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.
ABSTRACT
We formulated the composition and temperature dependence of the Si and Si1-xGe x Raman shift from the perspectives of bond order-length-strength correlation and local bond average approach. It is verified that the Raman shift Δω varies in the form of Δω â zE1/2/ d, with inclusion of bond length d and energy E changing with temperature and composition. Numerical reproduction of the thermally induced Si1-xGe x phonon softening indicates that bond thermal expansion and energy loss dictate the frequency redshift, which resulted in quantitative information on the bond energy and the reference frequencies from which the Raman shifts proceed. Observations not only gain deeper insight into the mechanism of the Raman shift but also demonstrate the revealing power of Raman technique for the bonding thermodynamics.
