  In this study, we have derived close form of the Casimir force for the
non-interacting ideal Bose gas between two slabs in harmonic-optical lattice
potential by using Ketterle and van Druten approximation. We find that
Bose-Einstein condensation temperature $T_{c}$ is a critical point for
different physical behavior of the Casimir force. We have shown that Casimir
force of confined Bose gas in the presence of the harmonic-optical potential
decays with inversely proportional to $d^{5}$ when $T\leq T_{c}$. However, in
the case of $T>T_{c}$, it decays exponentially depends on separation $d$ of the
slabs. Additionally we have discussed temperature dependence of Casimir force
and importance of the harmonic-optical lattice potential on quantum critical
systems, quantum phase transition and nano-devices.

Quantum Physics;Statistical Mechanics