In situ characterization of an optically thick atom-filled cavity

A means for precise experimental characterization of the dielectric susceptibility of an atomic gas inside an optical cavity is important for the design and operation of quantum light-matter interfaces, particularly in the context of quantum information processing. Here we present a numerically optimized theoretical model to predict the spectral response of an atom-filled cavity, accounting for both homogeneous and inhomogeneous broadening at high optical densities. We investigate the regime where the two broadening mechanisms are of similar magnitude, which makes the use of common approximations invalid. Our model agrees with an experimental implementation with warm caesium vapor in a ring cavity. From the cavity response, we are able to extract important experimental parameters, for instance the ground-state populations, total number density, and the magnitudes of both homogeneous and inhomogeneous broadening.

Figure 1

We consider the transmission response of a cavity containing some atomic medium, where the intracavity ensemble could be warm vapors, cold atoms, or solid-state systems.

Figure 2

(a) Schematic of the ring-cavity design experimentally implemented. (b) Energy-level $\mathrm{\Lambda }$ configuration of the caesium $D_2$ transition. The ensemble is initialized into the $F=4$ hyperfine ground state via optical pumping.

Figure 3

Extracted parameters as a function of measured temperature. Blue circles indicate values obtained using the automated fitting routine, and red crosses indicate those obtained using manual fits. (a) Optical pumping efficiency: the fall in pumping efficiency seen at $60{}^{\circ }\mathrm{C}$ indicates the temperature below which the automated fitting routine no longer converges. The plateau in polarization as the temperature is reduced (instead of increasing to unity), observed in these data, likely arises from a combination of imperfect mode overlap and limited pumping light entering the cavity. (b) Caesium number density: the green line gives the number density expected if the caesium reservoir were held at the temperature measured at the cell surface.

Figure 4

Example of (a) manual search result at $40{}^{\circ }\mathrm{C}$ and (b) automatic fit at $85{}^{\circ }\mathrm{C}$. The dashed lines indicate the frequencies corresponding to the center of the two hyperfine resonances, $F=4$ at $-9.2\mathrm{GHz}$ and $F=3$ at 0 detuning. Circles indicate experimental data, and the lines indicate the theoretical response for manually fitted parameters. (c) Comparison of modeled cavity response from automatic fit at $85{}^{\circ }\mathrm{C}$ [as in (b), red line] with cavity response with no atoms present (black dashed line).

Figure 5

Cavity transmission, locked to resonance at $6\mathrm{GHz}$ blue detuned from the $F=3$ resonance. Showing our model, from fitted parameters obtained from measurements at $5{}^{\circ }\mathrm{C}$ intervals. Blue surfaces indicate the frequencies of the two $D_2$ resonances, and the red surface indicates the position of the cavity lock. Solid red lines indicate the model obtained using a fitting routine; red dashed lines show the manually obtained models.