Zihan Yin

Probing quantum dynamics in the strong-field regime is critical for advancing our understanding of controlled quantum systems and developing robust quantum technologies. In this work, we experimentally investigate the dynamics of a trapped ion where the Rabi frequency (Omega) approaches the vibrational mode frequency (nu), pushing the system beyond the weak-field regime, where non-trivial quantum correlations emerge. We begin by setting the detuning (delta) - the frequency offset between the qubit transition and the driving field - to zero and varying Omega from low to high values, eventually reaching the vibrational frequency. Using quantum state tomography, we reconstruct the density matrix and track its evolution to assess non-Markovianity, revealing significant memory effects governed by the interplay between internal and motional degrees of freedom. Furthermore, by exploring the dynamics across various parameter pairs (Omega, delta), we find that non-Markovianity does not always increase monotonically with Omega for a fixed delta. Strikingly, when the condition delta squared plus Omega squared equals nu squared is met, the non-Markovianity exhibits a circular pattern of maxima. At this parameter combination, the system's Hamiltonian takes a form similar to the Jaynes-Cummings model, enabling the possibility of analytical insights into the observed dynamics. These results go beyond the conventional carrier and sideband regimes, uncovering novel features of strong-field quantum dynamics. Our findings establish a pathway for using trapped-ion platforms to investigate non-Markovianity, coherent control, and the fundamental behavior of open quantum systems in extreme regimes.

Trapped-ion qubits are among the most promising candidates for quantum computing, quantum information processing, and quantum simulation. In general, trapped ions are considered to have sufficiently long coherence times, which are mainly characterized under laser-free conditions. However, in reality, essential laser fields for quantum manipulation introduce residual light shift, which seriously degrades the coherence due to power fluctuations. Here, we present a comprehensive study of AC Stark shifts in the hyperfine energy levels of the $^{171}\mathrm{Yb}^+$ ion, revealing an asymmetric light shift between two circular polarizations in the clock qubit and pronounced vector light shifts in the Zeeman qubits. By precisely tuning these polarizations, a remarkable enhancement in coherence time is observed, reaching over a hundredfold for the clock qubit and more than tenfold for the Zeeman qubits, when comparing conditions of maximum and minimum shifts. These findings advance the practical realization of scalable trapped-ion quantum processors, enabling deep quantum circuit execution and long duration adiabatic operations.

The trapped-ion system has been a leading platform for practical quantum computation and quantum simulation since the first scheme of a quantum gate was proposed by Cirac and Zoller in 1995. Quantum gates with trapped ions have shown the highest fidelity among all physical platforms. Recently, sophisticated schemes of quantum gates such as amplitude, phase, frequency modulation, or multi-frequency application, have been developed to make the gates fast, robust to many types of imperfections, and applicable to multiple qubits. Here, we review the basic principle and recent development of quantum gates with trapped ions.