Prospects of reaching the quantum regime in Li-Yb$^+$ mixtures

TL;DR

This study uses numerical simulations to assess the feasibility of reaching the quantum regime in Li-Yb$^+$ mixtures, highlighting the importance of micromotion suppression and potential for quantum state control.

Contribution

It provides a detailed analysis of collision energies, micromotion effects, and buffer-gas cooling in Li-Yb$^+$ mixtures, demonstrating experimental conditions needed to achieve the quantum regime.

Findings

Collision energies can reach below the quantum limit with ideal conditions.

Suppression of excess micromotion is feasible within current experimental capabilities.

Buffer-gas cooling can reduce ion motion energy to 10-100 μK, enabling quantum regime studies.

Abstract

We perform numerical simulations of trapped $^{171}$Yb$^+$ ions that are buffer gas cooled by a cold cloud of $^6$Li atoms. This species combination has been suggested to be the most promising for reaching the quantum regime of interacting atoms and ions in a Paul trap. Treating the atoms and ions classically, we compute that the collision energy indeed reaches below the quantum limit for a perfect linear Paul trap. We analyze the effect of imperfections in the ion trap that cause excess micromotion. We find that the suppression of excess micromotion required to reach the quantum limit should be within experimental reach. Indeed, although the requirements are strong, they are not excessive and lie within reported values in the literature. We analyze the detection and suppression of excess micromotion in our experimental setup. Using the obtained experimental parameters in our simulation, we calculate collision energies that are a factor 2-11 larger than the quantum limit, indicating that improvements in micromotion detection and compensation are needed there. We also analyze the buffer-gas cooling of linear and two-dimensional ion crystals. We find that the energy stored in the eigenmodes of ion motion may reach 10-100 $\mu$K after buffer-gas cooling under realistic experimental circumstances. Interestingly, not all eigenmodes are buffer-gas cooled to the same energy. Our results show that with modest improvements of our experiment, studying atom-ion mixtures in the quantum regime is in reach, allowing for buffer-gas cooling of the trapped ion quantum platform and to study the occurrence of atom-ion Feshbach resonances.