Quantum Fisher information and spin squeezing

Quantum metrological sensors allow us to reach the fundamentally limited precision of measurements, the Heisenberg limit (HL), which scales as the number of atoms N in contrast to the standard quantum limit (SQL) scaling N^1/2 . A common strategy to achieve scaling beyond the SQL is the generation of spin squeezed states. These states are characterized by non-classical correlations that reduce the variance of one measurement quadrature in the collective state while increasing the variance of the quadrature orthogonal to the measurement. In this work we analyze spin squeezing generation by considering dynamics of a cold atomic ensemble subject to a nonlinear Hamiltonian (one-axis twisting). The analysis is done using Dicke state and Wigner distribution function representations. Quantum Fisher information of various entangled states is calculated and analyzed in parallel, to determine what kind of nonclassical correlations between atoms are responsible for the metrological gain in Ramsey-type measurement schemes.