Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system

We introduce a photonic crystal waveguide-cavity system for controlling single-photon cavity quantum electrodynamics (QED). Exploiting Bloch mode analysis and medium-dependent Green function techniques we demonstrate that the propagation of single photons can be accurately described analytically for integrated periodic waveguides with little more than four unit cells, including an output coupler. We verify our analytical approach by comparing to rigorous numerical calculations for a range of photonic crystal waveguide lengths. The semiconductor-based nanophotonics system allows one to nanoengineer various regimes of cavity QED with unprecedented control. We demonstrate maximum Purcell factors of greater than 500 and on-chip single-photon beta factors of about 80% efficiency. Both weak and strong-coupling regimes are investigated, and the important role of waveguide length on the output emission spectra is shown for vertically emitted emission and output waveguide emission.

Figure 1

(Color online) Schematic of the waveguide-cavity single-photon source, which is composed of one cavity, one waveguide, and a QD (indicated by green filled circle, which would nominally be located at the slab center). The PC waveguide length is $L$. The blue-circled holes are shifted outward to increase the cavity quality factor.

Figure 2

(Color online) Simple component diagram of the waveguide-cavity system to aid the description of the theoretical formalism; the components include one cavity, one finite-size PC waveguide, and an infinite (or sufficiently long) output target waveguide at the left $\left(x<0\right)$.

Figure 3

(Color online) (a) The TE-like band structure of the planar PC (W1) waveguide (see Fig. 1). The filled red dot indicating the waveguide-cavity resonant frequency ${\omega }_c=0.79\text{eV}$ $(\sim 192\text{THz})$, with a corresponding $k\left({\omega }_c\right)=0.75\pi /a$. (b) Theoretical maximum Purcell factors of waveguide-cavity system vs frequency when $L=6a$ (dashed curve), the resonant frequency is labeled by red circle. For reference, we also show the bare cavity results with the solid curve for a cavity surrounded by a large number of holes on all sides; the frequency shift is a result of the different boundary conditions for the finite-size cavity.

Figure 4

(Color online) The distribution of electric-field amplitude $\left[\left|\mathbf{E}\left({\omega }_c\right)\right|\right]$ at slab center plane on a logarithmic scale.

Figure 5

(Color online) The dependence of (a) Purcell factor and (b) beta factor as a function of waveguide length, $L$. The data indicated by red circles are obtained from the full 3D numerical simulation, while the blue curves show the results from the derived analytical expression.

Figure 6

(Color online) Spectrum emitted vertically from the cavity mode (blue solid curve) and on-chip via the output waveguide mode (red dashed curve); also shown is the finite-size coupling coefficient $A_{fs}$ (black dotted curve). (a–c) $d=30\text{D}$ for $L=9a,10a,11a$, respectively. (d–f) $d=50\text{D}$ and $r=0.21$, for $L=109a,110a,111a$, respectively.