Electromagnetically induced transparency and slow light in three-level ladder systems: Effect of velocity-changing and dephasing collisions

We present a theory of electromagnetically induced transparency (EIT) and slow light in a Doppler broadened three-level ladder (cascade) system incorporating residual Doppler broadening of two-photon coherence and velocity-changing and dephasing collision effects of a buffer gas. Both regimes of wave-vector mismatch occurring when either the probe frequency is higher than that of the (strong) control field or vice versa are considered. It is found that the velocity-changing collisions in general cause narrowing of EIT resonance linewidths which, in a particular wave-vector mismatch regime, can lead to large transparency and slow light generation at relatively low control field intensities. Large collisional dephasing of two-photon coherence in a ladder system, however, tends to mask these effects. A reduction in group velocity by more than 3 orders of magnitude is predicted in the regime where the probe frequency is lesser than that of the control field and in the absence of collisions.

Figure 1

Three-level ladder-system energy-level structure and interaction scheme.

Figure 2

Probe absorption $\left(\alpha /0.83{\alpha }_{\text{o}}\right)$ as a function of the two-photon detuning at a fixed control field amplitude ${\Omega }_{\text{c}}/{\gamma }_{\text{D}}=0.1$ and velocity-changing collisions rate ${\Gamma }_{31}/{\gamma }_{\text{D}}=0.1$ and for various collisional dephasing rate ${\gamma }_{\text{ph}}$. The value of the residual Doppler broadening is (i) $\delta k{v}_{\text{th}}/{\gamma }_{\text{D}}=+0.04$ and (ii) $\delta k{v}_{\text{th}}/{\gamma }_{\text{D}}=-0.04$. Curves a are the absorption profiles in the absence of buffer gas when ${\Gamma }_{31}={\gamma }_{\text{ph}}=0$, for which the origin and nature of EIT in the $k_{\text{p}}<k_{\text{c}}$ regime $\left(\delta k{v}_{\text{th}}/{\gamma }_{\text{D}}=-0.04\right)$ are explained in many earlier works [8, 11, 13]. Curves b, dotted, dashed, and solid lines, correspond to the dephasing rates, ${\gamma }_{\text{ph}}=0$, ${\Gamma }_{31}/10$, ${\Gamma }_{31}/2$, and ${\Gamma }_{31}$, respectively.

Figure 3

Peak absorption $\left(\alpha /0.83{\alpha }_{\text{o}}\right)$ at two-photon resonance $\left[{\Delta }_{\text{p}}={\Delta }_{\text{p}}\left(=0\right)\right]$ as a function of the control field amplitude $\left({\Omega }_{\text{c}}/{\gamma }_{\text{D}}\right)$ for (i) $\delta k{v}_{\text{th}}/{\gamma }_{\text{D}}=+0.04$ and (ii) $\delta k{v}_{\text{th}}/{\gamma }_{\text{D}}=-0.04$. Curves a are the results in the absence of buffer gas. Curves b, dotted, dashed, and solid lines, correspond to the dephasing rates, ${\gamma }_{\text{ph}}=0$, ${\Gamma }_{31}/10$, ${\Gamma }_{31}/2$, and ${\Gamma }_{31}$, respectively. The velocity-changing collision parameter is ${\Gamma }_{31}/{\gamma }_{\text{D}}=0.1$.

Figure 4

Group index $n_{\text{g}}$ as a function of the control field amplitude $\left({\Omega }_{\text{c}}/{\gamma }_{\text{D}}\right)$ for (i) $\delta k{v}_{\text{th}}/{\gamma }_{\text{D}}=+0.04$ and (ii) $\delta k{v}_{\text{th}}/{\gamma }_{\text{D}}=-0.04$. Curves a are the results in the absence of buffer gas. Curves b, dotted, dashed, and solid lines, correspond to the dephasing rates, ${\gamma }_{\text{ph}}=0$, ${\Gamma }_{31}/10$, ${\Gamma }_{31}/2$, and ${\Gamma }_{31}$, respectively. The velocity-changing collision parameter is ${\Gamma }_{31}/{\gamma }_{\text{D}}=0.1$. The vapor density is $N=2\times {10}^{12}\text{atoms}/{\text{cm}}^3$.