Entanglement storage by classical fixed points in the two-axis countertwisting model

We analyze a scheme for self-trapping of entangled state by classical stable fixed points in the two-axis counter-twisting model. A characteristic feature of the two-axis counter-twisting Hamiltonian is the existence of the four stable center and two unstable saddle fixed points in their mean-field phase space. The entangled state is generated dynamically from an initial spin coherent state located around an unstable saddle fixed point in a spin-1/2 ensemble. At an optimal moment of time the state is shifted to a position around stable center fixed points by a single rotation, where its dynamics and properties are approximately frozen. In this way one can store the entangled state of high value of the quantum Fisher information for further purposes. The effect of noise on the scheme is also discussed.