Holographic Storage of Multiple Coherence Gratings in a Bose-Einstein Condensate

We demonstrate superradiant conversion between a two-mode collective atomic state and a single-mode light field in an elongated cloud of Bose-condensed atoms. Two off-resonant write beams induce superradiant Raman scattering, producing two independent coherence gratings with different wave vectors in the cloud. By applying phase-matched read beams after a controllable delay, the gratings can be selectively converted into the light field also in a superradiant way. Because of the large optical density and the small velocity width of the condensate, a high conversion efficiency of $>70\%$ and a long storage time of $>120\mu \mathrm{s}$ were achieved.

Figure 1

(a) Geometry and (b) energy-level diagram of the experiment. L: lens, $\lambda /4$: quarter-wave plate, PBS: polarization beam splitter, and PMT: photo-multiplier tube.

Figure 2

(a) Observed superradiant anti-Stokes and Stokes pulses. Timing of the light beams is shown as the dashed lines in the lowest trace. The intensity of the write beam was $I_W=41\mathrm{mW}/{\mathrm{cm}}^2$ and that of the read beam was changed to $I_R=510$, 255, and $128\mathrm{mW}/{\mathrm{cm}}^2$ from upper to lower. The spatial profile of the end-fire mode is shown in the inset. A white bar represents the diffraction angle ${\theta }_d$. (b) Numerical simulations based on Eqs. (1, 2). The parameters were ${\Gamma }_a=2\pi \times 1.3\mathrm{kHz}$ and ${\gamma }_{\mathrm{AS}}=2\pi \times 160\mathrm{Hz}$. Three traces correspond to the scattering rate ratio ${\gamma }_S/{\gamma }_{\mathrm{AS}}=1.0$, 0.5, and 0.25 from upper to lower. (c) and (d) show the optical density of atoms after 34-ms ballistic expansion for just after the illumination of a $30\mathrm{\text{−}}\mu \mathrm{s}$ write pulse and a successive $30\mathrm{\text{−}}\mu \mathrm{s}$ read pulse, respectively.

Figure 3

Demonstration of two-mode anti-Stokes and Stokes SRS. (a)–(d) Bragg-selective readout of the Stokes photons with four different write-read configurations (shown in the inset of each panel). (e) Superradiant writing or reading of two independent coherence gratings. The light intensity was fixed to $I_W=41\mathrm{mW}/{\mathrm{cm}}^2$ for the write and $I_R=510\mathrm{mW}/{\mathrm{cm}}^2$ for the read beam (${\gamma }_S/{\gamma }_{\mathrm{AS}}\sim 1$). Timing of the light beams is depicted by the dashed lines.

Figure 4

Conversion efficiency versus interval time between the write and the read beam. Filled (open) circles represent the data for the single-mode (two-mode) storage of the grating.