Faithful Solid State Optical Memory with Dynamically Decoupled Spin Wave Storage

We report a high fidelity optical memory in which dynamical decoupling is used to extend the storage time. This is demonstrated in a rare-earth doped crystal in which optical coherences were transferred to nuclear spin coherences and then protected against environmental noise by dynamical decoupling, leading to storage times of up to 4.2 ms. An interference experiment shows that relative phases of input pulses are preserved through the whole storage and retrieval process with a visibility $\approx 1$, demonstrating the usefulness of dynamical decoupling for extending the storage time of quantum memories. We also show that dynamical decoupling sequences insensitive to initial spin coherence increase retrieval efficiency.

Figure 1

Upper part: hyperfine structure of ${\mathrm{Pr}}^{3+}$ ${}^3\mathrm{H}_4$ and ${}^1\mathrm{D}_2$ levels in ${\mathrm{Pr}}^{3+}\mathrm{\text{:}}{\mathrm{La}}_2({\mathrm{WO}}_4{)}_3$ and transitions used in this Letter. Lower part: laser sequences for one (a) or two (c) pulse storage. Pulses 1 and 4 were Gaussian with full width at half maximum (FWHM) lengths of 200 and 425 ns, respectively. Pulses 2 and 3 were secant hyperbolic with FWHM length of $2.25\mu \mathrm{s}$ and a 2 MHz chirp. The delay $t_{12}$, between pulse 1 and 2, and $t_{34}$ were set to $2\mu \mathrm{s}$. Comparing echo intensity with and without transfer pulses, we deduced a transfer efficiency for fields of 87% per pulse. (b) rf pulse sequence for hyperfine transition dynamical decoupling; the basic block showed in brackets is repeated $N$ times (see text).

Figure 2

Absorption spectrum after optical pumping.

Figure 3

Retrieval efficiency as a function of storage time using two rf pulses (a), KDD (b), and CPMG (c) dynamical decoupling sequences. The retrieval efficiency is normalized to the echo intensity extrapolated at zero delay, using transfer pulses but no rf pulses.

Figure 4

Interfering output pulses after storage of two input pulses, with 0° (a), $-270°$ (b), and $-180°$ (c) relative phases, for 3 ms. Open circles: experimental data, solid line: fit using two Gaussian pulses. (d) Normalized output light intensity averaged at $3.7\mu \mathrm{s}$ over 50 ns [gray area in (a)–(c)] as a function of the relative input pulse phase. Squares: experimental data, solid line: fit with a visibility expression (see text).