Developments in driving atomic transitions using the ponderomotive interaction

We describe recent developments in a novel spectroscopic method that couples Rydberg states using an intensity-modulated optical lattice. The method is fundamentally different from traditional microwave spectroscopy: it engages the $\mathbf{A} \cdot \mathbf{A}$ (ponderomotive) term rather than the $\mathbf{A} \cdot \mathbf{p}$ term of the atom-field interaction Hamiltonian. The method allows us to drive GHz-frequency transitions between Rydberg states with optical spatial resolution and is not subject to the usual electric-dipole selection rules (i.e., higher-order multipole transitions are driven in first-order time-dependent perturbation)\footnote{K.R. Moore, S.E. Anderson, and G. Raithel, \textbf{Nat. Comm.} 6, 6090 (2015)},\footnote{K.R. Moore and G. Raithel, \textbf{Phys. Rev. Lett.}, 115, 163003 (2015)},\footnote{B. Knuffman and G. Raithel, \textbf{Phys. Rev. A}, 75, 053401, (2007)}. We review our previous experimental results using cold atoms, including an extension of this method into the near-sub-THz regime via modulation harmonics. We present new theoretical results showing extensions of this method to odd-parity transitions. Finally, we discuss the proposed application of this method to a precision measurement of the Rydberg constant using circular-state Rydberg atoms.