Optimal atomic interferometry robust to detection noise using spin-1 atomic condensates

Implementation of the quantum interferometry concept to spin-1 atomic Bose-Einstein condensates is analyzed by employing a polar state evolved in time. In order to identify the best interferometric configurations, the quantum Fisher information is maximized. Three optimal configurations are identified, among which one was not reported in the literature yet, although it gives the highest value of the quantum Fisher information in experimentally achievable short time dynamics. Details of the most optimal configurations are investigated based on the error-propagation formula which includes the interaction-based readout protocol to reduce the destructive effect of detection noise. In order to obtain Heisenberg scaling accessible by present day experimental techniques, an efficient measurement and a method for the inversion of dynamics were developed, as necessary for the protocol's implementation.