Experimental Demonstration of Swift Analytical Universal Control over Nearby Transitions

We simultaneously drive two near-by transitions with a trapped ⁹Be⁺ ion by a time dependent waveform, demonstrating individual and simultaneous quantum control over the transitions even with the average Rabi rates close to their frequency separation[1]. Our demonstration is extended from recent theoretical proposals to simplify the parametrization of the waveform with analytical methods [2,3]. We achieve operation fidelities ranging from 99.2(3)% to 99.6(3)% with approximately an order of magnitude speed up comparing with weak square pulse, conventionally used to resolve nearby transitions. Our work may be able to extend towards working with complicated spectrum for scaled quantum system and high-spin systems, and may be beneficial to a broad range of systems, such as superconducting qubits, phonons in trapped ions.

[1] Y. Li et al. arXiv:2201.06246(2022). [2] E. Barnes, Phys. Rev. A 88, 013818(2013). [3] S. E. Economou et al, Phys. Rev. B 91, 161405(2015).