Figure 1

(a) Energy levels of ${}^{87}\mathrm{Rb}$ $D_2$-line transition for the $\mathsf{N}$-type EIT-based XPM experiment. Signal detuning is defined as ${\Delta }_s\equiv {\omega }_s-{\omega }_{24}$, where ${\omega }_s$ and ${\omega }_{24}$ are the frequencies of the signal field and the $|2\rangle \leftrightarrow |4\rangle$ transition, respectively. (b) ECDL, external-cavity diode laser; DL, diode laser; PBS, polarizing beam splitter; BS, beam splitter; AOM, acousto-optic modulator; $\lambda$/2, half-wave plate; $\lambda$/4, quarter-wave plate; POL, polarizer; SMF, single-mode fiber, PD, photodetector; P, pinhole; L, lens. (c) Schematic diagram of the probe and signal fields focused into the atomic cloud.Reuse & Permissions

Figure 2

(a) Nonlinear phase shift and (b) figure of merit as a function of mean photon number per signal pulse. The symbols and solid lines represent the measurement data and theoretical predictions, respectively. The inset shows the synchronous measurement of the probe transmission. The parameters for the blue theoretical curves are ${\Omega }_c=0.3\Gamma ,n{\sigma }_{13}L=16,{\gamma }_{21}=0.0025\Gamma ,{\gamma }_{31}={\gamma }_{42}=1.25\Gamma$, and ${\Delta }_s={\gamma }_{42}/2$. A 20-$\mu$s signal pulse containing $~80,000$ photons with a power of 1 nW corresponds to ${\Omega }_{s,\mathrm{eff}}=0.12\Gamma$, as calculated by Eq. (1). The parameter $\zeta$ represents the XPM figure of merit.Reuse & Permissions

Figure 3

Signal-detuning dependence of XPM phase shift with and without atoms. (a) In the presence of atoms. (b) In the absence of atoms. Squares and circles are the measured transmission and phase shift of the probe pulse, respectively. The parameters for the theoretical curves (solid lines) are ${\Omega }_c=0.3\Gamma ,n{\sigma }_{13}L=16,{\gamma }_{21}=0.0025\Gamma ,{\gamma }_{31}={\gamma }_{42}=1.25\Gamma$, and ${\Omega }_{s,\mathrm{eff}}=0.015\Gamma$ corresponding to 1200 photons per 20-$\mu$s signal pulse.Reuse & Permissions

Figure 4

Nonlinear phase shift and figure of merit as a function of signal photons. (a) XPM phase shift and corresponding probe transmission performed in the MOT (red) and in the SPOT (black). (b) XPM figure of merit in the two MOT systems (SPOT: black). The parameters for the theoretical curves are ${\Omega }_c=0.5\Gamma ,{\gamma }_{21}=0.0025\Gamma ,{\gamma }_{31}={\gamma }_{42}=1.25\Gamma$, and ${\Delta }_s={\gamma }_{42}/2$. $n{\sigma }_{13}L=16$ and 12 for the MOT and SPOT, respectively. A 10-$\mu$s signal pulse containing $~40,000$ photons with a power of 1 nW corresponds to ${\Omega }_{s,\mathrm{eff}}=0.12\Gamma$ in the MOT. In the SPOT, an 8-$\mu$s signal pulse containing $~32,000$ photons with a power of 1 nW corresponds to ${\Omega }_{s,\mathrm{eff}}=0.16\Gamma$.Reuse & Permissions