Fidelity of an Optical Memory Based on Stimulated Photon Echoes

We investigated the preservation of information encoded into the relative phase and amplitudes of optical pulses during storage and retrieval in an optical memory based on stimulated photon echo. By interfering photon echoes produced in a single-mode $\mathrm{Ti}\mathrm{\text{:}}\mathrm{Er}\mathrm{\text{:}}{\mathrm{LiNbO}}_3$ waveguide, we found that decoherence in the medium translates only as loss and not as degradation of information. We measured a visibility for interfering echoes close to 100%. These results may have important implications for future long-distance quantum communication protocols.

Figure 1

Illustration of the sequence of pulses for the interference of photon echoes. The data are read out twice and the phase between data (or read pulses) is changed to produce interference in the central time bin (see text for details).

Figure 2

Photon-echo signals for constructive and destructive interference. Inset: Central echo area ○, left ● and right ▵ side echo area as a function of phase. The phase modulation of both side peaks is synchronized and is opposite to the principle peak. (Note that the area of the side peaks are multiplied with a factor of 3.) This is due to an interference with a four-pulse photon echo (4PE) as described in more detail in the text.

Figure 3

The visibility as a function of the ratio between the two time-bin pulses is shown. Experimental points ○ are in good agreement with the theoretical prediction, which contains no free parameter. Inset: The area under the interfering photon echoes is plotted as a function of the phase for different incoming time-bin amplitude ratios (● $V=0.68$, ▴ $V=0.93$, ▿ $V=1.04$). The interference visibility ($V$) is extracted from a sinusoidal fit.

Figure 4

Area under the echo as a function of the phase of the second readout pulse. All four classical states, analogous to the quantum states used in four-state quantum cryptography protocols, are stored, retrieved, and analyzed with close to 100% fidelity. This is possible even though the probability of retrieval from the memory is only a few percent, limited by the efficiency of the photon-echo process and by decoherence processes in the storage material.