Quantum-limited measurements of atomic scattering properties

We propose a method to perform precision measurements of the interaction parameters in systems of N ultracold spin 1/2 atoms. The spectroscopy is realized by first creating a coherent spin superposition of the two relevant internal states of each atom and then letting the atoms evolve under a squeezing Hamiltonian. The nonlinear nature of the Hamiltonian decreases the fundamental limit imposed by the Heisenberg uncertainty principle to N^-2 , a factor of N smaller than the fundamental limit achievable with noninteracting atoms. We study the effect of decoherence and show that, even with decoherence, entangled states can outperform the signal to noise limit of nonentangled states. We present two possible experimental implementations of the method using Bose-Einstein spinor condensates and fermionic atoms loaded in optical lattices and discuss their advantages and disadvantages.