  The unique sensitivity of optical response to different types of symmetry
breaking can be used to detect and identify spontaneously ordered many-body
states in bilayer graphene. We predict a strong response at optical
frequencies, sensitive to electronic phenomena at low energies, which arises
because of nonzero inter-band matrix elements of the electric current operator.
In particular, the polar Kerr rotation and reflection anisotropy provide
fingerprints of the quantum anomalous Hall state and the nematic state,
characterized by spontaneously broken time reversal symmetry and lattice
rotation symmetry, respectively. These optical signatures, which undergo a
resonant enhancement in the near-infrared regime, lie well within reach of
existing experimental techniques.
