G. A. Prataviera

We investigate the dynamics of two trapped ions interacting with a common thermal reservoir, focusing on how cross-correlated dissipation influences heating, steady-state behavior, and parameter sensitivity. Starting from a microscopic system--reservoir model, we derive the corresponding Heisenberg--Langevin equations and show that reservoir-induced correlations generate collective decay channels and, when the cross-damping rate matches the local damping, a decoherence-free normal mode that preserves memory of the initial excitations. Using the Fisher information associated with motional population measurements, we identify the parameter regimes in which cross-damping enhances the estimability of both system and reservoir properties. For nonclassical initial states, we also show that reservoir-mediated correlations can generate or maintain entanglement, with the strongest effects occurring near the decoherence-free condition.

We apply estimation theory to a system formed by two interacting trapped ions. By using the Fisher matrix formalism, we introduce a simple scheme for estimation of the temperature of the longitudinal vibrational modes of the ions. We use the ions interaction to effectively infer the temperature of the individual ions, by optimising the interaction time evolution and by measuring only over one of the ions. We also investigate the effect of a non-thermal reservoir over the inference approach. The non-classicality of one of the ions vibrational modes, introduced due to a squeezed thermal reservoir, improves the indirect inference of the individual temperatures.