Visibility limit in multiparticle eigenstates of definite relative phase

We show that if two multiply occupied boson modes are in eigenstates of the Hermitian relative phase operator, then the visibility of fringes formed b y the interference between the modes is necessarily less than unity. For la rge total occupation numbers the visibility becomes V less than or equal to pi/4. States with definite relative phase and unit visibility do exist. Th ey are related to coherent states and are not orthogonal (not eigenstates o f a Hermitian phase operator). This visibility limitation may make it possi ble to investigate experimentally the physical role of the relative phase e igenstates in interference measurements such as those on Bose-Einstein cond ensates. [S1050-2947(99)01703-5].