Bosonic amplification of noise-induced suppression of phase diffusion

We study the effect of noise-induced dephasing on collisional phase-diffusion in the two-site Bose-Hubbard model. Dephasing of the quasi-momentum modes may slow down phase-diffusion in the quantum Zeno limit. Remarkably, the degree of suppression is enhanced by a bosonic factor of order $N/\log{N}$ as the particle number $N$ increases.