Fast programmable entanglement of Barium ion qubits using Rydberg states and AC-Stark shifts

Abstract: A scheme for excitation and individual addressing using Rydberg states of trapped Barium ions is presented for the purpose of fast gates and entanglement. Dipole matrix elements, dynamic polarizabilities, and one- and two-photon transition strengths are computed with a Supersymmetric Wentzel-Kramers-Brillouin (SWKB) method. A favorable two-photon excitation transition is identified, linking the 7s$1/2$ state to high-lying Rydberg states, with the strongest transition found to be 7s12->38s12. Additionally, the 7s1/2 state exhibits high polarizability around the telecom band at 1310 nm, enabling significant AC-Stark shift control with a turnkey laser at low power. This facilitates an individual addressing scheme by varying light intensity across an ion crystal, supporting sub-microsecond entangling gates between ion pairs with the strong and microwave-tunable Rydberg dipolar interaction. Selective addressing of individual ions by laser frequency tuning using the 6p3/2->7s1/2 transition is proposed.