Superradiance for Atoms Trapped along a Photonic Crystal Waveguide

We report observations of superradiance for atoms trapped in the near field of a photonic crystal waveguide (PCW). By fabricating the PCW with a band edge near the $D_1$ transition of atomic cesium, strong interaction is achieved between trapped atoms and guided-mode photons. Following short-pulse excitation, we record the decay of guided-mode emission and find a superradiant emission rate scaling as ${\overline{\mathrm{\Gamma }}}_{\mathrm{SR}}\propto \overline{N}{\mathrm{\Gamma }}_{1\mathrm{D}}$ for average atom number $0.19\lesssim \overline{N}\lesssim 2.6$ atoms, where ${\mathrm{\Gamma }}_{1\mathrm{D}}/{\mathrm{\Gamma }}^{\prime }=1.0\pm 0.1$ is the peak single-atom radiative decay rate into the PCW guided mode, and ${\mathrm{\Gamma }}^{\prime }$ is the radiative decay rate into all the other channels. These advances provide new tools for investigations of photon-mediated atom-atom interactions in the many-body regime.

Figure 1

Trapping and interfacing atoms with an APCW. (a) A SI beam is reflected from an APCW (gray shaded structure) to form a dipole trap to localize atoms. The red shaded region represents trapped atoms along the APCW. An incident field $E_{\text{in}}$ excites the TE-like mode and trapped atoms couple to this guided mode. The inset shows a SEM image of the APCW and corresponding single-atom coupling rate ${\mathrm{\Gamma }}_{1\mathrm{D}}$ along the $x$ axis at the center of the gap ($y=0$). (b) Normalized intensity cross section of the total intensity $I_{\mathrm{tot}}$ resulting from the SI beam and its reflection. Trap locations along the $z$ axis at $y=0$ are marked by $z_i$. Masked gray areas represent the APCW. (c) The single-atom coupling rate into the TE-like guided mode ${\mathrm{\Gamma }}_{1\mathrm{D}}(0,y,z)$ normalized to ${\mathrm{\Gamma }}_0$ where ${\mathrm{\Gamma }}_0$ is the Einstein-$A$ coefficient for free space.

Figure 2

Lifetime of trapped atoms near the APCW. (a) $1/e$ lifetime of ${\tau }_{\mathrm{fs}}=54\pm 5\mathrm{ms}$ is determined using free-space absorption imaging of the trapped atom cloud. (b) $1/e$ lifetime of ${\tau }_{\mathrm{GM}}=28\pm 2\mathrm{ms}$ is observed from the normalized transmission $T/T_0$ of a resonant GM probe.

Figure 3

Decay rate and atom number. (a) Fitted total decay rate ${\overline{\mathrm{\Gamma }}}_{\mathrm{tot}}$ normalized with ${\mathrm{\Gamma }}_0$ (circles) as a function of measurement time $t_m$. The solid line is an exponential fit to determine the superradiant decay rate ${\overline{\mathrm{\Gamma }}}_{\mathrm{SR}}/{\mathrm{\Gamma }}_0=1.1\pm 0.1$ and the single-atom decay rate ${\overline{\mathrm{\Gamma }}}_{\mathrm{tot}}^{(1)}/{\mathrm{\Gamma }}_0=2.0\pm 0.1$ with ${\tau }_{\mathrm{SR}}=17\pm 3\mathrm{ms}$. The inset shows the normalized temporal profiles of backward emission $I_p$. Exponential fits (solid curves): $t_m=3\mathrm{ms}$ (red), 13 ms (green), and 63 ms (blue). The black dashed curve shows exponential decay with ${\mathrm{\Gamma }}_0$. (b) Fitted total decay rate ${\overline{\mathrm{\Gamma }}}_{\mathrm{tot}}/{\mathrm{\Gamma }}_0$ as a function of the mean number of trapped atoms $\overline{N}$. We adjust $\overline{N}$ by changing the trap hold time (red) or atom loading time (blue). The black line is a linear fit to the combined data sets giving ${\overline{\mathrm{\Gamma }}}_{\mathrm{SR}}=\eta \overline{N}{\mathrm{\Gamma }}_{1\mathrm{D}}$ with $\eta =0.34\pm 0.06$.

Figure 4

Steady-state transmission spectra $T(\mathrm{\Delta })$ and fitted atomic linewidth ${\overline{\mathrm{\Gamma }}}_m$. (a) $T(\mathrm{\Delta })$ with $\mathrm{\Delta }=0$ corresponding to the free-space line center. The three sets of points are measured at relative densities $\rho /{\rho }_0=0.12$ (black), 0.24 (blue), and 1 (red). Solid curves are Lorentzian fits to determine the linewidth ${\overline{\mathrm{\Gamma }}}_m$. (b) Fitted linewidths (circles) normalized to ${\mathrm{\Gamma }}_0$ as a function of $\rho /{\rho }_0$. The solid line is a linear fit with intercept of ${\overline{\mathrm{\Gamma }}}_m^{(1)}/{\mathrm{\Gamma }}_0=2.1\pm 0.1$.