Abstract
We present a general quasimode formalism for the quantum treatment of quantum-dot–photon dynamics in coupled-cavity systems in photonic-crystal slabs. The coupled-cavity systems are characterized by a large number of discrete lossy nonorthogonal quasimodes that can be obtained using a combination of the finite-difference time-domain method and the tight-binding approach. We project the electric field Green tensor onto the quasimodes using a non-Hermitian projector and thereby avoid the prohibitive finite-difference time-domain calculation of the Green tensor in large systems. We extend our projection approach to show that the quantum dynamics can be derived from an effective non-Hermitian Hamiltonian that is the full Hamiltonian projected onto the quasimode basis. We demonstrate the equivalence of the effective Hamiltonian approach with the Green tensor approach for the case of spontaneous emission and show how it can be used to treat multiple-photon, multiple-dot dynamics. The effective Hamiltonian provides a systematic approach to treating interacting quantum-dot–photon dynamics in coupled-cavity systems with a moderate number of quantum dots and photons and can be easily generalized to include nonradiative decay and decoherence of the quantum dots. Finally, we use our approach to model spontaneous emission in an asymmetric two-cavity system in a photonic crystal slab. We show that results obtained using our approach are essentially identical to results using the full Green tensor in the weak-coupling regime. In the strong-coupling regime, we show that the spontaneous emission dynamics are strongly affected by the nonorthogonality of the quasimodes and the results can be easily understood in terms of the quasimode dressed states.
- Received 17 December 2007
DOI:https://doi.org/10.1103/PhysRevA.77.053805
©2008 American Physical Society