  The bound state in the continuum (BIC) in photonic system has been widely
used in the field of lasing and sensing. We here find the controllable BIC in
an artificial giant atom-dressed one-dimensional photonic waveguide. The giant
atom couples to the waveguide via two distant sites. We find that the energy
and the photonic distribution in the BIC can be controlled on demand by tuning
the frequency and the size of the giant atom as well as its coupling phase with
the waveguide. More interestingly, we predict the quantum beats in the atomic
and photonic dynamical evolution, which is induced by the oscillation between
the BIC and bound state outside the continuum (BOC). These findings provide an
approach to manipulate the waveguide system via the bound states, and can be
applied in the quantum information processing.
