A 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 (${}^{40}{\text{Ca}}^{+}$, ${}^{88}{\text{Sr}}^{+}$, ${}^{138}{\text{Ba}}^{+}$, ${}^{226}{\text{Ra}}^{+}$) 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 (${\text{Be}}^{+}$, ${\text{Mg}}^{+}$) 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 ${\sigma }^z{\sigma }^z$ 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 $\mu \text{m}$) 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.

16 pages, 5 figures