  Monochromatic coherent light traversing a disordered photonic medium evolves
into a random field whose statistics are dictated by the disorder level. Here
we demonstrate experimentally that light statistics can be deterministically
tuned in certain disordered lattices, even when the disorder level is held
fixed, by controllably breaking the excitation symmetry of the lattice modes.
We exploit a lattice endowed with disorder-immune chiral symmetry in which the
eigenmodes come in skew-symmetric pairs. If a single lattice site is excited, a
"photonic thermalization gap" emerges: the realm of sub-thermal light
statistics is inaccessible regardless of the disorder level. However, by
exciting two sites with a variable relative phase, as in a traditional two-path
interferometer, the chiral symmetry is judiciously broken and interferometric
control over the light statistics is exercised, spanning sub-thermal and
super-thermal regimes. These results may help develop novel incoherent lighting
sources from coherent lasers.
