Towards the Heisenberg limit in magnetometry with parametric down-converted photons

Recent theoretical and experimental papers have shown how one can achieve Heisenberg-limited measurements by using entangled photons. Here we show how the photons in a noncollinear down-conversion process can be used for improving the sensitivity of magneto-optical rotation by a factor of 4 which takes us towards the Heisenberg limit. Our results apply to sources with arbitrary pumping. We also present several generalizations of earlier results for the collinear geometry. The sensitivity depends on whether the two-photon or four-photon coincidence detection is used