Experimental observation of exact quantum critical states

TL;DR

This paper reports the first experimental observation of exact quantum critical states in a programmable quasiperiodic system, revealing their properties, mechanisms protecting them, and the transition dynamics between localized and critical phases.

Contribution

It provides the first experimental realization of exact quantum critical states with a rigorous mechanism and demonstrates their protection by quasiperiodic zeros in a superconducting qubit system.

Findings

Critical states coexist with delocalized dynamics.

Quasiperiodic zeros protect critical states.

Energy-dependent mobility edges are observed.

Abstract

Anderson localization physics features three fundamental types of eigenstates: extended, localized, and critical, with the third one exhibiting the exotic properties in-between the former two. Confirming the presence of critical states is challenging, as it typically necessitates either advancing the analysis to the thermodynamic limit or identifying a universal mechanism which can rigorously determine these states. Here we report the unambiguous experimental realization of critical states, governed by a rigorous mechanism for exact quantum critical states, and further observe a generalized mechanism that quasiperiodic zeros in hopping couplings protect the critical states. We implement a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials through a multiple superconducting qubit quantum system. By measuring the time-evolving observables, we identify the coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which are the defining features of the critical states. We map the localized-to-critical phase transition and demonstrate that critical states persist until quasiperiodic zeros are removed by strong long-range couplings, highlighting a novel generalized mechanism discovered in this experiment and shown with rigorous theory. Finally, we resolve the energy-dependent transition between localized and critical states, revealing the presence of anomalous mobility edges.