Precision requirements for spin-echo-based quantum memories

Spin-echo techniques are essential for achieving long coherence times in solid-state quantum memories for light because of inhomogeneous broadening of the spin transitions. It has been suggested that unrealistic levels of precision for the radio-frequency control pulses would be necessary for successful decoherence control at the quantum level. Here we study the effects of pulse imperfections in detail, using both a semiclassical and a fully quantum-mechanical approach. Our results show that high efficiencies and low noise-to-signal ratios can be achieved for the quantum memories in the single-photon regime for realistic levels of control pulse precision. We also analyze errors due to imperfect initial-state preparation (optical pumping), showing that they are likely to be more important than control pulse errors in many practical circumstances. These results are crucial for future developments of solid-state quantum memories.

Figure 1

Basic level scheme in the Duan-Lukin-Cirac-Zoller protocol[3]. (a) The far detuned write pulse scatters a write photon and creates a single collective atomic excitation (spin wave) in the state $s$. (b) Applying a $\pi$ pulse on the $g-s$ transition in the middle of the process interchanges the roles of $g$ and $s$, leading to rephasing at the end of the storage period. (c) Shining the read pulse transforms the single collective atomic excitation in $g$ into a read photon.

Figure 2

A schematic representation of the collective enhancement at a certain direction that is given by the phase-matching condition. Nondirectional re-emission is suppressed by a factor $1/N$, where $N$ is the number of atoms.