Phase coherence in a driven double-well system

We analyze the dynamics of a molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunneling in a double-well potential. The relative phase distribution of the molecular modes in each well and their phase coherence are shown to build up owing to quantum-mechanical fluctuations starting from the vacuum state. We identify three qualitatively different steady-state phase distributions, depending on the ratio of the molecule-molecule interaction strength to interwell tunneling, and examine the crossover from a phase-coherent regime to a phase-incoherent regime as this ratio increases.