  Connectivity has an essential and indispensable role in the cold atom qubit
platform. Whilst the two-qubit Rydberg blockade gate recently receives rapid
progress on the fidelity side, a pressing challenge is to improve the
connectivity in pursuit of genuine scalability, with the ultimate prospect of
fully-connected cold atom qubit array. It turns out that a solid step along
this direction can be made by introducing extra buffer atom to extend two-qubit
Rydberg blockade gate beyond a purely nearest-neighbor two-body interaction.
Through Rydberg dipole-dipole interactions, the buffer atom couples with the
two qubit atoms which do not directly exert any physical influence on each
other. The established method of off-resonant modulated driving is not only
convenient but also lays down the groundwork for this latest development.
Although the atomic linkage structure here exhibits nontrivial complications
compared to previous cases of mere two-body system, the population can
satisfyingly return to the ground state after the ground-Rydberg transition
with properly designed modulation waveforms. It can be instantiated via
one-photon and two-photon ground-Rydberg transitions in common practices.
Furthermore, with buffer atom relay or similar structures, it is possible to
realize two-qubit entangling gate between two far-away qubit atoms. Besides the
core issue that such solutions are attainable, the representative modulation
patterns are also analyzed, demonstrating the versatility of
buffer-atom-mediated two-qubit gate. Put in a broader perspective, these
efforts bring the cold atom qubit platform closer to the notions of wires and
junctions in solid state electronics.
