Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems

Most physical systems rapidly reach thermal equilibrium. Certain quantum-mechanical systems in the presence of strong applied disorder, however, can get stuck in nonequilibrium states forever. Such systems are said to be in the “many-body localized” phase. While this phase is well understood in one dimension, its nature and stability in higher dimensions is largely unexplored. How systems transition between the many-body localized phase and the more familiar “thermal” phase is also generally unclear. We experimentally explore these questions using ultracold potassium atoms loaded in quasiperiodic optical lattices.

Our setup mimics disorder but has some distinctive features, such as the lack of rare fluctuations present in disordered systems. We start our system far from equilibrium (with atoms loaded into alternate columns) and observe if the system preserves the memory of this pattern. Beyond a critical disorder strength, the relaxation of local observables remains incomplete up to extremely long time scales, which hints at the existence of a many-body localized phase in two dimensions. Moreover, we find that between a regime of fast relaxation at weak disorder and the apparent absence of relaxation at strong disorder, there exists a regime of extremely slow dynamics, in which local observables relax to their thermal equilibrium but do so on time scales that are much larger than the intrinsic time scales of our system.

Our work demonstrates absence of local thermalization in higher dimensions and paves the way for stabilizing exotic quantum phenomena, such as coherent quantum memories and topological phases, at temperatures at which they would be destroyed without disorder.

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