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

Abstract

We propose an optical scheme for generating entanglement between co-trapped identical or dissimilar alkaline-earth atomic ions ($^{40}\mathrm{Ca}^{+}$, $^{88}\mathrm{Sr}^{+}$, $^{138}\mathrm{Ba}^{+}$, $^{226}\mathrm{Ra}^{+}$) which exhibits fundamental error rates below ${10}^{\ensuremath{-}4}$ 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 (${\text{Be}}^{+}$, ${\text{Mg}}^{+}$) 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 ${\ensuremath{\sigma}}^{z}{\ensuremath{\sigma}}^{z}$ 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 $2\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$) 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.