Preservation of Energy-Time Entanglement in a Slow Light Medium

We demonstrate the preservation of entanglement of an energy-time entangled biphoton through a slow light medium. Using the $D_1$ and $D_2$ fine structure resonances of Rubidium, we delay one photon of the 1.5 THz biphoton by $\sim 1.3$ correlation lengths and measure the fourth order correlation fringes. After the group delay the fringe visibility is reduced from $97.0\pm 4.4\%$ to $80.0\pm 4.8\%$, but is still sufficient to violate a Bell inequality. We show that temporal broadening is the primary mechanism for reducing the fringe visibility and that smaller bandwidths lead to greatly reduced broadening.

Figure 1

Interferometric setup. Two unbalanced Michelson interferometers are used to measure the delay and preservation of entanglement of a photon traversing the heated Rb vapor cell slow light medium.

Figure 2

Normalized interference data. The dotted and solid lines trace the calculated interference fringe envelopes for scenarios (a), (b), and (c), as noted in the text. The normalized measured coincidences for scenarios (b) and (c) are shown by the triangles and circles, respectively. Inset plots are close up views of the measured fringes near the center of each fringe envelope. The tick marks on the horizontal axes of the inset plots indicate the expected fringe period of ${\lambda }_p/c$. The maximum and minimum coincidence counts ($M$, $m$) for scenarios (b) and (c) are (998,15) and (631,70), respectively. Signal and idler singles rates ($s$, $i$) for scenarios (b) and (c) were (12,28) and (12,25) kHz, respectively.

Figure 3

Calculated interference fringe envelopes. Calculated normalized fringe envelopes vs delay for (a) $\sigma =1\mathrm{nm}$ and (b) $\sigma =2\mathrm{nm}$ for temperatures $T=278$, 304, 320, 332, 342, and 350 ° C as compared to free-space fringes (left most envelope). The signal wavelength is at the zero second order dispersion wavelength, ${\lambda }_{s0}=788.4\mathrm{nm}$. The dashed lines correspond to the Bell inequality visibility (right axis) of 70.7% as discussed in the text. The points indicate the visibility (right axis) of the corresponding envelope.