Trapping States of a Trapped Ion, Revisited

A. Hashemloo, Claude M. Dion

We study the quantum stability of the dynamics of ions in a Paul trap. We revisit previous results that showed that quantum trajectories did not have the same region of stability as their classical counterpart, contrary to what is obtained from a Floquet analysis of the motion in the periodic trapping field. Using numerical simulations of the full wave-packet dynamics, we confirm that the classical trapping criterion is fully applicable to quantum motion, when considering both the expectation value of the position of the wave packet and its width.

Sascha Wallentowitz, W. Vogel, P. E. Toschek

Joel H. Parks

Aditi Sen De, Ujjwal Sen, Maciej Lewenstein +3 more

We report our research on disordered complex systems using cold gases and trapped ions, and address the possibility of using complex systems for quantum information processing. Two simple paradigmatic models of disordered complex systems are revisited here. The first one corresponds to a short range disordered Ising Hamiltonian (spin glasses), which can be implemented with a Bose-Fermi (Bose-Bose) mixture in a disordered optical lattice. The second model we address here is a long range disordered Hamiltonian, characteristic of neural networks (Hopfield model), which can be implemented in a chain of trapped ions with appropriately designed interactions.

Galina A. Nemova

T. Tassis, F. L. Semião

Trapped ions driven by electromagnetic radiation constitute one of the most developed quantum technologies to date. The scenarios range from proof-of-principle experiments to on-chip integration for quantum information units. In most cases, these systems have operated in a regime where the magnitude of the ion-radiation coupling constant is much smaller than the trap and electronic transition frequencies. This regime allows the use of simple effective Hamiltonians based on the validity of the rotating-wave approximation. However, novel trap and cavity designs now permit regimes in which the trap frequency and the ion-radiation coupling constant are commensurate. This opens up new avenues for faster quantum gates and state transfers from the ion to a photon and other quantum operations. From the theoretical side, however, there is not yet much known in terms of models and applications that go beyond the weak-driving scenario. In this work, we present two main results in the scenario of stronger driving. First, we revisit a known protocol to reconstruct the motional Wigner function and expand it to stronger-driving lasers. This extension is not trivial because the original protocol makes use of effective Hamiltonians valid only for weak driving. The use of stronger fields or faster operations is desirable since experimental reconstruction methods of that kind are usually hindered by decoherence. We then present a model that allows the analytical treatment of stronger driving and that works well for nonresonant interactions, which are generally out of the reach of previous models.