanostructure for positive frequency [62]. One just needs to calculate the photon GF in the real frequency domain, in which no particular assumption about the permittivity of the material, such as the Drude model, should be made It removes most limitations, such as the usual tight-binding or a quadratic dispersion assumption for the case of a cavity array or photonic crystal, encountered in previous analytical approaches and allows us to solve the exact decay dynamics for an open system in an almost fully numerical way. The performance of the above methods for energy level shift in negative frequency domain, condition for the existence of bound state, excited-state population in the steady state and non-Markovian dynamics are shown.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
