Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate

We consider an antiferromagnetic Bose-Einstein condensate in a transverse 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 the magnetization. We exploit both types of system criticality as a resource in the precise estimation of the control parameter value. We quantify the achievable precision by the quantum Fisher information. We demonstrate supersensitivity and show that the precision scales with the number of atoms up to N4 around criticality. In addition, we study the precision based on the error-propagation formula, which provides a simple-to-measure signal whose scaling coincides with the quantum Fisher information. Finally, we take into account the effect of nonzero temperature and show that sub-shot-noise sensitivity in the estimation of the control parameter is achievable in the low-temperature limit.