Experimental verification of the inertial theorem control protocols

• Published in: New journal of physics Vol. 23; no. 9; pp. 93048 - 93060
• Main Authors: Hu, Chang-Kang, Dann, Roie, Cui, Jin-Ming, Huang, Yun-Feng, Li, Chuan-Feng, Guo, Guang-Can, Santos, Alan C., Kosloff, Ronnie
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.09.2021
• Subjects: Adiabatic flow; Algebra; Control theory; Deviation; Exact solutions; inertial theorem; Physics; quantum control; Qubits (quantum computing); System dynamics; Theorems; trapped ytterbium; Ytterbium
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ac2710

An experiment based on a trapped ytterbium ion validates the inertial theorem for the SU(2) algebra. The qubit is encoded within the hyperfine states of the atom and controlled by RF fields. The inertial theorem generates analytical solutions for non-adiabatically driven systems that are ‘accelerated’ slowly, bridging the gap between the sudden and adiabatic limits. These solutions are shown to be stable to small deviations, both experimentally and theoretically. By encoding a two-level system into hyperphine structure of a trapped ytterbium, we explore the high control over the system dynamics in order to validate range of applicability of the inertial theorem in our system. For large deviations from the inertial condition, the experimental results show that the phase remains accurate while the amplitude diverges, so the inertial theorem has good robustness in the phase estimate. As a result, we experimentally showed that the inertial solutions pave the way to rapid quantum control of closed, as well as open quantum systems.