Dynamics of Quantum Fisher Information under One-Axis Twisting Hamiltonian

Creation of highly correlated states (entanglement) of quantum systems is a key element for precision measurement improvement when the sensor precision is restricted by the Heisenberg limit, which scales as the number of atoms N in contrast to the standard-quantum-limit (SQL) scaling as N^1/2. Various quantum-correlated states of atoms, such as spin squeezed states and Dicke states, allow to achieve scaling beyond the SQL, ultimately reaching the HL scaling. A simplified proposal to generate spin squeezed and Dicke states is based on engineering an effective atom-atom interaction, described by a one-axis twisting (OAT) Hamiltonian. In this work, we analyze dynamics of atoms under the OAT Hamiltonian and quantify the capacity of various entangled states for quantum metrology by evaluating the quantum Fisher information which defines the ultimate precision of the measurements.