Abstract Active interferometers are designed to enhance phase sensitivity beyond the standard quantum limit by generating entanglement inside the interferometer. An atomic version of such a device can be constructed by means of a spinor Bose–Einstein condensate with an F = 1 groundstate manifold in which spin-changing collisions (SCCs) create entangled pairs of m = ±1 atoms. We use Bethe Ansatz techniques to find exact eigenstates and eigenvalues of the Hamiltonian that models such SCCs. Using these results, we ex…