  When a system thermalizes it loses all local memory of its initial
conditions. This is a general feature of open systems and is well described by
equilibrium statistical mechanics. Even within a closed (or reversible) quantum
system, where unitary time evolution retains all information about its initial
state, subsystems can still thermalize using the rest of the system as an
effective heat bath. Exceptions to quantum thermalization have been predicted
and observed, but typically require inherent symmetries or noninteracting
particles in the presence of static disorder. The prediction of many-body
localization (MBL), in which disordered quantum systems can fail to thermalize
in spite of strong interactions and high excitation energy, was therefore
surprising and has attracted considerable theoretical attention. Here we
experimentally generate MBL states by applying an Ising Hamiltonian with
long-range interactions and programmably random disorder to ten spins
initialized far from equilibrium. We observe the essential signatures of MBL:
memory retention of the initial state, a Poissonian distribution of energy
level spacings, and entanglement growth in the system at long times. Our
platform can be scaled to higher numbers of spins, where detailed modeling of
MBL becomes impossible due to the complexity of representing such entangled
quantum states. Moreover, the high degree of control in our experiment may
guide the use of MBL states as potential quantum memories in naturally
disordered quantum systems.
