Trapped ions beyond low intensity regimes
The understanding of quantum properties of controllable physical systems, with perspectives for the development of practical applications, has been one of the central themes in physics in recent decades. Many different physical systems have been used for these applications, and the one formed by trapped ions interacting with lasers occupies a prominent position in quantum technologies. Among its advantages are the high degree of possible control over the system and its dynamics, and the good ability to isolate it from disturbances iinduced by the external environment. In this system, the speed of operations or quantum gates is limited by the intensity of the incident laser. It is widely known that, in the limit of low intensities, it is possible to make approximations that considerably simplify the description of the dynamics of the system and, in fact, most of the results obtained with trapped ions take this limit into account. But, aiming for faster operations, it is desirable to look for effective descriptions also for higher intensities. The central objective of our work has been precisely the description and exploration of these new regimes. In particular, one of the main results we have already achieved was an effective Hamiltonian that interpolates the weak intensity and intermediate intensity regimes, when the frequency of the transitions is of the order of the oscillation frequency of the ion's center of mass (arXiv:2212.12612) . This and other results, partial or already obtained, will be discussed in this qualifying exam.