  In this paper, I study the oxygen isotope effect (OIE) in cuprates. I
introduce a simple model that can explain experiments both qualitatively and
quantitatively. In this theory, isotope substitution only affects the
superfluid density, but not the pseudo-gap. Within the spin-charge separation
picture, I argue that the spinon-phonon interaction is in the adiabatic limit,
and therefore within the Migdal-Eliashberg theory, there is no isotope effect
in the spinon mass renormalization. On the other hand, I show that the
holon-phonon interaction is in the non-adiabatic limit. Therefore, the small
polaron picture is applicable and there is a large mass enhancement in an
isotope-dependent way. Our theory explains why upon $^{16}$O/$^{18}$O
substitution, the superconducting transition temperature changes only in
underdoped cuprates, while there is no considerable OIE at the optimal doped as
well as the overdoped cuprates. Additionally, in contrast to the conventional
superconductors, we obtain OIE on the superfluid density for whole
superconducting region in agreement with the experimental observations.

Superconductivity;Strongly Correlated Electrons