Using a quantum SWAP engine to experimentally validate thermodynamic uncertainty relations

Thermodynamic uncertainty relations (TURs) arise from the bounds on fluctuations of thermodynamic quantities during a non-equilibrium process, and they impose constraints on the corresponding process. We experimentally implement a quantum SWAP engine on a nuclear magnetic resonance setup and demonstrate that a Gibbs thermal state can be prepared in two different ways, either directly from a thermal equilibrium state or by first initializing the system in a pseudopure state. We show that the quantum SWAP engine can work both as a heat engine and as a refrigerator. Starting from a pseudopure state, we construct the SWAP engine and investigate the validity of two different TURs, namely, a generalized TUR and a tighter, more specific TUR. Our results validate that the generalized TUR is obeyed in all the working regimes of the SWAP engine, while the tighter TUR is violated in certain regimes.