Projection of a quantum state on eigenstates of average Hamiltonian

A scheme for projecting an arbitrary quantum state on eigenstates of average Hamiltonian is described. As an experimental example, projection on entangled Bell states, which are eigenstates of specially constructed average Hamiltonian, is demonstrated for a system of two dipolar-coupled nuclear spins. The results of a direct and time-reversed evolution are added to average out the coherences between different eigenstates and accomplish the projection.