Heisenberg limit superradiant superresolving metrology

We propose a superradiant metrology technique to achieve the Heisenberg limit superresolving displacement measurement by encoding multiple light momenta into a three-level atomic ensemble. We use 2N coherent pulses to prepare a single excitation superradiant state in a superposition of two timed Dicke states that are 4N light momenta apart in momentum space. The phase difference between these two states induced by a uniform displacement of the atomic ensemble has 1/4N sensitivity. Experiments are proposed in crystals and in ultracold atoms.