Understanding thermodynamics at the quantum level is one of the big challenges in the field of physics. Ultracold atoms are a promising platform to tackle this challenge as they allow a high degree of control over their internal and external states and to prepare samples with controlled interactions with the environment. Hence, the quantum properties of these systems can be easily controlled and studied.

We have recently built a machine which cools and traps samples of ultracold Rubidium and Potassium atoms for the study of thermodynamics in the quantum regime. One of our major goals is to demonstrate the working of ultracold single atom quantum heat engines. Recently, we proposed a scheme for building a single atom quantum heat engine based on ultracold atom technologies~\cite{barontini_ultra-cold_2019}. In this proposal we show that the three paradigmatic heat engines, Carnot, Otto and Diesel are within reach of state-of-the-art technology, and their performances can be benchmarked experimentally. We will discuss how we wish to implement these engines in our experiment and we will report on the experimental progress.

We will also present the results of a related experiment with the same machine, where we realize a method to produce non-equilibrium Bose Einstein condensates with purities that cannot be reached by equilibrium samples with the same parameters. To do this, we immerse an ultracold Bose gas of $^{87}$Rb in a cloud of $^{39}$K with substantially higher temperatures, providing a controlled source of dissipation.
We demonstrate that our out-of-equilibrium samples are long-lived and do not reach equilibrium in a time that is accessible for our experiment. The controlled dissipative environment is therefore a promising tool for the engineering of systems thermodynamically out of equilibrium.