A model of two 1D ideal Bose gases $A$ and $B$ with strong odd-wave $AB$ attractions induced by a $p$-wave $AB$ Feshbach resonance is studied. The model is solved exactly by a Bose-Bose duality mapping, and it is shown that there is no $A$-component or $B$-component Bose-Einstein condensation and no $AB$-pair off-diagonal long-range order (ODLRO), but both $AA$-pair and $BB$-pair ODLRO. After generalization by adding even-wave $AA$ and $BB$ repulsions and reducing the strength of the odd-wave $AB$ attraction by Feshbach resonance detuning, a quantum phase transition occurs between a phase with $AB$ contact nodes and one with no such nodes.

• Received 5 May 2009

DOI:https://doi.org/10.1103/PhysRevLett.102.245303