Quantum correlations in the Kerr Ising model

Abstract

In this article we present a full description of the quantum Kerr Ising model—a linear optical network of parametrically pumped Kerr nonlinearities. We consider the non-dissipative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally, we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities.

Keywords

• Ising model
• Kerr nonlinearity
• quantum correlations
• coherent Ising machine