  We study correlations originating from the quantum nature of gluons in a
hadronic wave function. Bose-Einstein correlation between identical particles
lead to the enhancement in the number of pairs of gluons with the same quantum
numbers and small relative momentum. We show that these preexisting
correlations can be probed in Deep Inelastic Scattering experiments at high
energy. Specifically, we consider diffractive dijet plus a third jet
production. The azimuthal dependence displays a peak at the zero relative angle
between the transverse momentum imbalance of the photon-going dijet and the
transverse momentum of the hadron-going jet. Our calculations explicitly show
that the peak originates from Bose enhancement. Comparing electron-proton to
electron-nucleus collisions, we demonstrate that the nuclear target enhances
the relative strength of the peak. With the future high luminosity Electron-Ion
Collider the proposed measurements of gluon Bose enhancement become
experimentally feasible.
