Theory of quantum entanglement and structure of the two-mode squeezed antiferromagnetic magnon vacuum

Recently, investigations of the quantum properties of an antiferromagnet in the spin wave approximation have identified the eigenstates as two-mode squeezed sublattice-magnon states. The uniform magnon states were shown to display a massive sublattice entanglement. Here we extend this idea and study the squeezing properties of all sublattice Fock states throughout the magnetic Brillouin zone. We derive the full statistics of the sublattice magnon number with wave number (kappa) over right arrow in the ground state and show that sublattice magnons occur in pairs with opposite wave vectors, hence, resulting in entanglement of both modes. To quantify the degree of entanglement we apply the Duan-Giedke-Cirac-Zoller inequality and show that it can be violated for all modes. The degree of entanglement decreases towards the corners of the Brillouin zone. We relate the entanglement to measurable correlations of components of the Neel and the magnetization vectors, thus allowing one to experimentally test the quantum nature of the squeezed vacuum. The distinct k-space structure of the entanglement shows that the squeezed vacuum has a nonuniform shape that is revealed through the (kappa) over right arrow -dependent correlators for the magnetization and the Neel vectors.

Automated summary

Recently, investigations have found that the quantum properties of an antiferromagnet in the spin wave approximation can be described by two-mode squeezed sublattice-magnon states. By studying the squeezing properties of all sublattice Fock states throughout the magnetic Brillouin zone, it has been shown that sublattice magnons occur in pairs with opposite wave vectors, resulting in entanglement of both modes. The degree of entanglement can be quantified using the Duan-Giedke-Cirac-Zoller inequality and decreases towards the corners of the Brillouin zone. The entanglement can be experimentally tested by measuring the correlations of components of the Neel and the magnetization vectors.