Discrete Entanglement Distribution with Squeezed Light

We show how one can entangle distant atoms by using squeezed light. Entanglement is obtained in steady state, and can be increased by manipulating the atoms locally. We study the effects of imperfections, and show how to scale up the scheme to build a quantum network.

Figure 1

Schemes for entanglement creation over long distances. (a) Entanglement is obtained by the emission and subsequent absorption of a photon. (b) A detection of a photon projects the atoms in an entangled state. (c) Both cavities are driven by a common source of two-mode squeezed light. In the steady state, the atoms become entangled.

Figure 2

Atomic level schemes. Double lines indicate coupling to cavity modes, and single to lasers: (a) $|g⟩$ and $|e⟩$ are used for entanglement creation; $|g^{\prime }⟩$ to store the qubit once the entanglement has been obtained; $|g^{\prime \prime }⟩$ for entanglement concentration. (b) The four internal ground levels are coupled to two cavity modes ($a$ and $b$) by Raman transitions as indicated.

Figure 3

EoF of the atoms in steady state as a function of $ϵ$ and $N$: (a) without generalized measurement; (b) with generalized measurement. The solid line indicates the optimal value and the inset gives the $N$ for which the EoF is optimal.

Figure 4

(a) EoF of the atoms in steady state as a function of the parameter $s$, for $N=0.5$. Upper (lower) two curves correspond to the case with (without) measurement after preparation. (b) EoF of the atomic state as a function of the one corresponding to the squeezed state ${\rho }_{\mathrm{i}\mathrm{n}}$.