Beyond standard Heisenberg limit through many-body correlated tunneling

It is well known that the uncertainty of classical measurement scales as 1/$\backslash $sqrt\textbraceleft N\textbraceright , where N refers to the total number of the copies of the probes. And in quantum measurement, the uncertainty can achieve an improved scaling of 1/N, using entangled or squeezed states as the probe. Recently, it has been experimentally proved that the scaling of the uncertainty could even reach 1/N\textasciicircum \textbraceleft k\textbraceright , by engineering a k-body interaction. In this talk, we propose that, instead of the k-body interaction, the k-body correlated tunneling could also give rise to a new scaling of 1/J\textasciicircum k, where J is the strength of the effective k-body tunneling. Moreover, we will introduce detailed measurement schemes based on the realizable k-body correlated tunnelings of ultracold atoms. These schemes are also analyzed by the calculation of the quantum and classical Fisher information, which confirms the new scaling in these setups.