Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide

We present an intuitive photon Green function formalism to study strong coupling via reflection or transmission of light in a planar-photonic-crystal waveguide that is side coupled to a nanocavity containing only one quantum dot. Analytical results allow physical insight and useful formulas to optimally design such integrated systems in a realistic way and we subsequently demonstrate that strong coupling should be achievable using present day photonic crystals and quantum dots, yielding single-exciton vacuum Rabi splittings of around $0.1–1\mathrm{meV}$.

Figure 1

Schematic of the proposed PC waveguide/nanocavity coupling scheme, showing a plan view. The quantum dot (QD) is located within the nanocavity which has an exciton resonance close to the cavity resonance. The propagating field excites the defect cavity ${\mathbf{e}}_c$, which couples to the propagating Bloch mode ${\mathbf{e}}_k$ and to the embedded exciton. The modes are shown by the concentric circles. The pitch in the direction of propagation ($x$ direction) is $a$, and the grey circles represent the air holes in a semiconductor photonic crystal stucture.

Figure 2

Reflection versus frequency for on (solid curce) and off (dashed curve) resonance with the quantum dot for three different effective mode volumes (see text). (a) Nominal parameters as given in the text. (b) The ratio of $d^2∕V_m$ increased by a factor of 10. (c) The ratio of $d^2∕V_m$ decreased by a factor of 10.

Figure 3

Reflection versus frequency corresponding to Fig. 2a but with a near-resonance (solid curve) cavity detuning $({\omega }_d-{\omega }_c)$ of (a) $0.3\mathrm{meV}$, (b) $0.6\mathrm{meV}$, and (c) $0.9\mathrm{meV}$.

Figure 4

Reflection versus frequency corresponding to Fig. 2a with (a) nominal dephasing rate ($0.002\mathrm{meV}$; see text), (b) 10 times larger dephasing rate, and (c) 100 times larger dephasing rate.