  We investigate the non-Markovian dynamics of two giant artificial atoms
interacting with a continuum of bosonic modes in a one-dimensional (1D)
waveguide. Based on the diagrammatic method, we present the exact analytical
solutions, which predict the rich phenomena of collective radiance. For the
certain collective states, the decay rates are found to be far beyond that
predicted in the the Dicke model and standard Markovian framework, which
indicates the occurrence of super-superradiance. The
superadiance-to-subradiance transition could be realized by adjusting the
exchange symmetry of giant atoms. Moreover, there exists multiple bound states
in continuum (BICs), with photons/phonons bouncing back and forth in the
cavity-like geometries formed by the coupling points. The trapped
photons/phonons in the BICs can also be re-released conveniently by changing
the energy level splitting of giant atoms. The mechanism relies on the joint
effects of the coherent time-delayed feedback and the interference between the
coupling points of giant atoms. This work fundamentally broadens the fields of
giant atom collective radiance by introducing non-Markovianity. It also paves
the way for a clean analytical description of nonlinear open quantum system
with more complex retardation.
