  Neutral atom arrays are promising for large-scale quantum computing
especially because it is possible to prepare large-scale qubit arrays. An
unsolved issue is how to selectively excite one qubit deep in a 3D atomic array
to Rydberg states. In this work, we show two methods for this purpose. The
first method relies on a well-known result: in a dipole transition between two
quantum states driven by two off-resonant fields of equal strength but opposite
detunings $\pm\Delta$, the transition is characterized by two counter-rotating
Rabi frequencies $\Omega e^{\pm i\Delta t}$~[or $\pm\Omega e^{\pm i\Delta t}$
if the two fields have a $\pi$-phase difference]. This pair of detuned fields
lead to a time-dependent Rabi frequency $2\Omega \cos(\Delta t)$~[or $2i\Omega
\sin(\Delta t)$], so that a full transition between the two levels is
recovered. We show that when the two detuned fields are sent in different
directions, one atom in a 3D optical lattice can be selectively addressed for
Rydberg excitation, and when its state is restored, the state of any nontarget
atoms irradiated in the light path is also restored. Moreover, we find that the
Rydberg excitation by this method can significantly suppress the fundamental
blockade error of a Rydberg gate, paving the way for a high-fidelity entangling
gate with commonly used quasi-rectangular pulse that is easily obtained by
pulse pickers. Along the way, we find a second method for single-site Rydberg
addressing in 3D, where a selected target atom can be excited to Rydberg state
while preserving the state of any nontarget atom due to a spin echo sequence.
The capability to selectively address a target atom in 3D atomic arrays for
Rydberg excitation makes it possible to design large-scale neutral-atom
information processor based on Rydberg blockade.
