Electro-Optic Quantum Memory for Light Using Two-Level Atoms

We present a simple quantum memory scheme that allows for the storage of a light field in an ensemble of two-level atoms. The technique is analogous to the NMR gradient echo for which the imprinting and recalling of the input field are performed by controlling a linearly varying broadening. Our protocol is perfectly efficient in the limit of high optical depths and the output pulse is emitted in the forward direction. We provide a numerical analysis of the protocol together with an experiment performed in a solid state system. In close agreement with our model, the experiment shows a total efficiency of up to 15%, and a recall efficiency of 26%. We suggest simple realizable improvements for the experiment to surpass the no-cloning limit.

Figure 1

(a) Schematic of the electro-optic quantum memory. (i) The input light field enters the sample at $z=-z_0$ and $t=-t_0$; (ii) the light field is imprinted onto the broadened two-level atomic ensemble, (iii) to recall the light field, the polarity of the quadrupole electric field is flipped at $t=0$, (iv) an output field is retrieved at $z=z_0$ and $t=t_0$. With no decoherence $\gamma =0$, and the optical depth chosen to be $gN/\eta =10/3$, (b) and (c) show the space-time grid plots of the light field intensity and the atomic polarization, respectively. The input pulse duration is $t_{\mathrm{pulse}}=t_0/4$ and the quadrupole induced broadening is $2/t_{\mathrm{pulse}}$.

Figure 2

Memory efficiency as a function of optical depth when (a) the Stark shift is linear with position and (b) when the Stark shift is nonmonotonic. Solid lines represent the efficiency of the memory; dashed lines, the fraction of transmitted light; and dot-dashed lines, the total energy exiting the medium. Shaded regions are the no-cloning regimes.

Figure 3

Real part of the optical field in a moving frame at $c$. At $t=-t_0$, the light field enters the sample and is gradually absorbed by the medium. At $t=0$, the quadrupole field is flipped and the time reverse process commences producing a forward propagating pulse. For the parameters given in Fig. 1, with a storage time of $8t_{\mathrm{pulse}}$, (a) shows a small phase shift across the retrieved pulse. With a storage time $80t_{\mathrm{pulse}}$, (b) shows a near ideal pulse retrieval. The arrows denote the wave front of the light fields.

Figure 4

Energy level diagram and spectral scheme for the praseodymium dopants in yttrium orthosilicate ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5(0.05\%)$. The light at frequency $A$ is the light stored by the electro-optic memory. The natural inhomogeneous linewidth of the sample, ${\omega }_{\mathrm{nat}}$, is a few GHz wide. To set up the experiment, the applied light is swept around frequency $A$ to create a spectral hole a few MHz wide, ${\omega }_{\mathrm{hole}}$. Light at frequencies $B$ and $C$ is then applied to prepare a narrow antihole around $A$ with linewidth ${\omega }_{\mathrm{anti}}$. Although the diagram shows the use of the $\pm 1/2$ excited states, there are ions contributing to the antihole from the $\pm 3/2$ and $\pm 5/2$ excited states due to inhomogeneous broadening in the optical transition. In our experiment ${\omega }_{\mathrm{antihole}}=30\mathrm{kHz}$.

Figure 5

Experimental results (solid lines) and numerical simulations (dashed lines) of the electro-optic echo setup. Trace (a) shows the input pulse detected after transmission through the sample when no antihole is prepared. Trace (b) shows the transmitted pulse and (c) the stored-and-recalled pulse components. The vertical line at $3.7\mu \mathrm{s}$ denotes the time at which the polarity of the Stark-shifting electric field is flipped.