Storage and retrieval of time-bin qubits with photon-echo-based quantum memories

Quantum memories based on the photon-echo principle (with controlled reversible inhomogeneous broadening) allow in principle perfect reconstruction of the stored light. In the retrieval process, the envelope of the absorbed wave packet is reversed in time, but the evolution of the phase of the carrier wave is unchanged. We discuss the consequences of this fact for the relative phase of pulses with a certain time delay, and thus for the storage of time-bin qubits. As an illustration, we show that the combination of photon-echo-based memories and unbalanced interferometers leads to a counterintuitive interference effect, allowing one to measure a path length difference $\Delta L$ using pulses that are much shorter than $\Delta L$.

Figure 1

A short pulse is sent into an unbalanced interferometer. At each exit there are two components, depending on whether the pulse has taken the long $\left(l\right)$ or the short $\left(s\right)$ arm. Storage and retrieval with a photon-echo-based quantum memory inverts the order of the pulses, but the pulse $l$ keeps the phase $\alpha$ it has acquired on the first pass through the interferometer (see text). As a consequence, after the second pass there is interference with a phase difference $2\alpha$ between the pulse that took the long arm twice $\left(\mathit{ll}\right)$ and the pulse that took the short arm twice $\left(\mathit{ss}\right)$.