Experimental observation of thermalisation with noncommuting charges

Noncommuting charges have recently emerged as an area at the intersection of quantum thermodynamics and quantum information. There is a flurry of papers being published in this rapidly developing subfield. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. As noncommutation underlies quantumness, such systems are of particular interest. Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalisation. We initiate the experimental testing of its predictions with a trapped-ion simulator. We initialize 6–21 qubits in an approximate microcanonical subspace, a recently theorized generalisation of the microcanonical subspace for accommodating noncommuting charges. The noncommuting charges are the three spin components. We report the first experimental observation of an equilibrium state predicted within quantum-information thermodynamics in 2016: the non-Abelian thermal state. Despite the threat of decoherence breaking multiple conservation laws, thanks to our use of dynamical decoupling, our many-body system is shown to exhibit quantum-thermodynamical effects only described in theory until now. This work initiates the experimental testing of a recently emerged subfield that has so far remained theoretical.