Quantum optimal control of ten-level nuclear spin qudits in 87Sr

We study the ability to implement unitary maps on states of the I = 9/2 nuclear spin in Sr-87, a d = 10 dimensional (qudecimal) Hilbert space, using quantum optimal control. Through a combination of nuclear spin resonance and a tensor ac Stark shift, by solely modulating the phase of a radio-frequency magnetic field, the system is quantum controllable. Alkaline-earth-metal atoms, such as Sr-87, have a very favorable figure of merit for such control due to narrow intercombination lines and the large hyperfine splitting in the excited states. We numerically study the quantum speed limit, optimal parameters, and the fidelity of arbitrary state preparation and full SU(10) maps, including the presence of decoherence due to optical pumping induced by the light-shifting laser. We also study the use of robust control to mitigate some dephasing due to inhomogeneities in the light shift. We find that with an rf Rabi frequency of Omega(rf) and 0.5% inhomogeneity in the the light shift we can prepare an arbitrary Haar-random state in a time T = 4.57 pi/Omega(rf) with average fidelity (F-psi) = 0.9992, and an arbitrary Haar-random SU(10) map in a time T = 247 pi /Omega(rf) with average fidelity (F-U) = 0.9923.

Automated summary

In this study, we investigate the implementation of unitary maps on the nuclear spin of Sr-87, a d = 10 dimensional Hilbert space, using quantum optimal control. The system is found to be controllable through a combination of nuclear spin resonance and a tensor ac Stark shift, solely modulating the phase of a radio-frequency magnetic field. Alkaline-earth-metal atoms like Sr-87 offer favorable characteristics for such control, allowing for high fidelity preparation of arbitrary Haar-random states and SU(10) maps.