Robust Creation of Entanglement between Remote Memory Qubits

In this Letter we propose a robust quantum repeater architecture building on the original Duan-Lukin-Cirac-Zoller (DLCZ) protocol [L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature (London) 414, 413 (2001)]. The architecture is based on two-photon Hong-Ou-Mandel–type interference which relaxes the long-distance stability requirements by about 7 orders of magnitude, from subwavelength for the single photon interference required by DLCZ to the coherence length of the photons. Our proposal provides an exciting possibility for robust and realistic long-distance quantum communication.

Figure 1

Setup for entanglement generation between sites $A$ and $B$. Forward-scattered Stokes photons, generated by an off-resonant write laser pulse via spontaneous Raman transition, are subject to BSM-I at the middle point. The Stokes photons generated at the same site are assumed to have different polarization, i.e., $|H⟩$ and $|V⟩$. PBS (${\mathrm{PBS}}_{\pm }$) reflects photons with polarization $|V⟩$ ($|-⟩$) and transmits photons with polarization $|H⟩$ ($|+⟩$), where $|\pm ⟩=(1/\sqrt{2})(|H⟩\pm |V⟩)$. After passing through the ${\mathrm{PBS}}_{\pm }$ and PBS successively, the Stokes photons are detected by single photon detectors. A coincidence count between single photon detectors $D_1$ and $D_4$ ($D_1$ and $D_3$) or $D_2$ and $D_3$ ($D_2$ and $D_4$) will project the four atomic ensembles into the complex entangled state $|\psi {⟩}_{AB}$ up to a local unitary transformation. The inset shows the atomic level structure, with the ground state $|g⟩$, metastable state $|s⟩$, and excited state $|e⟩$.

Figure 2

Setup for entanglement connection between sites $A$ and $D$ via entanglement swapping. Complex entangled states have been prepared in the memory qubits between sites ($A,B$) and ($C,D$). The memory qubits at sites $B$ and $C$ are illuminated by near resonant read laser pulses, and the retrieved anti-Stokes photons are subject to BSM-II at the middle point. The anti-Stokes photons at the same site have different polarizations $|H⟩$ and $|V⟩$. After passing through PBS and ${\mathrm{PBS}}_{\pm }$ successively, the anti-Stokes photons are detected by single photon detectors. Coincidence count between $D_1$ and $D_4$ ($D_1$ and $D_3$) or $D_2$ and $D_3$ ($D_2$ and $D_4$) are registered. The memory qubits will be projected into an effectively maximally entangled state ${\rho }_{AD}$ up to a local unitary transformation. Note that the PBS arrangement in BSM-II and BSM-I is different.

Figure 3

Setup for quantum entanglement purification. Effectively entangled states have been prepared in the memory qubits between two distant sites $A$ and $D$. The memory qubits at the two sites are illuminated by near resonant read laser pulse, and the retrieved entangled photon pairs are directed to two PBSs, respectively. The photons in modes $b_1$ and $b_2$ are detected in $|\pm ⟩=(1/\sqrt{2})(|H⟩\pm |V⟩)$ basis and the left photons in modes $a_1$ and $a_2$ are restored in the memory qubits at the two sites, respectively.