Bose-Einstein Condensates beyond Mean Field Theory: Quantum Backreaction as Decoherence

We propose an experiment to measure the slow $\log \left(N\right)$ convergence to mean field theory (MFT) around a dynamical instability. Using a density matrix formalism instead of the standard macroscopic wave function approach, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state.