  In quantum-optics experiments with both natural and artificial atoms, the
atoms are usually small enough that they can be approximated as point-like
compared to the wavelength of the electromagnetic radiation they interact with.
However, superconducting qubits coupled to a meandering transmission line, or
to surface acoustic waves, can realize "giant artificial atoms" that couple to
a bosonic field at several points which are wavelengths apart. Here, we study
setups with multiple giant atoms coupled at multiple points to a
one-dimensional (1D) waveguide. We show that the giant atoms can be protected
from decohering through the waveguide, but still have exchange interactions
mediated by the waveguide. Unlike in decoherence-free subspaces, here the
entire multi-atom Hilbert space is protected from decoherence. This is not
possible with "small" atoms. We further show how this decoherence-free
interaction can be designed in setups with multiple atoms to implement, e.g., a
1D chain of atoms with nearest-neighbor couplings or a collection of atoms with
all-to-all connectivity. This may have important applications in quantum
simulation and quantum computing.
