Towards entanglement of two individual atoms using the Rydberg blockade

The Rydberg blockade is of great interest for many quantum information processing schemes, since it provides a way to deterministically entangle two or more atoms and to drive fast quantum gates [1]. Recently, experimental efforts into this direction succeeded in the first observation of the Rydberg blockade between two $^{87}$Rb atoms individually trapped in two neighboring dipole traps [2,3]. Furthermore, in the two atom system the Rabi frequency for oscillations between the ground state $|gg\rangle$ and \emph{one} atom in the Rydberg state is enhanced by $\sqrt 2$ with respect to the Rabi frequency for a single atom [3]. This indicates the production of an entangled state $(|gr\rangle+ e^{i\textbf{k}\Delta \textbf{r}}|rg\rangle)/\sqrt 2$, where $\textbf{k}$ is related to the wave vector of the exciting lasers and $\Delta \textbf{r}$ is the distance between the atoms. The variation of the interatomic distance from shot-to-shot leads to a random phase in the produced entangled state. However, when the Rydberg state is mapped onto another ground state $|g'\rangle$ before the atoms move, this random phase cancels. The resulting entangled state $(|gg'\rangle+ |g'g\rangle)/\sqrt 2$ could then be tested in a Bell measurement or a state tomography. Rotations of the measurement basis are done with a pair of Raman lasers coupling $|g\rangle$ and $|g'\rangle$. The atomic state is read out observing the fluorescence of the remaining atoms after ejecting atoms in state $|g\rangle$ from the trap. The current status of the experiment will be reported.\\[4pt] [1] D.~Jaksch et al., \emph{Phys. Rev. Lett.} \textbf{85}, 2208 (2000). M.D.~Lukin et al., \emph{Phys. Rev. Lett.} \textbf{87}, 037901 (2001).\\[0pt] [2] E.~Urban et al., \emph{Nature Phys.} (2009)(accepted, see also \emph{arxiv:0805.0758}).\\[0pt] [3] A.~Ga\"etan et al., \emph{Nature Phys.} (2009) (accepted, see also \emph{arxiv:0810.2960}).