Entanglement detection by Bragg scattering

We show how to measure the structural witnesses proposed previously [P. Krammer et al., Phys. Rev. Lett. 103, 100502 (2009)] for detecting entanglement in a spin chain using photon scattering. The procedure allows one to measure the two-point correlation function of the spin array. This proposal could be performed in existing experimental platforms, realizing ion chains in Paul traps or atomic arrays in optical lattices.

Figure 1

An entanglement witness for a spin array can be constructed by means of a pump-probe experiment. The intensity of the scattered light allows one to determine the expectation value of the witness operator. The collection efficiency can be increased when the probe field is the mode of a high-finesse resonator [6].

Figure 2

A possible excitation scheme, where two hyperfine states of the ground-state multiplet are the spin states. In the scheme here discussed, the realization of the witness lies on the capability to adjust the amplitude and the relative phase of the lasers with Rabi frequencies ${\Omega }_0$ and ${\Omega }_1$.