Observation of a tripartite quantum phase for coexisting extended, localized, and critical states

TL;DR

This study demonstrates the experimental realization of a tripartite quantum phase with coexisting extended, localized, and critical states in a quasiperiodically driven optical lattice using ultracold atoms.

Contribution

The paper reports the first experimental observation of a tripartite phase with all three state types coexisting in a quasiperiodic system, supported by exact theoretical analysis.

Findings

Successful creation of a tripartite phase in a quasiperiodic optical lattice.

Distinct transport properties of the three state types confirmed.

Development of a protocol for precise preparation and detection of quantum states.

Abstract

The disordered quantum world hosts three fundamental types of states: extended, localized, and critical, of which the critical states are confined to fine-tuned critical points or mobility edges in randomly disordered systems. The tripartite phase, with all three types of states coexisting over finite spectral windows, represents a hallmark distinction between quasiperiodic and truly random systems in the localization physics. Here, we report the realization of this exotic phase in a quasi-periodically driven orbital optical lattice with ultracold atoms. The optical lattice with a quasiperiodic Floquet modulation coupling s and p orbitals is realized in experiment and shown to host the tripartite phase from exact theory. We develop a two-stage protocol to precisely prepare and detect the three types of quantum states. The characteristic exponents of these states are determined from expansion dynamics, showing their distinct universal transport properties. Our study marks a significant advancement in exploring unconventional critical phenomena and localization physics with ultracold atoms.