Creation of massive entanglement with optimized multiple spin squeezing

Quantum entanglement is an important resource in many areas such as precision measurement, quantum information processing and quantum computation. Controlled creation of quantum entanglement between a large number of particles is a goal to which significant theoretical and experimental efforts have been devoted. For a large collection of spins, spin squeezing is an experimentally relevant approach to entanglement creation. Two-axis spin squeezing was shown to achieve the Heisenberg limit for phase sensitivity, which scales as 1/N and N is the particle number. However the required Hamiltonian H=(Sy$^2$-Sx$^2$) is usually not readily available in experimental systems. Here we propose an optimized control scheme to approach the Heisenberg limit with only a single-axis spin squeezing Hamiltonian combined with an external magnetic field. Essentially the scheme consists of multiple spin squeezing with optimized parameters. And squeezing parameter achieved seems even better than two-axis squeezing. Moreover this scheme can be employed to prepare the |S, Sz$=0>$ Dicke state.