Lorenzo Oghittu, Dissertation, Fachbereich Physik der Universität Hamburg, 2024 :

"Quantum Dynamics of an Ion in a Quantum Gas – An Open System Approach"



Summary

Kurzfassung


Titel

Kurzfassung

Summary

We present an open system approach to the study of the quantum dynamics of a single ion immersed in a bath of ultracold atoms. On this purpose, we derive a master equation in the limit of weak-coupling and Lamb-Dicke approximation for the reduced density matrix of the ion, which allows us to capture the dependence of the ion’s temperature, position and velocity as a function of the parameters involved in the description. This approach is applied to different scenarios that are relevant for experiments involving ionic impurities in ultracold Fermi or Bose gases. The master equation is first derived for a Paul-trapped ion, whereas the bath is rep- resented by either a Bose gas below or above the critical temperature of condensation, or by a spin-polarized Fermi gas. Our numerical results show that the ion temperature averaged over the micromotion induced by the Paul trap saturates to a final value, which depends on the temperature of the bath and on the atom-ion scattering length. The density of the bath, on the other hand, only weakly affects the final temperature of the ion while strongly influencing the saturation time. As expected, the latter is shorter for a higher density. Interestingly, we find that for temperatures of the gas lower than the Fermi temperature, the gas statistics sensibly affects the final temperature of the ion. In particular, a Fermi bath allows the ion to reach lower temperatures. A similar approach is then applied to the case of an untrapped ion moving inside a Bose-Einstein condensate with an initial finite momentum. We observe that the ion temperature is reduced by several orders of magnitude in a time scale on the order of microsecond for a 87Rb+ ion in a 87Rb Bose-Einstein condensate with a density between 1013 cm−3 and 1014 cm−3. The aforementioned behavior is noticeably affected by the density of the condensate, with a higher density corresponding to faster cooling. The initial momentum of the ion, on the contrary, only weekly affects this dynamics. In the same time scale in which the cooling is observed, the ion velocity is also strongly reduced, making the position of the ion converge to a final value. Therefore, our findings predict the cooling and pinning of the ion due to the interaction with the Bose-Einstein condensate. Furthermore, we consider the possibility of using an ionic impurity as a probe for the temperature of a Fermi gas. According to the thermometric protocol proposed by M. T. Mitchison et al. [Phys. Rev. Lett. 125, 080402 (2020)] for a neutral impurity, the ion is considered as a two-level spin particle undergoing pure dephasing due to the coupling with the bath. By means of the theory of quantum estimation, we study how the performance of the thermometric measurement is affected by some of the parameters of the system, such as the temperature of the gas, the probing time and the atom-ion scattering length. Comparing our results with those obtained with a neutral impurity, we find that the long-range tail of the atom-ion potential has a profound impact on the thermometric performance: for certain values of the interaction parameter, it strongly enhances the sensitivity of the probe, making the ion a better sensor for the temperature of the Fermi gas.