Stopped Light and Image Storage by Electromagnetically Induced Transparency up to the Regime of One Minute

The maximal storage duration is an important benchmark for memories. In quantized media, storage times are typically limited due to stochastic interactions with the environment. Also, optical memories based on electromagnetically induced transparency (EIT) suffer strongly from such decoherent effects. External magnetic control fields may reduce decoherence and increase EIT storage times considerably but also lead to complicated multilevel structures. These are hard to prepare perfectly in order to push storage times toward the theoretical limit, i.e., the population lifetime $T_1$. We present a self-learning evolutionary strategy to efficiently drive an EIT-based memory. By combination of the self-learning loop for optimized optical preparation and improved dynamical decoupling, we extend EIT storage times in a doped solid above 40 s. Moreover, we demonstrate storage of images by EIT for 1 min. These ultralong storage times set a new benchmark for EIT-based memories. The concepts are also applicable to other storage protocols.

Figure 1

Experimental setup and level scheme in ${\mathrm{Pr}}^{3+}\mathrm{\text{:}}{\mathrm{Y}}_2{\mathrm{SiO}}_5$. (a) Experimental setup. (b) Energy level diagram of a single ensemble of ${\mathrm{Pr}}^{3+}$ ions, without and with external magnetic field. Green arrows indicate the action of the second step of the preparation pulse sequence (compare with Fig. 2) onto the population distribution in the specific ensemble. Gray, dashed arrows indicate decay processes during optical pumping. Red arrows indicate an additional cleaning pulse.

Figure 2

Control, probe, and rf pulse sequence in the experiment. The three graphs show power and frequency profiles of the optical control pulse ($C$), optical probe pulse ($P$), and rephasing rf pulses in time. Power profiles (left axis) are drawn as solid lines and frequencies (right axis) as dashed lines. We define all frequencies as detunings relative to the control transition [compare with Fig. 1b]. Please note that for better visibility, we interrupted and stretched the time axis during the final retrieval step.

Figure 3

Evolution of the self-learning loop toward an optimized preparation pulse. The graph shows the signal pulse energy after light storage (i.e., the “fitness” of the preparation pulses, determined by the evolutionary algorithm) vs the number of generations in the loop. The red dots depict the averaged result of all individuals (i.e., pulses) of a particular generation. The reference (blue squares) corresponds to a single arbitrarily chosen individual of the first generation. The constant reference indicates stable experimental conditions during optimization.

Figure 4

Signal pulse energy and retrieved images vs storage time. The three data sets correspond to different cycling times in the dynamical decoupling sequence: $T_C=100\mu \mathrm{s}$, $T_C=1\mathrm{ms}$, and $T_C=50\mathrm{ms}$. The data are fitted by exponential decays. Dynamical decoupling at the fastest cycling time results in a storage duration of $T_2=42.3\mathrm{s}$ ($1/e$ time). The insets show the results of image storage and retrieval in the setup, with storage times $\Delta t$ of 0.1, 1, 10, and 60 s (from left to right). For image storage, we used a decoupling sequence with cycling time $T_C=100\mu \mathrm{s}$.