  A novel neutron spin resonance technique is presented based on the well-know
neutron spin echo method. In a first proof-of-principle measurement using a
monochromatic neutron beam, it is demonstrated that relative velocity changes
of down to a precision of $4 \times 10^{-7}$ can be resolved, corresponding to
an energy resolution of better than 3~neV. Currently, the sensitivity is only
limited by counting statistics and not by systematic effects. An improvement by
another two orders of magnitude can be achieved with a dedicated setup,
allowing for energy resolutions in the 10~peV regime. The new technique is
ideally suited for investigations in the field of precision fundamental neutron
physics, but will also be beneficial in scattering applications.
