  We show that a new type of two-body interaction, which depends on the
momentum of the center of mass (CoM) of these two particles, can be realized in
ultracold atom gases with a laser-modulaed magnetic Feshbach resonance (MFR).
Here the MFR is modulated by two laser beams propagating along different
directions, which can induce Raman transition between two-body bound states.
The Doppler effect causes the two-atom scattering length to be strongly
dependent on the CoM momentum of these two atoms. As a result, the effective
two-atom interaction is CoM-momentum dependent, while the one-atom free
Hamiltonian is still the simple kinetic energy ${\bf p}^2/(2m)$.
