Superluminal and ultraslow light propagation in optomechanical systems

We consider an optomechanical double-ended cavity under the action of a coupling laser and a probe laser in an electromagnetically induced transparency configuration. It is shown how the group delay and advance of the probe field can be controlled by the power of the coupling field. In contrast to single-ended cavities, which only allow for superluminal propagation, the possibility of both superluminal and subluminal propagation regimes is found. The magnitudes of the group delay and the advance are calculated to be $\sim$1 ms and about $-2$ s, respectively, at a very low pumping power of a few microwatts. In addition, the interaction of the optomechanical cavity with a time-dependent probe field is investigated for controlled excitations of mirror vibrations.

Figure 1

Schematic of a double-ended cavity with a moving nanomechanical mirror, adapted from Ref. [14].

Figure 2

The real (black solid line) and the imaginary (red dashed line) parts of ${\varepsilon }_T\left(\delta \right)$ as a function of $\delta$ for an input coupling laser power of $P_c=5\mu$ W. The parameters used are length of the cavity $L=6.7$ cm, wavelength of the laser $\lambda =2\pi c/{\omega }_c=1064$ nm, $m=40$ ng, ${\omega }_m=2\pi \times 134$ kHz, $\gamma =0.76$ Hz, $\kappa ={\omega }_m/10$, mechanical quality factor $Q=1.1\times {10}^6$, and $\Delta ={\omega }_m$.

Figure 3

Phase as a function of frequency $\delta$ for input coupling laser power $P_c=1$ $\mu$W. The parameters are the same as in Fig. 2.

Figure 4

Advance of the reflected probe field as a function of the pump power in the presence of the coupling field. All parameters are the same as those in Fig. 2.

Figure 5

Group delay of the transmitted probe field as a function of the pump power in the presence of the coupling field. All parameters are the same as those in Fig. 2.

Figure 6

The reflection spectrum $R\left(\delta \right)$ as a function of normalized frequency. $P_c=0$ solid, 5$\mu$W (dashed). All parameters are the same with those of Fig. 2.

Figure 7

The transmission spectrum $T\left(\delta \right)$ as a function of normalized frequency. $P_c=0$ solid, 5$\mu$W (dashed). All parameters are the same with those of Fig. 2.

Figure 8

EIT width $\Gamma \left(P_c\right)$ as afunction of power $P_c$ $\Gamma$ is normalized by $1\times {10}^4$ 1/s. All parameters are the same with those of Fig. 2.

Figure 9

$q_{+}\left(t\right)$ as a function of time with $\Delta ={\omega }_m$. All parameters are the same as those in Fig. 2.

Figure 10

Time dependence of $q\left(t\right)$ for $\Delta ={\omega }_m$ and $\delta ={\omega }_m$. All parameters are the same as those in Fig. 2.