  Quantum thermalization occurs in a broad class of systems from elementary
particles to complex materials. Out-of-equilibrium quantum systems have long
been understood to either thermalize or retain memory of their initial states,
but not both. Here we achieve the first simultaneous demonstration of
thermalization and memory in a quantum system. Using a Rydberg atom array, we
observe quantum thermalization restricted to Hilbert space fragments, where the
thermalized system retains characteristics of the initial configuration.
Intriguingly, states from different subspaces do not thermalize with each other
even when they have the same energy. Our work challenges established ideas of
quantum thermalization while experimentally resolving the longstanding tension
between thermalization and memory. These results may be applied to control
entanglement dynamics in quantum processors and quantum sensors.
