Heisenberg Limit Superradiant Superresolving Metrology

We propose a superradiant metrology technique to achieve the Heisenberg limit super-resolving 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.