  We consider a composite system consisting of coupled particles, and
investigate decoherence due to coupling of the center-of-mass degree of freedom
with the internal degrees of freedom. For a simple model of two bound
particles, we show that in general such a decoherence effect exists, and leads
to suppression of interference between different paths of the center-of-mass.
For the special case of two harmonically-bound particles moving in an external
potential in one dimension, we show that the coupling between the
center-of-mass and internal degrees of freedom can be approximated as
parametric driving, and that nontrivial coupling depends on the second
derivative of the external potential. We find a partial solution to this
parametric driving problem. For a simple interference experiment, consisting of
two wave packets scattering off of a square well, we perform numerical
simulations and show a close connection between suppression of interference and
entanglement between the center-of-mass and internal degrees of freedom. We
also propose a measure of compositeness which quantifies the extent to which a
composite system cannot be approximated as a single, indivisible particle. We
numerically calculate this quantity for our square well example system.
