Method of images applied to driven solid-state emitters

Abstract

Increasing the collection efficiency from solid-state emitters is an important step towards achieving robust single photon sources, as well as optically connecting different nodes of quantum hardware. A metallic substrate may be the most basic method of improving the collection of photons from quantum dots, with predicted collection efficiency increases of up to 50%. The established 'method-of-images' approach models the effects of a reflective surface for atomic and molecular emitters by replacing the metal surface with a second fictitious emitter which ensures appropriate electromagnetic boundary conditions. Here, we extend the approach to the case of driven solid-state emitters, where exciton-phonon interactions play a key role in determining the optical properties of the system. We derive an intuitive polaron master equation and demonstrate its agreement with the complementary half-sided cavity formulation of the same problem. Our extended image approach offers a straightforward route towards studying the dynamics of multiple solid-state emitters near a metallic surface

Optimal power generation using dark states in dimers strongly coupled to their environment

“…is a product of displacement operators, themselves defined by [22][23][24]. After applying the polaron transformation to the full Hamiltonian(6), we subsequently partition the terms into system, environment and interaction Hamiltonians in the usual way [22,24,28]. We find that both the photon and phonon environment Hamiltonians are unchanged.…”

“…The monomer electronic transition rates, w G m ( ) j in (27) are discussed in appendix A.3. These cannot be derived analytically and the usual approximation would be to assume that the photon spectral density is flat for frequencies near to the eigenfrequencies of the system [22,28]. This is the flat spectral density approximation (FSDA).…”

Analytic expression for the optical exciton transition rates in the polaron frame

“…A commonly used method to derive master equations in the strong vibrational coupling regime is to use the polaron transformation [10,18,22,23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. A two-level exciton system coupled to only a vibrational bath that is displaced depending on the system eigenstate can be exactly diagonalized using the polaron transformation [18,41,42]-this is the independent boson model.…”

An analytic expression for the optical exciton transition rates in the polaron frame

“…A commonly used method to derive master equations in the strong vibrational coupling regime is to use the polaron transformation [10,18,22,23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. A twolevel exciton system coupled to only a vibrational bath that is displaced depending on the system eigenstate can be exactly diagonalised using the polaron transformation [18,41,42]-this is the independent boson model.…”

“…Thus, * bwl4@st-andrews.ac.uk a second-order master equation derived in the polaron frame will not break down due to strong vibrational coupling so long as the system is driven weakly [18,29]. The caveat is that the optical transition rates in the polaron frame are difficult to solve analytically owing to the nonadditive interaction, and are numerically tractable only in special cases [18,30,31,33].…”