Stationary Light Pulses in Cold Atomic Media and without Bragg Gratings

We study the creation of stationary light pulses (SLPs), i.e., light pulses without motion, based on the effect of electromagnetically induced transparency with two counterpropagating coupling fields in cold atoms. We show that the Raman excitations created by counterpropagating probe and coupling fields prohibit the formation of SLPs in media of cold and stationary atoms such as laser-cooled atom clouds, Bose condensates or color-center crystals. A method is experimentally demonstrated to suppress these Raman excitations and SLPs are realized in laser-cooled atoms. Furthermore, we report the first experimental observation of a bichromatic SLP at wavelengths for which no Bragg grating can be established. Our work advances the understanding of SLPs and opens a new avenue to SLP studies for few-photon nonlinear interactions.

Figure 1

(a) and (c) Relevant energy levels and laser excitations in the experiments. (b) Schematic experimental setup. BS: beam splitter cube; PBS: polarizing beam splitter cube; $\lambda /4$: quarter-wavse plate; L1-L3: lenses ($f$ indicates the focal length in units of mm); CPL: optical fiber coupler; M: mirror; PD: photo detector; APD: avalanche photo detector. L2 focused the probe beam onto the atom cloud. L1 transformed the coupling beam into a plane wave in the region of the atom cloud. L3 collimated the transmitted probe beam.

Figure 2

Numerical simulations of the probe intensity ($|{\Omega }_p^{+}{|}^2+|{\Omega }_p^{-}{|}^2$) as a function of time and position for the timing sequence depicted in (a). The gray level indicates the amplitude. In (b), a medium of hot atoms is considered with ${\rho }_{21}^{+-}\equiv 0\equiv {\rho }_{21}^{-+}$. In (c) and (d), a medium of cold atoms is considered with ${\gamma }_2=0$. The detunings are $\Delta =0$ (c) and $1.0\Gamma$ (d). The other parameters common to all plots are $\alpha =2000$, ${\Omega }_c^{\pm }=3.5\Gamma$, and ${\gamma }_1=0$.

Figure 3

The four Raman excitations that describe the interaction between the two light fields and media of cold atoms. For hot media, only the copropagating Raman excitations in (a) and (b) need to be considered and the counterpropagating Raman excitations in (c) and (d) are negligible.

Figure 4

Experimental data (symbols) and theoretical predictions (lines) of the probe transmission through a medium of cold atoms. (a) The output $|{\Omega }_p^{+}{|}^2$ (blue circles) with the constant presence of $|{\Omega }_c^{+}{|}^2$ (not shown) and storage and retrieval of $|{\Omega }_p^{+}{|}^2$ (blue squares) by $|{\Omega }_c^{+}{|}^2$ (black line). (b) Storage of $|{\Omega }_p^{+}{|}^2$ by $|{\Omega }_c^{+}{|}^2$ (black line) and retrieval of $|{\Omega }_p^{-}{|}^2$ (red triangles) by $|{\Omega }_c^{-}{|}^2$ (light gray line). (c) $|{\Omega }_p^{+}{|}^2$ (blue circles) with the constant presence of $|{\Omega }_c^{-}{|}^2$ (not shown). (d) Theoretical prediction of the probe transmission through a hot medium calculated with ${\rho }_{21}^{+-}\equiv 0\equiv {\rho }_{21}^{-+}$. (e) No SLP is formed for $\Delta =0$. (f) Formation of a SLP for $\Delta =-0.5\Gamma$. The parameters are ${\Omega }_c^{\pm }=0.69\Gamma$ in (a), (b),(d),(e), and (f); ${\Omega }_c^{-}=0.86\Gamma$ in (c); ${\gamma }_2=0.016\Gamma$ in (c),(e), and (f); $\alpha =30$ and ${\gamma }_1=5.0\times {10}^{-4}\Gamma$ in all plots. The input $|{\Omega }_p^{+}{|}^2$ (magenta diamonds) is scaled down by a factor of 0.2. Because of different detection efficiencies in the forward and backward directions, the data representing the experimental $|{\Omega }_p^{-}{|}^2$ in (b) is scaled up by a factor of 1.4.

Figure 5

Creation of a monochromatic SLP at 780 nm in (a) and a bichromatic SLP at 780 nm and 795 nm in (b). Lines, symbols, and colors are used as in Fig. 4. ${\Omega }_c^{\pm }=0.77\Gamma$, $\alpha =39$, ${\gamma }_1=7.0\times {10}^{-4}\Gamma$, ${\gamma }_2=0.016\Gamma$, and $\Delta =-0.5\Gamma$ in (a). ${\Omega }_c^{+}=0.75\Gamma$, ${\Omega }_c^{-}=0.77\Gamma$, $\alpha =39$, ${\gamma }_1=4.6\times {10}^{-4}\Gamma$ with ${\rho }_{21}^{+-}\equiv 0\equiv {\rho }_{21}^{-+}$ in (b). The input $|{\Omega }_p^{+}{|}^2$ is scaled down by a factor of 0.2. In order to plot the experimental $|{\Omega }_p^{-}{|}^2$ in (b) without having to change the vertical scale, we did not scale the experimental backward signals in (a) and (b) by a factor of 2.4 to account for different detection efficiencies in the forward and backward directions (the factor differs from the one in Fig. 4 due to a slightly changed beam alignment).