Superluminal light propagation via quantum interference in decay channels

We examine the propagation of a weak probe light through a coherently driven $\mathsf{Y}\mathsf{\text{−}}\mathsf{type}$ system. Under the condition that the excited atomic levels decay via the same vacuum modes, the effects of quantum interference in decay channels are considered. It is found that the interference in decay channels results in a lossless anomalous dispersion between two gain peaks. We demonstrate that the probe pulse propagation can, in principle, be switched from subluminal to superluminal due to the decay-induced interference. We also show that the system exhibits a high index of refraction with negligible absorption for the driving fields. A dressed-state picture of the atom-light interaction is described to explain the numerical results.

Figure 1

(a) The level scheme of a $\mathsf{Y}\mathsf{\text{−}}\mathsf{type}$ four-level atom driven by pump and probe fields. (b) The arrangement of field polarizations with respect to the atomic dipole moments. The pump and probe fields each act on only one transition.

Figure 2

Real (solid curve) and imaginary (dashed curve) parts of the susceptibility as a function of the probe detuning ${\mathrm{\Delta }}_1$ for the parameters ${\gamma }_2=1,{\gamma }_1={\gamma }_3=0.01,{\mathrm{\Delta }}_2={\mathrm{\Delta }}_3=0,{\mathrm{\Omega }}_2={\mathrm{\Omega }}_3=4/\sqrt{2},W_{12}=-\sqrt{{\mathrm{\Omega }}_2^2+{\mathrm{\Omega }}_3^2}$, and (a) $\theta ={90}^{\circ }$ and (b) $\theta ={15}^{\circ }$.

Figure 3

Real (solid curve) and imaginary (dashed curve) parts of the susceptibility as a function of the probe detuning ${\mathrm{\Delta }}_1$ for the parameters ${\gamma }_2=1,{\gamma }_1={\gamma }_3=0.01,{\mathrm{\Delta }}_2={\mathrm{\Delta }}_3=0,{\mathrm{\Omega }}_2={\mathrm{\Omega }}_3=0.75/\sqrt{2},W_{12}=-\sqrt{{\mathrm{\Omega }}_2^2+{\mathrm{\Omega }}_3^2}$, and $\theta ={15}^{\circ }$.

Figure 4

Normalized group velocity $[(c/v_g)-1]/K$ at ${\mathrm{\Delta }}_1=0$ as a function of the interference parameter $p=cos\left(\theta \right)={\gamma }_{12}/\sqrt{{\gamma }_1{\gamma }_2}$. The other parameters for the calculation are the same as in Fig. 3.

Figure 5

(a) The level scheme of a $\mathsf{V}\mathsf{\text{−}}\mathsf{type}$ three-level atom interacting with pump and probe fields. (b) Susceptibility $\chi$ versus the probe detuning ${\mathrm{\Delta }}_1$ of the $\mathsf{V}\mathsf{\text{−}}\mathsf{type}$ atom for ${\mathrm{\Omega }}_2=4{\gamma }_2$. (c) Susceptibility $\chi$ versus the probe detuning ${\mathrm{\Delta }}_1$ of the $\mathsf{V}\mathsf{\text{−}}\mathsf{type}$ atom for ${\mathrm{\Omega }}_2=2{\gamma }_2$. The solid (dashed) curve represents the real (imaginary) part of the susceptibility. The common parameters for (b) and (c) are ${\gamma }_2=1,{\gamma }_1=0.01,{\mathrm{\Delta }}_2=0,W_{12}=-{\mathrm{\Omega }}_2$, and $\theta ={15}^{\circ }$.

Figure 6

Steady-state populations ${\overline{\rho }}_{11}$ (solid curve), ${\overline{\rho }}_{22}$ (dashed curve), and ${\overline{\rho }}_{33}$ (dot-dashed curve) as a function of the detuning ${\mathrm{\Delta }}_2$ under the condition ${\mathrm{\Delta }}_2+{\mathrm{\Delta }}_3=0$. The parameters for the calculation are the same as in Fig. 2.

Figure 7

Time evolution of atomic populations in the states ${\rho }_{11}$ (solid curve), ${\rho }_{--}$ (dashed curve), and ${\rho }_{++}$ (dot-dashed curve). The parameters for the calculation are the same as in Fig. 2. The population ${\rho }_{dd}$ (not shown) is given by ${\rho }_{dd}=1-{\rho }_{11}-{\rho }_{++}-{\rho }_{--}$ due to the trace condition.

Figure 8

Real and imaginary parts of the coherence ${\rho }_{23}$ as a function of the pump-field detuning ${\mathrm{\Delta }}_2$ under the condition ${\mathrm{\Delta }}_2+{\mathrm{\Delta }}_3=0$. The parameters are ${\gamma }_2=1,{\gamma }_1=5,{\gamma }_3=0.01,{\mathrm{\Omega }}_2={\mathrm{\Omega }}_3=30/\sqrt{2}$, and $W_{12}=-\sqrt{{\mathrm{\Omega }}_2^2+{\mathrm{\Omega }}_3^2}$. The solid (dashed) curves are for $\theta ={10}^{\circ } \left(\theta ={90}^{\circ }\right)$. The results for ${\rho }_{34}$ (not shown) are identical to those of ${\rho }_{23}$.