Efficient Multiparticle Entanglement via Asymmetric Rydberg Blockade

We present an efficient method for producing $N$ particle entangled states using Rydberg blockade interactions. Optical excitation of Rydberg states that interact weakly, yet have a strong coupling to a second control state is used to achieve state dependent qubit rotations in small ensembles. On the basis of quantitative calculations, we predict that an entangled quantum superposition state of eight atoms can be produced with a fidelity of 84% in cold Rb atoms.

Figure 1

Level scheme (left) and sequence of operations for entangled state generation (right). $\Omega$ is the effective Rabi frequency coupling states $|0⟩$, $|1⟩$.

Figure 2

Calculated blockade shifts as a function of the angle of the molecular axis for ${}^{87}\mathrm{Rb}$, $|s⟩=|41s_{1/2},m=1/2⟩$, $|p⟩=|40p_{3/2},m=1/2⟩$ with magnetic field $B={10}^{-7}\mathrm{T}$ at $d=3\mu \mathrm{m}$. The interaction ${\Delta }_{pp}$ includes contributions from the indicated Förster channels.

Figure 3

Error of the $N=8$ entangled state calculated from Eq. (7) using the parameters of Fig. 2, and ${\tau }_p=57\mu \mathrm{s}$ for $n_p=40$.