Super-sensitive Metrology using Induced Coherence

We theoretically analyze the phase sensitivity of the well-known ``Induced-Coherence Interferometer'', including the case where the sensitivity is ``boosted'' into the sub-shot-noise-limit regime with coherent-light seeding. We find scaling which reaches below the standard quantum limit, even when seeding the spatial mode which does not interact with the sample. This allows bright, super-sensitive phase estimation of an object with different light fields for interaction and detection, with various potential applications, especially in cases where the sample may be sensitive to light or is most interesting in frequency domains outside what is easily detected. It is a hybrid of a linear and non-linear interferometers, and aside from the super-sensitivity, is distinguished from other systems by ``preferring'' an imbalance in the gains of the two nonlinearities, and non-monotonic behavior of the sensitivity as a function of the gain of the coherence-inducing medium. We use an analysis in terms of general squeezing and show that super-sensitivity occurs only in this case - that is, the effect is not present in the spontaneous-parametric-down-conversion regime, which previous analyses and experiments have focused on.