Figure 1

Experimental setup and example data. (a) Photograph of experimental nanocell used in the experiment. The cell has a wedge profile (shown schematically) resulting in a tunable vapor thickness. (b) Schematic of experimental setup. For details see main text. AOM—acousto-optic modulator, SM—single mode fiber, BS—$50:50$ beam splitter, FPD1/2—fast photodiodes. (c) Beat frequency between shifted and unshifted beams for each detector, from which a phase difference is measured. As the laser frequency is scanned, we obtain transmission (d) and relative phase shift (e) information, shown here for a vapor thickness $\ell =\lambda /2$ and $T=250°\mathrm{C}$ across the $D2$ resonance, fitted to theory (solid black lines). Panel (f) shows the inferred refractive indices for the shifted (dashed) and unshifted (solid) beams—the solid line in (e) is the difference of these two curves. Zero on the detuning axis represents the weighted line center of the $D2$ line.Reuse & Permissions

Figure 2

(a) Calculated refractive index as a function of temperature and detuning for the Rb $D2$ resonance. Solid (dashed) contour lines denote positive (negative) values. The maximum predicted index is 1.31. The density-dependent redshift can clearly be seen, and has a significant effect on the position of the maximum index. The dotted line shows the positions of the unshifted Doppler-broadened lines. (b, c) Experimental data for a thickness $\ell =250\mathrm{nm}$ and $T=330°\mathrm{C}$ ($N=5\times {10}^{16}{\mathrm{cm}}^{-3}$). Close to resonance, the large optical depth reduces signal to the point where accurate phase information is lost. Despite this, the fit is reasonable and we infer a maximum index $n=1.26\pm 0.02$.Reuse & Permissions

Figure 3

(a) Calculated group index as a function of temperature and detuning. The dashed black line represents the carrier detuning for the superluminal pulse. (b,c) Superluminal propagation of a 800 ps pulse through a vapor thickness $\ell =\lambda /2$ and temperature $T=255°\mathrm{C}$. Solid lines are experiment, dashed black lines are theory with an 800 ps FWHM Gaussian input pulse. The dashed green line is the theory without dipole-dipole interactions. Off resonance (${\Delta }_{\mathrm{c}}=-13\mathrm{GHz}$, thin red line) there is no interaction at this temperature and the pulse propagates through the vapor as it would through vacuum. On resonance, (${\Delta }_{\mathrm{c}}=-1.2\mathrm{GHz}$, thick blue line), the pulse is attenuated and arrives $(0.13\pm 0.01)\mathrm{ns}$ earlier than the off-resonance reference pulse, corresponding to a group index $n_g=-(1.0\pm 0.1)\times {10}^5$. (d) Total integrated counts for both signals verifies preservation of causality—the probability of detecting a photon is always higher in the reference pulse.Reuse & Permissions