Addressable Rydberg excitation in arrays of single neutral atoms with a strongly focused flat-top beam

We present a method for generating a laser beam with flat intensity and phase profiles in the focal region where the beam interacts with neutral ${}^{87}$Rb atoms in an array of optical dipole traps. We synthesize the beam as a superposition of Hermite–Gaussian or Laguerre–Gaussian modes. Then we give analytical expressions for the coefficients of such a superposition, an analysis of beam propagation along the $z$ axis in the vicinity of the waist, and several other related theoretical issues. Rydberg two-qubit dynamics driven by this flat-top profile are analyzed through numerical solutions of the Lindblad master equation using our in-house Julia package. Beam preparation is demonstrated on a neutral-atom experimental platform. Measurements reveal a difference in the visibility of Rabi oscillations for addressed atoms compared with neighboring ones, confirming the effective spatial selectivity provided by the flat-top beam profile.