Phase variation and shape distortion of light pulses in electromagnetically induced transparency media

We have experimentally studied the propagation behaviors of light pulses in an electromagnetically induced transparency (EIT) medium. Both phase variation in different parts of a pulse and distortion of the pulse shape are observed. The consistency between the experimental data and theoretical predictions is satisfactory. Our study explains the physical origins of the phase variation and the shape distortion, shows that the phase variation should be taken into consideration in applications utilizing the EIT scheme in which two-photon detuning must exist, and provides better understanding of the propagation behavior of the slow light.

Figure 1

Experimental data in (a) and (b) and theoretical predictions in (c) and (d). Black and gray solid lines are the input and output probe pulses, respectively; black dashed lines are the Gaussian fits of the output pulses. The $1∕e$ full widths of the input and output pulses are 6.1 and $6.4\mu \mathrm{s}$ in (a); 1.5 and $2.8\mu \mathrm{s}$ in (b). ${\Omega }_{p0}=0.1\Gamma$, ${\Omega }_c=0.35\Gamma$, $\gamma =0.003\Gamma$, and $\eta =3.75\Gamma ∕L$.

Figure 2

Theoretical predictions of the EIT pulses based on Eqs. (10, 11). Black and gray solid lines are the input and output probe pulses, respectively; black dashed lines are the Gaussian fits of the output pulses. In (a), (b), and (c), the gray solid and black dashed lines are coincident. The $1∕e$ full width of the input pulse is $1.5\mu \mathrm{s}$, ${\Omega }_{p0}=0.1\Gamma$, ${\Omega }_c=0.35\Gamma$, $\gamma =0.003\Gamma$, and $\eta =3.75\Gamma ∕L$. In the calculation, we include only the constant term of Eq. (10) for (a); the constant and $(\omega -{\omega }_L)$ terms for (b); the constant, $(\omega -{\omega }_L)$, and ${(\omega -{\omega }_L)}^2$ terms for (c); the constant, $(\omega -{\omega }_L)$, ${(\omega -{\omega }_L)}^2$, and ${(\omega -{\omega }_L)}^3$ terms for (d).

Figure 3

The phase shifts of different parts of the probe pulse. $t_{\text{peak}}$ in the label of the horizontal axis denotes the peak position of the output pulse. Up triangles, squares, and down triangles are the experimental data measured at $\delta ={\Delta }_p-{\Delta }_c=0.0136\Gamma ,0$, and $-0.0136\Gamma$ (80, 0, and $-80\mathrm{kHz}$), respectively. ${\Omega }_{p0}=0.1\Gamma$ and ${\Omega }_c=0.30\Gamma$. The three solid lines are the theoretical predictions from the numerical calculation of Eqs. (1, 2, 3, 4, 5, 6). In the calculation, ${\Delta }_c=0$, ${\Delta }_p=0.0136\Gamma ,0,-0.0136\Gamma$ (top to bottom), $\gamma =0.003\Gamma$, and $\eta =4.5\Gamma ∕L$. The vertical scale of the experimental data is shown in the left axis of the figure and that of the theoretical predictions is shown in the right axis.