A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the QE is partially stabilized in its excited state. We put forward a general approach for calculating the energy level shift at a negative freque
ncy $omega$, which is just the negative of the nonresonant part for the energy level shift at positive frequency $-omega$. 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 in the presence of a bound state can be obtained by the method based on the Greens function expression for the evolution operator. A general criterion for identifying the existence of a bound state is presented. These are numerically demonstrated for a QE located around a nanosphere and in a gap plasmonic nanocavity. These findings are instructive in the fields of coherent light-matter interactions.
We put forward a general approach for calculating the quantum energy level shift for emitter in arbitrary nanostructures, in which the energy level shift is expressed by the sum of the real part of the scattering photon Green function (GF) and a simp
le integral about the imaginary part of the photon GF in the real frequency range without principle value. Compared with the method of direct principal value integral over the positive frequency axis and the method by transferring into the imaginary axis, this method avoids the principle value integral and the calculation of the scattering GF with imaginary frequency. In addition, a much narrower frequency range about the scattering photon GF in enough to get a convergent result. It is numerically demonstrated in the case for a quantum emitter (QE) located around a nanosphere and in a gap plasmonic nanocavity. Quantum dynamics of the emitter is calculated by the time domain method through solving Schr{o}dinger equation in the form of Volterra integral of the second kind and by the frequency domain method based on the Greens function expression for the evolution operator. It is found that the frequency domain method needs information of the scattering GF over a much narrower frequency range. In addition, reversible dynamics is observed. These findings are instructive in the fields of coherent light-matter interactions.
Photon Green function (GF) is the vital and most decisive factor in the field of quantum light-matter interaction. It is divergent with two equal space arguments in arbitrary-shaped lossy structure and should be regularized. We introduce a finite ele
ment method for calculating the regularized GF. It is expressed by the averaged radiation electric field over the finite-size of the photon emitter. For emitter located in homogeneous lossy material, excellent agreement with the analytical results is found for both real cavity model and virtual cavity model. For emitter located in a metal nano-sphere, the regularized scattered GF, which is the difference between the regularized GF and the analytical regularized one in homogeneous space, agrees well with the analytical scattered GF.
The effect of the dipole polarization on the quantum dipole dipole interaction near an Ag nanosphere (ANS) is investigated. A theoretical formalism in terms of classical Green function is developed for the transfer rate and the potential energy of th
e dipole dipole interaction (DDI) between two polarized dipoles. It is found that a linear transition dipole can couple to a left circularly polarized transition dipole much stronger than to a right circularly polarized transition dipole. This polarization selectivity exists over a wide frequency range and is robust against the variation of the dipoles position or the radius of the ANS. In contrast, a right circularly polarized transition dipole, can change sharply from coupling strongly to another right circularly polarized dipole to coupling strongly to a left circularly polarized dipole with varying frequency. However, if the two dipoles are placed in the same radial direction of the sphere, the right circularly polarized transition dipole can only couple to the dipole with the same polarization while not to the left circularly polarized transition dipole. These findings may be used in solid-state quantum-information processing based on the DDI.
Dipole-dipole interaction between two two-level `atoms in photonic crystal nanocavity is investigated based on finite-difference time domain algorithm. This method includes both real and virtual photon effects and can be applied for dipoles with diff
erent transition frequencies in both weak and strong coupling regimes. Numerical validations have been made for dipoles in vacuum and in an ideal planar microcavity. For dipoles located in photonic crystal nanocavity, it is found that the cooperative decay parameters and the dipole-dipole interaction potential strongly depend on the following four factors: the atomic position, the atomic transition frequency, the resonance frequency, and the cavity quality factor. Properly arranging the positions of the two atoms, we can acquire equal value of the cooperative decay parameters and the local coupling strength. Large cooperative decay parameters can be achieved when transition frequency is equal to the resonance frequency. For transition frequency varying in a domain of the cavity linewidth around the resonance frequency, dipole-dipole interaction potential changes continuously from attractive to repulsive case. Larger value and sharper change of cooperative parameters and dipole-dipole interaction can be obtained for higher quality factor. Our results provide some manipulative approaches for dipole-dipole interaction with potential application in various fields such as quantum computation and quantum information processing based on solid state nanocavity and quantum dot system.
