Experimental exploration of fragmented models and non-ergodicity in tilted Fermi-Hubbard chains.

Thermalization of isolated quantum many-body systems can be understood as a redistribution of quantum information within the system. In this redistribution, macroscopic variables acquire a thermal value, which is independent of the initial state, and remain experimentally accessible. While microscopic variables, that contain most of the details of the initial state recede into experimentally inaccessible parts of the observable space. Therefore, a question of fundamental importance to quantum information theory is when do quantum many-body systems fail to thermalize, i.e., feature non-ergodicity. A useful test-bed for the study of one type of non-ergodicity is the tilted Fermi-Hubbard model, which is directly accessible in experiments with ultracold atoms in optical lattices. Here we experimentally study non-ergodic behavior in this model by observing the evolution of an initial charge-density wave over a wide range of parameters, where we find a remarkably long-lived initial-state memory [1]. In the limit of large tilts, we identify the microscopic processes which the observed dynamics arise from. These processes constitute an effective Hamiltonian and we experimentally show its validity [2]. This effective Hamiltonian features the novel phenomenon of Hilbert space fragmentation. In the intermediate tilt regime, while these effective models are no longer valid, we show that the features of fragmentation are still vaguely present in the dynamics.