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A model of two 1D ideal Bose gases A and B with strong AB attractions inducedby a p-wave AB Feshbach resonance is studied. The model is solved exactly by aBose-Bose duality mapping, and it is shown that there is no A-component orB-component Bose-Einstein condensation and no AB-pair off-diagonal long-rangeorder (ODLRO), but both AA-pair and BB-pair ODLRO. After generalization byadding even-wave AA and BB repulsion and reducing the strength of the odd-waveAB attraction by Feshbach resonance detuning, a quantum phase transition occursbetween a phase with AB contact nodes and one with no such nodes.

Pairing, off-diagonal long-range order, and quantum phase transition in strongly attracting ultracold Bose gas mixtures in tight waveguides