Control of light speed: From slow light to superluminal light

A scheme for controlling light speed from slower-than-$c$ to faster-than-$c$ in an atomic system is presented in this paper. The scheme is based on far detuning Raman effect. Two far detuning coupling fields with small frequency difference will produce two absorptive peaks for the probe field in a $\Lambda$ structure, and an optical pump between the two ground states can change the absorptive peaks into enhanced peaks, which makes the normal dispersion between the two peaks change into anomalous dispersion, so the probe field can change from slow light to superluminal propagation.

Figure 1

Atomic level diagram. $E_{c1}$ and $E_{c2}$ are the two coupling fields, which have equal intensity and a small frequency difference of $2\Delta$. The center frequency of the two coupling fields has a detuning of ${\Delta }_c$ from $|2⟩\to |3⟩$ transition. $E_p$ is the probe field, which is detuning from $|2⟩\to |3⟩$ transition by ${\Delta }_p$. Level $|5⟩$ is used for optical pump, the pumping rate is $R_{\text{op}}$.

Figure 2

(Color online) $\chi$ and $d\chi /d\omega$ with different values of coupling fields strength and $\Delta$ when $R_{\text{op}}=0$. Left figures show the $\chi$ versus two photon detuning, in which the red solid line and green dashed line represent the real and imaginary parts of $\chi$, respectively. The right figures show the real part of $d\chi /d\omega$ (red solid line) and the imaginary part of $\chi$ (green dashed line) between the two Raman peaks. (a),(b) ${\Omega }_c=20{\Gamma }_3$, $\Delta =0.1{\Gamma }_3$; (c),(d) ${\Omega }_c=30{\Gamma }_3$, $\Delta =0.2{\Gamma }_3$.

Figure 3

(Color online) $\chi$ and $d\chi /d\omega$ versus two photon detuning with different optical pump rates, when ${\Omega }_c=30{\Gamma }_3$ and $\Delta =0.2{\Gamma }_3$. The figures layout are the same as Fig. 2. (a),(b) $R_{\text{op}}=0.06$; (c),(d) $R_{\text{op}}=0.4{\Gamma }_3$.

Figure 4

(Color online) Simulation of a $1\mu \text{s}$ Gaussian wave packet transmitting through 1 mm cold ${}^{87}\text{R}\text{b}$ cloud with atomic density of $5\times {10}^{11}/{\text{cm}}^3$. The frequency difference of the coupling fields is $2\Delta =0.4{\Gamma }_3$. The Rabi frequencies of the coupling fields are ${\Omega }_c=30{\Gamma }_3$. The red solid line is corresponding to the optical pump rate of $R_{\text{op}}=0$, and $n_g=1.9\times {10}^5$. The green dashed line is corresponding to the optical pump rate of $R_{\text{op}}=0.4{\Gamma }_3$, and $n_g=-1.1\times {10}^5$. The gray dot line is the reference.

Figure 5

(Color online) Comparing the slow light effect with the EIT scheme. Line 1 is the slow light effect of EIT with different coupling strength, wave packets from right to left are corresponding to ${\Omega }_c=0.5{\Gamma }_3$ and $1{\Gamma }_3$, and $n_g=5.9\times {10}^5$ and $1.6\times {10}^5$. Line 2 is the slow light effect with different optical pump rate when ${\Omega }_c=55{\Gamma }_3$, wave packets from right to left are corresponding to $R_{\text{op}}=0$, $0.17{\Gamma }_3$ and $n_g=6.0\times {10}^5$ and $1.6\times {10}^5$. The gray dot line is the reference.

Figure 6

(Color online) The relation between $n_g$ and the optical pump rate when ${\Omega }_c=30{\Gamma }_3$, $\Delta =0.2{\Gamma }_3$, using the same system parameters as Fig. 4. Line 1: without Doppler broadening, line 2: with Doppler broadening. The Doppler broadening is calculated using the data of ${}^{87}\text{R}\text{b}$ at 320 K.