Enhancing the precision of multi-parameter estimation for two-level open quantum system by mixed control

In this paper, a mixed control scheme including an appropriate adaptive feedback control and an additional adaptive control is proposed to improve the precision limit of multi-parameter estimation in an atom-cavity system, where the magnitude of a magnetic field and a decoherence parameter need to be simultaneously estimated. The effect of three different feedback types on the simultaneous estimation of these two parameters is analyzed. It is shown that the precision limit can be effectively improved under the cooperation between the adaptive feedback control and the additional adaptive control induced by an additional inverse magnetic field. In particular, the optimal feedback strength depends on the estimate of the decoherence parameter and therefore will be adaptively updated. We analyze the reason why the precision limit is improved and find that our scheme can automatically give priority to the improvement of the precision limit of the magnetic field estimation and thereby achieve the improvement of the precision limit of simultaneous estimation for the two parameters.