Realization of Trapped Ion Dynamics in the Strong-Field Regime and Non-Markovianity

TL;DR

This paper experimentally explores the complex quantum dynamics of a trapped ion in the strong-field regime, revealing non-Markovian effects and novel behaviors beyond traditional models, with implications for quantum control and open system understanding.

Contribution

It demonstrates the realization and analysis of non-Markovian quantum dynamics in a trapped ion system beyond the weak-field regime, including the identification of parameter conditions leading to maximal memory effects.

Findings

Non-Markovianity varies non-monotonically with Rabi frequency.

Maxima of non-Markovianity occur when delta^2 + Omega^2 = nu^2.

System dynamics resemble the Jaynes-Cummings model at specific parameters.

Abstract

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.