Fig. 1: Operation principle of the quantum heat engine.

a Individual laser-cooled Cs atoms (green) are immersed in an ultracold Rb cloud (orange); both are confined in a common optical dipole trap (DT). External magnetic fields and microwave (MW) radiation, respectively, implement the power strokes of the quantum heat engine and distinguish the high- from the low-energy bath. The inset shows typical m_F-resolved fluorescence images of single Cs atoms for t = t_B = 300 ms after initialization, from which the quantized spin, and thus heat exchange, can be determined. The position of the bath cloud is indicated in orange with a width of 4σ. b The experimental Otto cycle consists of a heating stage, during which average heat 〈Q_H〉 is absorbed, and a power stroke induced by an adiabatic change of the magnetic field. A microwave field then switches the bath from high to low energy. The cycle is further completed by a cooling step, during which average heat 〈Q_C〉 is released, and an additional power stroke when the magnetic field is adiabatically brought back to its initial value. c The heat transfer between the Cs atom (engine) and a Rb (bath) atom occurs via inelastic spin-exchange collisions. In each collision, a single quantum of spin associated with a certain energy quantum is exchanged. Spin polarization of the Rb atoms and spin-conservation in individual collisions allow only up to six exo- or endothermal processes, corresponding to heating or cooling. d Owing to the difference of atomic Landé factors between Cs and Rb, the quantum heat engine (green) absorbs heat 〈Q_H〉 and releases heat 〈Q_C〉 (to produce work 〈W〉), while the bath releases more energy. The lost energy is irreversibly dissipated during an average of ten elastic collisions and is described by a heat leak 〈Q_L〉 from the high-energy bath.