Decoherence-free Interaction between Giant Atoms in Waveguide QED

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 surface acoustic waves, can realize "giant artificial atoms" that couple to a bosonic field at several points which are wavelengths apart. In previous work, we have shown that a single such giant atom has a frequency-dependent relaxation rate and Lamb shift due to interference effects arising from the multiple coupling points. In the present work, we generalize this to multiple giant atoms coupled at multiple points to a 1D waveguide. We show that the waveguide can mediate pairwise exchange interactions between the atoms even though the atoms do not decay through emission to the waveguide. 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-neighbour couplings or a collection of atoms with all-to-all connectivity.