  We have discovered from first-principles an unusual polar state in the low n
Sr$_{n+1}$Ti$_n$O$_{3n+1}$ Ruddlesden-Popper (RP) layered perovskites in which
ferroelectricity is nearly degenerate with antiferroelectricity, a relatively
rare form of ferroic order. We show that epitaxial strain plays a key role in
tuning the "perpendicular coherence length" of the ferroelectric mode, and does
not induce ferroelectricity in these low dimensional RP materials as is well
known to occur in SrTiO$_3$. These systems present an opportunity to manipulate
the coherence length of a ferroic distortion in a controlled way, without
disorder or a free surface.
