Counterdiabatic driving in spin squeezing and Dicke state preparation

A method is presented to transfer a system of two-level atoms from a spin coherent state to a maximally spin squeezed Dicke state, relevant for quantum metrology and quantum information processing. The initial state is the ground state of an initial linear Hamiltonian which is gradually turned into a final quadratic Hamiltonian whose ground state is the selected Dicke state. We use compensating operators to suppress diabatic transitions to unwanted states that would occur if the change were not slow. We discuss the possibilities of constructing the compensating operators by sequential application of quadratic Hamiltonians available in experiments.