Optimal spin squeezed steady state induced by the dynamics of non-hermtian Hamiltonians

Abstract

In this work, we study the time evolution of a Coherent Spin State under the action of a Non-hermitianHamiltonian. The Hamiltonian is modeled by a one-axis twisting term plus a Lipkin-type interaction. We show that when the Lipkin interaction is switched on, depending on the relative values of the coupling constants, the initial state evolves into a Steady Spin Squeezed State which minimizes the Uncertainty Relations, intelligent spin state. We apply this result to look for the generation of a steady intelligent spin state from an ensemble of nitrogen-vacancy colour centers in diamond coupled to a mechanical resonator.