Detection of spin correlations in optical lattices by light scattering

We show that spin correlations of atoms in an optical lattice can be reconstructed by coupling the system to the light, and by measuring correlations between the emitted photons. This principle is the basis for a method to characterize states in quantum computation and simulation with optical lattices. As examples, we study the detection of spin correlations in a quantum magnetic phase, and the characterization of cluster states.

Figure 1

(Color online) Relative error between ${\mathcal{N}}_{yy}^{{\Omega }_{\theta ,\varphi =0}}$ and ${\tilde{N}}_{yy}^{{\Omega }_{\theta ,\varphi =0}}\left(T\right)$, with respect to the number of emitted photons with $\alpha =y$, integrating all over $\theta$ for $\varphi =0$. Triangles, $J∕B=-0.5$; boxes, $J∕B=-0.1$; stars, $J∕B=-0.01$. Inset: Number of $y$-polarized photons for each value of $\theta$ with $\varphi =0$, $T=0.001$ (units of ${\Gamma }_0=1$), and $J∕B=-0.5$. Triangles, ${\mathcal{N}}_{yy}^{{\Omega }_{\theta ,\varphi =0}}={\Gamma }_{0}N{\int }_0^{T}dt⟨J_x^{\theta ,\varphi =0}\left(t\right)J_x^{\theta ,\varphi =0}\left(t\right)⟩$ (emitted photons). Squares, ${\tilde{N}}_{yy}^{{\Omega }_{\theta ,\varphi =0}}\left(T\right)={\Gamma }_{0}NT⟨J_x^{\theta ,\varphi =0}\left(0\right)J_x^{\theta ,\varphi =0}\left(0\right)⟩$ (emitted photons that correspond to the ground state).