Visibility is not a good measure of a well-defined relative phase

• In a recent paper Marburger and Das [J. H. Marburger III and K. K. Das, Phys. Rev. A 59, 2213 (1999)] considered an interference visibility experiment involving two weakly interacting Bose-Einstein condensates. It was shown that condensate eigenstates of the Hermitian relative phase operator do not give interference fringes with unit visibility in a Young's double slit type of experiment. The authors concluded that ... these states are not especially well suited to describe weakly interacting multiply occupied coherent bosonic systems. In this work we suggest a criterion for states with a well-defined relative phase. Subsequently we show that the relative phase operator eigenstates satisfy this criterion. This suggests that the concept of interference visibility can, and should, be generalized, since it is widely believed that interference visibility is a measure of the relative phase properties. We therefore propose a broader, but still operational, definition of interference visibility, which we call generalized visibility, and prove that the relative phase operator eigenstates indeed can show unit generalized visibility. We also derive a simple, but general, criterion for states which can display a unit generalized visibility. Somewhat surprisingly, this criterion is weaker than the criterion for a well-defined relative phase. Finally, we discuss which two-mode states can display unit (ordinary) visibility.

Keyword

bose-einstein condensation

output coupler

quantum phase

atom laser

interference

states

evolution

symmetry

number

gas

Publication and Content Type

ref (subject category)

art (subject category)