Design and analysis of photonic crystal coupled cavity arrays for quantum simulation

We performed an experimental study of coupled optical cavity arrays in a photonic crystal platform. We find that the coupling between the cavities is significantly larger than the fabrication-induced disorder in the cavity frequencies. Satisfying this condition is necessary for using such cavity arrays to generate strongly correlated photons, which has potential application in the quantum simulation of many-body systems.

Figure 1

Scanning electron micrograph (SEM) images of CCA with (a) 4 cavities, (b) 9 cavities, and (c) 16 cavities. The simulated electric field profiles for each of the two supermodes of the coupled cavities are shown: (d), (e) for ${60}^{\circ }$ coupled cavities; (f), (g) for laterally coupled cavities; (h), (i) for vertically coupled cavities.

Figure 2

The PL spectra of the CCA for (a) 4, (b) 9, and (c) 16 cavities. We can clearly identify all the cavity array modes. We focus on several specific separations between the CCA modes labeled ${\Delta }_1$ through ${\Delta }_6$ in the plots and perform statistical analysis. We also observed several low-$Q$ modes at long wavelengths for several cavity arrays, as can be seen in part (a). These modes are not the actual coupled cavity modes under study, which is confirmed by monitoring the resonance frequencies of single (uncoupled) $L3$ cavities fabricated in the same chip. (d) PL spectra collected from the bulk QDs. (e) Lorentzian fits to the highest frequency modes [shaded in (a), (b), and (c)] to estimate the quality factors. The estimated quality factors for the highest frequency mode in 4, 9, and 16 CCA are $\sim$1800, $\sim$2800, and $\sim$2500, respectively.

Figure 3

FDTD simulation of the effect of disorder on the observed mode separations in a photonic molecule: (a) perturbation where a side hole in the cavity is changed; (b) perturbation where a hole in between two cavities is changed; (c) the observed mode separations as a function of the perturbed hole radius for two cases shown in (a) and (b). The unperturbed hole radius is 60 nm.

Figure 4

Numerically calculated eigenspectra of the coupled cavities: the eigenfrequencies as a function of the disorder standard deviation ${\sigma }_f$ for (a) 4, (b) 9, and (c) 16 cavities in the arrays. The spacings between the cavities are the same as the structures shown in the SEM images in Figs. 1a, 1b, 1c. The differences in the subsequent eigenvalues are shown as a function of ${\sigma }_f$ for (d) 4, (e) 9, and (f) 16 cavities in the arrays. We note that the mode separations increase linearly with increasing ${\sigma }_f$ when ${\sigma }_f$ is much greater than the coupling strengths, as found in the theory from a simple photonic molecule. Insets magnify the region of low disorder, and we identify the mode separations ${\Delta }_1\to {\Delta }_6$.

Figure 5

The mode separations ${\Delta }_1\to {\Delta }_6$ as a function of the photonic crystal hole radius. A decreasing trend in the separation is observed with the increasing hole radius (the photonic crystal lattice periodicity $a$ is 246 nm). For comparison, the inset shows the numerically simulated (FDTD) coupling strength between two cavities placed diagonally as a function of the hole radius.