Towards simulation of coherent and dissipative processes using metastable states in Ytterbium ions

Trapped ions offer a platform for quantum simulation of spin and spin-boson models with high control over the Hamiltonian parameters. In particular, Ytterbium ions feature several metastable atomic states that can be used for multiple purposes ranging from sympathetic cooling to coherent manipulations. This project focusses on using the S_1/2 to D_3/2 quadrupole transition in two ways: the first one is to implement σ_zσ_z spin-spin interactions on clock states of Yb⁺ ions^[1]. We discuss a setup wherein a spatial light modulator is used to generate beam shaped arrays that can couple to axial modes of motion with beams orthogonal to the trap axis^[2]. Combining this scheme with σ_xσ_x and σ_yσ_y Molmer-Sorensen gates will enable us to simulate the Heisenberg-XYZ model. The second goal is to use the D_3/2 state for resolved sideband cooling of motional modes. By trapping ions of different species, we can sympathetically cool the collective motional states by addressing just one ion species while coherently manipulating the others. The Hamiltonian of such a system can be mapped onto a driven two-level system interacting with an engineered bath^[3]. To address this narrow transition, we need to ensure that the linewidth of the laser is reduced to at least a few kHz. Therefore, we discuss the laser locking setup to an Ultra-Low Expansion (ULE) cavity, its stabilization and characterization of the quadrupole transition in Yb⁺ ions.

[1] Baldwin et al 2021 Phys. Rev. A, vol. 103, no. 1, p. 012603

[2] Adam D West et al 2021 Quantum Sci. Technol. 6 024003

[3] Frank et al 2021 PRX Quantum 2, 010314