  We study the phase diagram of two weakly coupled one-dimensional dipolar
boson chains at half-odd-integer fillings. We find that the system contains a
rich phase diagram. Four different phases are found. They are the Mott
insulators, the single-particle resonant superfluid, the paired superfluid, and
the bond- or inter-chain density waves. Moreover, the Mott insulating phase can
be further classified according to a hidden string order parameter, which is
analogous to the one investigated recently in the one-dimensional boson Mott
insulator at integer fillings.
