Demonstration of the Interaction between Two Stopped Light Pulses

This study reports the first experimental demonstration that two light pulses were made motionless and interacted with each other through a medium. The scheme with motionless light pulses maximizes the interaction time and can achieve a considerable efficiency even below single-photon level. To demonstrate the enhancement of optical nonlinear efficiency, the experiment in this study used the process of one optical pulse switched by another based on the effect of electromagnetically induced transparency. Moving light pulses activate switching at an energy per area of 2 photons per atomic absorption cross section as discussed in [Phys. Rev. Lett. 82, 4611 (1999)]. This study demonstrates that motionless light pulses can activate switching at 0.56 photons per atomic absorption cross section, and that the light level can be further reduced by increasing the optical density of the medium. The result of this work enters a new regime of low-light physics.

Figure 1

(a) and (b) Relevant energy levels and laser excitations in the experiment. ${\Omega }_p$ and ${\Omega }_c$ form the 795 nm EIT system of stored light. ${\Omega }_s^{\pm }$ and ${\Omega }_{cs}^{\pm }$ form the 780 nm EIT system of SLP. (c) Timing sequence of stored light switched by stationary light. (d) Schematic experimental setup and image of the atom cloud. PMT1 and PMT2: photo multipliers, APD: avalanche photo detector, PMF: polarization-maintained optical fiber, CPL: optical fiber coupler, BS: cubed beam splitter, PBS: cubed polarizing beam splitter, DBS: dichroic beam splitter, $\lambda /4$: zero-order quarter-wave plate, and $L1\mathrm{\text{−}}L5$: lenses with the focal length $f$ specified in units of mm.

Figure 2

(a) Switching efficiency versus the ratio of OD in the 795 nm EIT system to the square of the coupling Rabi frequency in the case of slow light switched by speed-of-$c$ light. ${\alpha }_p=3–50$ and ${\Omega }_c=0.77–0.92\Gamma$. (b) Probe attenuation versus the number of switching photons per atomic absorption cross section in the two cases of slow light switched by speed-of-$c$ light (squares) and stored light switched by stationary light (circles). In the first case, ${\alpha }_p=70$ and ${\Omega }_c=0.73\Gamma$; in the second case, ${\alpha }_p=72$, ${\Omega }_c=0.73\Gamma$, ${\alpha }_s=110$, ${\Omega }_{cs}^{\pm }=0.75\Gamma$, and the SLP duration is $5.0\mu \mathrm{s}$. Black solid lines are the theoretical predictions. Green, red, and blue dashed lines, located from top to bottom, are the plots of Eq. (12) with $\psi =0.45$, 1.49, and 1.64.

Figure 3

(a) SLP decay time constant versus OD of the SLP, i.e., the stationary switching pulse. The dashed line is the best fit with a linear function. Inset: SLP remaining energy versus SLP duration at ${\alpha }_s=115$ (red, located around the upper line) and 53 (blue, located around the lower line). The dashed lines are the best fits with an exponential decay function, showing the time $\mathrm{constant}=3.45$ and $1.28\mu \mathrm{s}$. (b) Switching efficiency versus ${\alpha }_s$. The circles are the experimental data taken under ${\alpha }_p=68–72$, ${\Omega }_c=0.70–0.73\Gamma$, and ${\Omega }_{cs}^{\pm }=0.74–0.76\Gamma$. The black solid line is the theoretical prediction calculated at ${\alpha }_p=70$, ${\Omega }_c=0.72\Gamma$, and ${\Omega }_{cs}^{\pm }=0.75\Gamma$; the blue dashed line is the best fit with a linear function. Inset: The total OD is equal to the sum of ${\alpha }_s$ and ${\alpha }_p$. The black (more curved) line is calculated with ${\alpha }_p=70$; the red (more straight) line with ${\alpha }_s={\alpha }_p$.