Quantum Dynamics of Atomic Coherence in a Spin-1 Condensate: Mean-Field versus Many-Body Simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a ``ferromagnetic'' state with all spins aligned along the $y$ axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.