Collective emission and selective radiance in atomic clouds and arrays coupled to a microring resonator

Abstract

We theoretically investigate the collective dipole-dipole interactions in atoms coupled to a nanophotonic microring resonator. The atoms can interact with each other through light-induced dipole-dipole interactions mediated by free space and through the resonator whispering-gallery modes. The differing characteristics and mismatched wavenumbers of these modes give rise to complex dynamics and provide new opportunities for controlling light-matter interactions. We explore these phenomena in the context of an experimentally realized atom cloud and study the potential of the proposed sub-wavelength atom arrays.

Figures (7)

• Figure 1: Schematic of the experimental system. (a) Cold atoms are trapped above the microring resonator, interacting with a WGM. The WGM is circularly polarized to drive the $\sigma^{+}$ cycling transition $\ket{g}\rightarrow\ket{e}$. The microring resonator has a total circumference of around $120 \mathrm{\mu m}$. (b,c) Interacting atomic ensemble (with $2 \mathrm{\mu m}$ r.m.s. along the y-direction) and organized atom array collectively emit photons into the WGM and the free space modes with photon emission rates $R_c$ and $R_f$, respectively.
• Figure 2: (a,b) Ensemble averaged decay rate into free space when an atom cloud is excited to (a) the steady state (SS) or (b) the timed-Dicke state (TDS) with a WGM of wavenumber $k_{\mathrm{wg}}$. The color scale depicts the number of atoms in the atom cloud. (c,d) Histograms of the distribution of the excitation decay rate into (c) free space and (d) into the cavity when taking individual random realizations of the atomic cloud with $N = 60$ atoms and $C_1 = 0.05$. The average value of the histogram has been plotted as vertical dashed lines of the corresponding color. The results are averages over 5000 random configurations.
• Figure 3: The measured and calculated linewidth of the steady state transmission spectrum as a function of the number of atoms for $C_1 = 0.05$. Blue squares with error bars denote experimental data. Red circles with lines show theoretical calculations. The black triangles and orange diamonds with dashed lines show the theoretical calculation of hypothetical situations where there is no free space collective dipole-dipole interaction or when there are no stochastic effects.
• Figure 4: The ratio of decay rates for a cloud of atoms with uniform $C$ for the TDS and the SS. In both cases, the excitation decay ratio $\gamma_c/\gamma_f$ tends to be close to $NC_1$. The photon rate decay ratio $\Gamma_c/\Gamma_f$ increases or decreases depending on the type of excitation. The results are averaged over 2000 random configurations.
• Figure 5: The decay rate into free space when a perfect atom array with 20 atoms is excited to the TDS through the resonator, as the separation $d$ and the WGM wavenumber $k_{\mathrm{wg}}$ are varied. The white point denotes the proposed parameters of the experiment, giving $\gamma_f = 0.035 \Gamma_0$.