Observation and Measurement of Interaction-Induced Dispersive Optical Nonlinearities in an Ensemble of Cold Rydberg Atoms

We observe and measure dispersive optical nonlinearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical nonlinearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the “blockaded fraction” of atoms within the atomic ensemble.

Figure 1

(a) An ensemble of $N$ three-level atoms inside an optical cavity is excited by a strong (blue) coupling field, and a weak (red) signal field, all detuned from resonance with respect to the $5S_{1/2}\to 5P_{3/2}\to n{D}_{5/2}$ transitions in Rubidium 87. (b) Principle of the measurements. Lower part: black: cavity scan without atoms, red: without the blue beam, blue: with blue light at very low red intensity. $\theta$ is the signal laser-cavity detuning (in units of cavity linewidth), scanned with the cavity length. Upper part: corresponding real part of susceptibilities. The effect of blockade is indicated by the green arrows. (c) Measured transmission versus $\theta$ with the coupling field on (green or right) or off (red or left) for different normalized red intensities $Y$ in the case of the $n=61$ state. The differential peak shift, denoted by $\Phi (Y)$, is reduced by the blockade for increasing intensities (see text).

Figure 2

(a) Normalized cavity shift $\Phi (Y)/\Phi (0)$ versus normalized input red intensity $Y$, for several Rydberg states with $n=46$ (black triangles), 50 (green diamonds), 56 (red circles), 61 (blue squares). The full lines correspond to the initial slopes of the curves, which are expected to be of the form $1-s_{n}Y$. (b) Value of $s_n$ as a function of ($n\mathrm{\text{−}}d$), in logarithmic scales. The slope of this curve gives the expected power law behavior. (c) Normalized cavity shift $\Phi (Y)/\Phi (0)$ as a function of the normalized input red intensity $Y$, for the Rydberg state $n=61$, for two different atomic densities ${\rho }_{\mathrm{low}}\sim 0.02\mathrm{at}/\mu {\mathrm{m}}^3$ (orange circles), and ${\rho }_{\mathrm{high}}\sim 0.04\mathrm{at}/\mu {\mathrm{m}}^3$ (blue squares) but for the same number of atoms coupled to the probe mode. The observed change in slope is consistent with the expected ratio ${\rho }_{\mathrm{high}}/{\rho }_{\mathrm{low}}\sim 2$ of the densities.