Enhanced Cross-Phase Modulation Based on a Double Electromagnetically Induced Transparency in a Four-Level Tripod Atomic System

We report experimental observations on the simultaneous electromagnetically induced transparency (EIT) effects for probe and trigger fields (double EIT) as well as the enhanced cross-phase modulation (XPM) between the two fields in a four-level tripod EIT system of the $D1$ line of ${}^{87}\mathrm{Rb}$ atoms. The XPM coefficients (larger than $2\times {10}^{-5}{\mathrm{cm}}^2/\mathrm{W}$) and the accompanying transmissions (higher than 60%) are measured at a slight detuning of the probe field from the exact EIT-resonance condition. The system and enhanced cross-Kerr nonlinearities presented here can be applied to quantum information processes.

Figure 1

Experimental setup.

Figure 2

The measured simultaneous EIT windows for (a) probe and (b) trigger beams created by a coupling beam with a power of 14 mW at detuning ${\Delta }_C=0$.

Figure 3

The measured probe absorption [(a) and (e)] as well as dispersion [(b) and (f)], and trigger absorption [(c) and (g)] as well as dispersion [(d) and (h)] signals as the function of ${\Delta }_P$ for ${\Delta }_C={\Delta }_T=0$ and $Pc=14\mathrm{mW}$.

Figure 4

Curves (A) and (B) are the measured probe and trigger XPM coefficients at ${\Delta }_P-{\Delta }_C\approx -0.5\mathrm{MHz}$ as a function of ${\Delta }_C$, respectively, for $P_P\approx P_T\approx 14\mu \mathrm{W}$. Curves ($A^{\prime }$) and ($B^{\prime }$) are corresponding theoretical results with experimental parameters ${\gamma }_0=3.5\mathrm{MHz}$, ${\gamma }_1=0.5\mathrm{MHz}$, ${\gamma }_2=1.5\mathrm{MHz}$, ${\gamma }_3=1.0\mathrm{MHz}$, ${\Omega }_C=70\mathrm{MHz}$, ${\Omega }_P={\Omega }_T=4\mathrm{MHz}$, and $N=3.72\times {10}^{11}/{\mathrm{cm}}^3$. Curves (C) and (D) in the inset are the accompanying transmissions of probe and trigger beams at ${\Delta }_P-{\Delta }_C\approx -0.5\mathrm{MHz}$.