Heisenberg-limited two-parameter estimation with weighted three-mode Schrödinger cat states in a triple-well Bose-Einstein condensate system
Phys. Rev. A 113, 062606 – Published 2 June, 2026
DOI: https://doi.org/10.1103/389g-d3sy
Abstract
High-precision multiparameter estimation is critical in quantum metrology studies, where the precision (cost function) is expressed as a weighted sum of the covariances of the vector estimator. It necessitates the preparation of different input states to achieve optimal precision with varying weighted matrices. In this article, we propose to prepare a highly adjustable weighted three-mode cat state (WTCS) with a triple-well condensate system, then apply it to realize Heisenberg-level two-parameter estimation. The parameters are encoded with the ground-state energy imbalance between the three wells, estimated with the data acquired via particle number measurement after a proper rotation. Significantly, by manipulating the strength and asymmetry of the interwell hopping, we can fine-tune the WTCS prepared according to the weights adopted in defining the cost function. As a result, the precision of this two-parameter estimation scheme achieves the Heisenberg level consistently. We expect this scheme to be utilized in estimating vector parameters such as the magnetic fields.
