Better-than-Heisenberg scaling of sensitivity with light and cold atomic ensembles

This work considers an atom-light interface consisting of pulses of polarized light that interacts with an ensemble of 10⁶ cold ⁸⁷Rb in dipole trap. Measurements of polarization changes in the light is used in probing the atomic state. In such polarization-based atom-light interface, a Hamiltonian nonlinear in the Stokes operators can be produced through optical nonlinearities. This work investigates the application of light and cold atomic ensembles to precision measurements with better-than-Heisenberg scaling. The effective nonlinear polarizability of atoms due to ns-duration illumination pulses and the resulting polarization rotation are also calculated in detail.