An advanced wave model is applied to a two-photon interference experim
ent to show that the observed interference effect is due to the geomet
rical phase of a two-photon state produced in spontaneous parametric d
own-conversion. The polarization state of the signal-idler pair is cha
nged adiabatically so that the ''loop'' on the Poincare sphere is open
ed in the signal channel and closed in the idler channel. Therefore, w
e observed an essentially nonlocal geometrical phase, shared by the en
tangled photon pair, or a biphoton.