  Using a 3D spin-dependent optical lattice, we study thermalization and energy
exchange between two ultracold Bose gases, one of which is bound to the lattice
and another that is free from the lattice potential. Disruption of
inter-species thermalization is revealed through measurements of condensate
fraction after the lattice is superimposed on the parabolic confining
potential. By selectively heating the lattice-bound species and measuring the
rate of heat transfer to the free state, suppression of energy exchange is
observed. Comparison with a Fermi's golden rule prediction confirms that this
effect is caused by a dispersion mismatch that reduces the phase space
available for elastic collisions. This result has critical implications for
methods proposed to cool strongly correlated lattice gases.
