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 Rb-87 ensembles. With these Hamiltonians, metrologically relevant atomic properties, e. g. the collective spin, can be measured better than the 'Heisenberg limit' proportional to 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.