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We describe nonlinear quantum atom-light interfaces and nonlinear quantummetrology in the collective continuous variable formalism. We develop anonlinear effective Hamiltonian in terms of spin and polarization collectivevariables and show that model Hamiltonians of interest for nonlinear quantummetrology can be produced in $^{87}$Rb ensembles. With these Hamiltonians,metrologically relevant atomic properties, e.g. the collective spin, can bemeasured better than the "Heisenberg limit" $\propto 1/N$. In contrast to otherproposed nonlinear metrology systems, the atom-light interface allows bothlinear and non-linear estimation of the same atomic quantities.

Nonlinear metrology with a quantum interface