Weak-value amplification of the fast-light effect in rubidium vapor

We use weak-value amplification to enhance the polarization-sensitive fast-light effect from induced Raman absorption in hot rubidium vapor. We experimentally demonstrate that projecting the output signal into an appropriate polarization state enables a pulse advancement of $4.2\mu \mathrm{s}$, which is more than 15 times larger than that naturally caused by dispersion. More significantly, we show that combining weak-value amplification with the dispersive response of an atomic system provides a clear advantage in terms of the maximum pulse advance achievable for a given value of loss. This technique has potential applications for designing novel quantum-information-processing gates and optical buffers for telecommunication systems.

Figure 1

Top panel: The absorption profile of a Lorentzian lineshape. Middle panel: The refractive index associated with the absorption line can be calculated using the Kramers-Kronig relations. Bottom panel: The group index for the same line. The horizontal axis for all the panels are identical and denote the frequency detuning from resonance, normalized by the line width of the Lorentzian line shape.

Figure 2

Left panel: Schematic diagram of a three-level $\mathrm{\Lambda }$ system. Right panel: The hyperfine energy levels of ${}^{85}\mathrm{Rb}$.

Figure 3

Schematic of the experimental setup. The continuous wave laser beam is divided to two copies using a nonpolarizing beam splitter. The signal is frequency shifted using an acousto-optic modulator (AOM1) in double path (the figure shows a single path to simplify visualization). AOM2 is used to shape the signal beam to Gaussian pulses. The polarization state of the pump and the signal are controlled using wave plates. The postselection is done using a polarizer and a fast detector. The output photocurrent is analyzed by an oscilloscope.

Figure 4

Power transmission as a function of frequency detuning from Raman absorption. The blue curve presents the experimental data and the red curves shows the theoretical fit assuming a Lorentzian (with $2\gamma =34$ kHz) line shape for the susceptibility.

Figure 5

Top: Measured optical power as a function of time for $|H\rangle ,|V\rangle$, and for the output corresponding to the postselection angles $\theta =-{40}^{\circ }$ and $\theta =-{50}^{\circ }$. The origin of time is set to the center of the pulse for the vertical polarization state. The markers are added to aid visualization and do not represent the data points. Bottom: The amplification factor as a function of postselection angle. The blue curve shows theory prediction from Eq. (7). The amplification factor is inferred from data by performing a Gaussian fit. The error bars correspond to the $95\%$ confidence interval.

Figure 6

Maximum achievable time advance as a function of transmission efficiency (calculated from theory).