  Photonic states with large and fixed photon numbers, such as Fock states,
enable quantum-enhanced metrology but remain an experimentally elusive
resource. A potentially simple, deterministic and scalable way to generate
these states consists of fully exciting $N$ quantum emitters equally coupled to
a common photonic reservoir, which leads to a collective decay known as Dicke
superradiance. The emitted $N$-photon state turns out to be a highly entangled
multimode state, and to characterise its metrological properties in this work
we: (i) develop theoretical tools to compute the Quantum Fisher Information of
general multimode photonic states; (ii) use it to show that Dicke superradiant
photons in 1D waveguides achieve Heisenberg scaling, which can be saturated by
a parity measurement; (iii) and study the robustness of these states to
experimental limitations in state-of-art atom-waveguide QED setups.

Quantum Physics