  ABC-stacked trilayer graphene/hBN moir\'e superlattice (TLG/hBN) has emerged
as a playground for correlated electron physics. We report spectroscopy
measurements of dual-gated TLG/hBN using Fourier transformed infrared
photocurrent spectroscopy. We observed a strong optical transition between
moir\'e mini-bands that narrows continuously as a bandgap is opened by gating,
indicating a reduction of the single particle bandwidth. At half-filling of the
valence flat band, a broad absorption peak emerges at ~18 meV, indicating
direct optical excitation across an emerging Mott gap. Similar photocurrent
spectra are observed in two other correlated insulating states at quarter- and
half-filling of the first conduction band. Our findings provide key parameters
of the Hubbard model for the understanding of electron correlation in TLG/hBN.
