Experimental demonstration of the validity of the quantum heat-exchange fluctuation relation in an NMR setup.*

We experimentally explore the validity of the Jarzynski and Wöjcik quantum heat-exchange fluctuation relation by implementing an interferometric technique in liquid-state nuclear magnetic resonance setup and study the heat-exchange statistics between two coupled spin-1/2 quantum systems. We experimentally emulate two models—(i) the XY-coupling model, containing an energy conserving interaction between the qubits, and (ii) the XX-coupling model—and analyze the regimes of validity and violation of the fluctuation symmetry when the composite system is prepared in an uncorrelated initial state with individual spins prepared in local Gibbs thermal states at different temperatures.We further extend our analysis for heat exchange by incorporating correlation in the initial state. We support our experimental findings by providing exact analytical results. Our experimental approach is general and can be systematically extended to study heat statistics for more complex out-of-equilibrium many-body quantum systems.