Nonlinear metrology with a quantum interface

We describe nonlinear quantum atom–light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in 87Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the ‘Heisenberg limit’ ∝1/N, where N is the number of photons. In contrast to other proposed nonlinear metrology systems, the atom–light interface allows both linear and nonlinear estimation of the same atomic quantities.