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

TLDR

Many-body localization breaks the ergodic hypothesis, creating a new phase, yet its occurrence in higher dimensions remains an outstanding experimental and theoretical challenge. The study experimentally investigates relaxation dynamics of an interacting fermionic potassium gas in a two‑dimensional optical lattice with varying quasi‑periodic potentials. The authors load the fermionic potassium gas into a two‑dimensional optical lattice with quasi‑periodic potentials along both axes and monitor its relaxation dynamics. The experiments show a dramatic slowdown of relaxation at intermediate disorder due to rare‑region effects, negligible relaxation beyond a critical disorder suggesting a two‑dimensional MBL transition, and reveal a distinct interplay of interactions, disorder, and dimensionality that informs theory.

Abstract

In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down completely, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge both for experiments and theory. Here, we experimentally explore the relaxation dynamics of an interacting gas of fermionic potassium atoms loaded in a two-dimensional optical lattice with different quasi-periodic potentials along the two directions. We observe a dramatic slowing down of the relaxation for intermediate disorder strengths and attribute this partially to configurational rare-region effects. Beyond a critical disorder strength, we see negligible relaxation on experimentally accessible timescales, indicating a possible transition into a two-dimensional MBL phase. Our experiments reveal a distinct interplay of interactions, disorder, and dimensionality and provide insights into regimes where controlled theoretical approaches are scarce.