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In an ensemble of two-level atoms that can be described in terms of acollective spin, entangled states can be used to enhance the sensitivity ofinterferometric precision measurements. While non-Gaussian spin states canproduce larger quantum enhancements than spin-squeezed Gaussian states, theiruse requires the measurement of observables that are nonlinear functions of thethree components of the collective spin. In this paper we develop strategiesthat achieve the optimal quantum enhancements using non-Gaussian statesproduced by a nonlinear one-axis-twisting Hamiltonian, and show thatmeasurement-after-interaction techniques, known to amplify the output signalsin quantum parameter estimation protocols, are effective in measuring nonlinearspin observables. Including the presence of the relevant decoherence processesfrom atomic experiments, we determine analytically the quantum enhancement ofnon-Gaussian over-squeezed states as a function of the noise parameters forarbitrary atom numbers.

Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study