The use of multi-particle entangled states has the potential to drastically increase the sensitivity of atom interferometers and atomic clocks. The twist-and-turn (TNT) Hamiltonian can create multiparticle entanglement much more rapidly than the ubiquitous one-axis twisting (OAT) Hamiltonian in the same spin system. In this paper, we consider the effects of detection noise -a key limitation in current experiments -on the metrological usefulness of nonclassical states generated under TNT dynamics. We also consider a variety of interaction-based readouts to maximize their performance. Interestingly, the optimum interaction-based readout is not the obvious case of perfect time reversal.

We consider an antiferromagnetic Bose-Einstein condensate in a traverse magnetic field with a fixed macroscopic magnetization. The system exhibits two different critical behaviors corresponding to transitions from polar to broken-axisymmetry and from antiferromagnetic to broken-axisymmetry phases depending on the value of magnetization. We exploit both types of system criticality as a resource in the precise estimation of control parameter value. We quantify the achievable precision by the quantum Fisher information. We demonstrate the super-sub-shot noise sensitivity and show that the precision scales with the number of atoms up to N 4 around critically. In addition, we study the precision based on the error-propagation formula providing the simple-to-measure signal which coincides its scaling with the quantum Fisher information. Finally, we take into account the effect of non-zero temperature and show that the sub-shot noise sensitivity in the estimation of the control parameter is achievable in the low-temperature limit.

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