  We revisit the implementation of a two-qubit entangling gate, the
M{\o}lmer-S{\o}rensen gate, using the adiabatic Rydberg dressing paradigm for
neutral atoms as studied in [Phys. Rev. A 101, 030301 (R) (2020)]. We study the
implementation of rapid adiabatic passage using a two-photon transition, which
does not require the use of an ultra-violet laser, and can be implemented using
only amplitude modulation of one field with all laser frequencies fixed. We
find that entangling gate fidelities, comparable to the one-photon excitation,
are achievable with the two-photon excitation. Moreover, we address how the
adiabatic dressing protocol can be used to implement entangling gates outside
the regime of a perfect Rydberg blockade. We show that using adiabatic dressing
we can achieve scaling of gate fidelity set by the fundamental limits to
entanglement generated by the Rydberg interactions while simultaneously
retaining a limited population in the doubly-excited Rydberg state. This allows
for fast high fidelity gates for atoms separated beyond the blockade radius.

Quantum Physics