Super-radiant super-resolving displacement estimation via multiple photons by the Wang’s method

In this paper, we propose a super-radiant measurement scheme to achieve Heisenberg limit super-resolving displacement estimation by encoding multiple light momenta into a three-level atomic ensemble with multiple q photons. And by the Wang's method (Phys. Rev. Lett. 2014, 113, 083601), we use 2N coherent pulses to prepare a q-excitation super-radiant state in a super-position of two timed Dicke states that are 4qN light momenta apart in the momentum space. The phase difference between these two states induced by a uniform displacement of the atomic ensemble has 1/4qN sensitivity. In the end, we introduce two experiments based on Ramsey interferometry in crystal and in ultracold atoms.