Wavelength-insensitive, multispecies entangling gate for group-2 atomic ions

We propose an optical scheme for generating entanglement between co-trapped identical or dissimilar alkaline-earth atomic ions (⁺⁴⁰Ca, ⁺⁸⁸Sr, ⁺¹³⁸Ba, ⁺²²⁶Ra) which exhibits fundamental error rates below 10^-4 and can be implemented with a broad range of laser wavelengths spanning from ultraviolet to infrared. We also discuss straightforward extensions of this technique to include the two lightest group-2 ions (Be⁺,Mg⁺) for multispecies entanglement. The key elements of this wavelength-insensitive geometric phase gate are the use of a ground (S_{1 /2}) and a metastable (D_{5 /2}) electronic state as the qubit levels within a σ^zσ^z light-shift entangling gate. We present a detailed analysis of the principles and fundamental error sources for this gate scheme which includes photon scattering and spontaneous emission decoherence, calculating two-qubit-gate error rates and durations at fixed laser beam intensity over a large portion of the optical spectrum (300 nm to 2 μ m ) for an assortment of ion pairs. We contrast the advantages and disadvantages of this technique against previous trapped-ion entangling gates and discuss its applications to quantum information processing and simulation with like and multispecies ion crystals.