Optical magnetism and wavefront control by arrays of strontium atoms

By analyzing the parameters of electronic transitions, we show how bosonic Sr atoms in planar optical lattices can be engineered to exhibit optical magnetism and other higher-order electromagnetic multipoles that can be harnessed for wavefront control of incident light. Resonant $\lambda\simeq 2.6\mu$m light for the $^3D_1\rightarrow {^3}P_0$ transition mediates cooperative interactions between the atoms while the atoms are trapped in a deeply subwavelength optical lattice. The atoms then exhibit collective excitation eigenmodes, e.g., with a strong cooperative magnetic response at optical frequencies, despite individual atoms having negligible coupling to the magnetic component of light. We provide a detailed scheme to utilize excitations of such cooperative modes consisting of arrays of electromagnetic multipoles to form an atomic Huygens' surface, with complete $2\pi$ phase control of transmitted light and almost no reflection, allowing nearly arbitrary wavefront shaping. In the numerical examples, this is achieved by controlling the atomic level shifts of Sr with off-resonant ${^3P}_J\rightarrow {^3D}_1$ transitions, which results in a simultaneous excitation of arrays of electric dipoles and electric quadrupoles or magnetic dipoles. We demonstrate the wavefront engineering for a Sr array by realizing the steering of an incident beam and generation of a baby-Skyrmion texture in the transmitted light via a topologically nontrivial transition of a Gaussian beam to a Poincar\'{e} beam, which contains all possible polarizations in a single cross-section.