  Non-Hermitian systems with complex-valued energy spectra provide an
extraordinary platform for manipulating unconventional dynamics of light. Here,
we demonstrate the localization of light in an instantaneously reconfigurable
non-Hermitian honeycomb photonic lattice that is established in a
coherently-prepared atomic system. One set of the sublattices is optically
modulated to introduce the absorptive difference between neighboring lattice
sites, where the Dirac points in reciprocal space are extended into
dispersionless local flat bands. When these local flat bands are broad enough
due to larger loss difference, the incident beam is effectively localized at
one set of the lattices with weaker absorption, namely, the commonly seen power
exchange between adjacent channels in photonic lattices is effectively
prohibited. The current work unlocks a new capability from non-Hermitian
two-dimensional photonic lattices and provides an alternative route for
engineering tunable local flat bands in photonic structures.
