# Thermalization of a Trapped Single Atom with an Atomic Thermal Bath
## 4 Conclusions  
In conclusion, we investigated the thermalization of an atom trapped in an optical tweezer interacting with a thermal gas of ultracold atoms of a different species. We discussed the theory we used to understand how collisions between a trapped atom and the bath atoms translate into changes in the trapped atom's vibrational levels. With the help of a Monte Carlo simulation, we have shown how these changes lead to the trapped atom's cooling if the bath is at a lower temperature compared to the trapped atom. For parameters of practical interest, we found that the cooling rate in the radial direction is two orders of magnitude faster than the cooling rate in the axial direction. We have also shown the dependence of these cooling rates on the bath temperature, the tweezer's trapping frequency, and the single atom's starting temperature. Finally, we simulated a bath undergoing evaporative cooling and demonstrated that the trapped atom can be sympathetically cooled. We have shown that this could be an efficient scheme for cooling the single trapped atom, also considering three-body losses that limit the final efficiency.  
Besides the implementation of single atom quantum engines, this kind of system is a promising approach to studying out-of-equilibrium physics [13]. The system studied here could be modified to obtain a pristine realization of several instances of the spin-boson model or other open quantum system models like the Caldeira-Leggett model [16]. There are several additional exciting avenues that could be explored as extensions of this work. One could be to investigate the thermalization process in non-Markovian regimes, where the number of bath atoms is small or the scattering length is large. Another could be to increase the thermalization times inspired by the recents works in References [17; 18]. Alternatively, one could study a system in which the bath is realized with a pure Bose-Einstein condensate. The heat capacity of a Bose-Einstein condensate vanishes, making the feedback from the single atom significant. An exotic system could be realized with a partially condensed cloud, where two phases coexist and quantum and thermal fluctuations compete, or by trapping a single ion in the tweezer. Additionally, the use of squeezed states in the bath could lead to interesting quantum features that could boost the thermalization rate [19; 20; 21].  
Figure 5: Three-body loss during thermalization. (**a**) The red dashed line shows the percentage of times the trapped atom will be lost due to three-body collisions during the evaporative cooling shown in Figure 4. (**b**) Effect of change in scattering length on (i) thermalization time (red dashed) and (ii) the percentage of times the single atom will be lost due to a three-body collision during one thermalization period (blue solid). Here, \(T_{B}=1\)\(\mu\)k and \(n_{B}=10\times 10^{12}\) cm\({}^{-3}\) for (**b**).  
**Author Contributions:** All authors have equally contributed. All authors have read and agreed to the published version of the manuscript.  
**Funding:** All authors are supported by the Leverhulme Trust Research Project Grant UltraQuTe (grant number RGP-2018-266). A.M. is supported by the Erasmus programme.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.