Collective dipole-dipole interactions in planar nanocavities

The collective response of an atomic ensemble is shaped by its macroscopic environment. We demonstrate this effect in the near-resonant transmission of light through a thermal rubidium vapor confined in a planar nanocavity. Our model reveals density-dependent line shifts and broadenings beyond continuous electrodynamics models that oscillate with cavity width and have been observed in recent experiments. We predict that the amplitudes of these oscillations can be controlled by coatings that modify the cavity's finesse.

Figure 1

(a) Free-space (solid blue or dark gray line) and cavity-mediated (solid orange or light gray line) atom-atom and atom-wall interactions (dashed lines). (b) Sketch of the setup: Incident light is scattered by atoms in a cavity of width $d$ and focused onto a detector by a lens of radius $R$.

Figure 2

Slope of collective shift (top) and broadening (bottom) over width $d$ of a vapor-filled sapphire cavity in simulation (${}^{85}\mathrm{Rb}$, room temperature, density $\simeq 1k^3$) and experiment [16] (${}^{39}\mathrm{K}$, temperature varied up to $600\mathrm{K}$, density up to $100k^3$). In textbook electrodynamics, a constant Lorentz-Lorenz shift (dotted line) and no additional broadening is expected. Simulation error bars correspond to $1\sigma$, and solid lines are spline interpolations.

Figure 3

Cavity designs of finesse $\mathcal{F}$ with (a) no, (b) antireflection, or (c), (d) Bragg mirror coating with $\lambda /\left(4n\right)$ layers.

Figure 4

Slope of collective shift (top) and broadening (bottom) over width $d$ of an atomic layer in free space and in the coated cavities depicted in Fig. 3. Error bars correspond to $1\sigma$, and solid lines are spline interpolations.