# Thermodynamics in linear Paul traps

**Single Ion Heat Engine**

While thermodynamic systems are generally treated by averaging over many body systems, we scale such a system down to the ultimate limit of a single quantum particle. We analyze an experimental scheme for a nano-heat engine using a single ion as working gas. An Otto cycle may be implemented by confining the ion in a linear Paul trap with tapered geometry and coupling it to engineered reservoirs. Are the classical thermodynamic laws, based on the dynamics of large ensembles, still valid for a single particle? Do they have to be modified when employing quantum reservoirs?

To realize an Otto cycle the single ion is trapped in a linear Paul trap with tapered geometry. It is the coupled to reservoirs which are engineered by detuned laser radiation or tailored electronic noise on the electrodes. These heat baths heat and cool the radial thermal state of the ion alternately. The cycle of heating and cooling is repeated resonantly with the axial eigenfrequency of the ion, transducing a change in temperature in the radial state into a coherent movement along the trap axis. From this oscillation the power of the engine can be determined. Monte-Carlo simulations have demonstrated the feasibility of this system with realistic experimental conditions, leading to an efficiency at maximum power of 30%.