  The Casimir effect arises not only in the presence of material boundaries but
also in space with nontrivial topology. In this paper, we choose a topology of
the flat $(D+1)$-dimensional spacetime, which causes the helix boundary
condition for a Hermitian massless scalar field. Especially, Casimir effect for
a massless scalar field on the helix boundary condition is investigated in two
and three dimensions by using the zeta function techniques. The Casimir force
parallel to the axis of the helix behaves very much like the force on a spring
that obeys the Hooke's law when the ratio $r$ of the pitch to the circumference
of the helix is small, but in this case, the force comes from a quantum effect,
so we would like to call it \textit{quantum spring}. When $r$ is large, this
force behaves like the Newton's law of universal gravitation in the leading
order. On the other hand, the force perpendicular to the axis decreases
monotonously with the increasing of the ratio $r$. Both forces are attractive
and their behaviors are the same in two and three dimensions.
