Five phases of localization physics observed in a single quantum system

Team tests out their photonic Floquet platform. Credit: Jingyun Fan

Physicists in China have observed five phases in localization physics within a single quantum system. Using an advanced photonic platform, the team, led by Yucheng Wang and Jingyun Fan at the Southern University of Science and Technology, Shenzhen, has demonstrated that localization physics is likely far richer than physicists anticipated. Their results have been published in Physical Review Letters .

Theory of a third phase

In 1958, American physicist Philip Anderson made the foundational discovery that disordered media are better at trapping waves than orderly lattice structures. Described mathematically by "localization phases," this phenomenon now underpins our understanding of both condensed matter and wave physics.

So far, theory has distinguished between two distinct localization phases: one exhibiting "extended" states, which support wave transport, and the other associated with "localized" states, which suppress it. Yet through recent theoretical work, physicists uncovered a third distinct phase, named the "critical phase."

"These states exhibit fractal spatial structures and anomalous transport properties, giving rise to new localization phases beyond the traditional paradigm," Wang explains. "However, experimental realization of critical states, especially those coexisting with other types of states, has remained an outstanding challenge."

A Floquet photonic platform

In their study, Wang and Fan's team set out to observe the critical phase and coexisting phases directly. To achieve this, they designed an experimental platform based on the principles of Floquet physics : when systems are driven by a periodic force, the interplay between that driving rhythm and the system's own behavior gives rise to new effective properties.

The team's setup involved a programmable photonic Floquet platform, where a laser pulse circulated between sites inside an optical loop. Each round trip implemented three operations in sequence: site-dependent spin rotations, hopping between nearest-neighbor sites, and onsite energy potentials.

After each round trip, the setup also bled off and detected a small amount of light, providing a snapshot of the spatiotemporal distribution across the synthetic lattice.

By tracking how this distribution evolved over time, the researchers could determine whether it spread ballistically, stayed confined to the initial site, or exhibited oscillatory dynamics, corresponding to the presence of extended, localized or critical states, respectively.

To switch between phases, they adjusted two independent controls governing the relative weight of quasiperiodic modulations in the hopping amplitudes and onsite potentials. "This capability makes it possible to realize and investigate a rich hierarchy of localization phases within a single experimental system," Fan describes.

Five distinct phases

With their Floquet platform, Wang and Fan's team observed the critical phase—confirming earlier theoretical predictions of a third pure phase in localization physics—and clearly demonstrated its dynamical distinction from extended and localized phases. Beyond that, they also revealed the existence of two coexisting phases within the same system: an extended-localized coexisting phase and a localized-critical coexisting phase, each producing unique patterns of evolution observed on the platform.

Together, the clear experimental identification of five distinct phases suggests that localization physics is remarkably rich. "To our knowledge, this is the most comprehensive realization of localization phases achieved so far within a single controllable quantum system," Fan says.

"More broadly, the platform provides a versatile framework for exploring multifractal critical phases, mobility-edge physics, and a broad spectrum of localization and transport phenomena in a highly controllable setting."

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Publication details

Yao Qin et al, Observation of Five Distinct Localization Phases in a 1D Floquet System, Physical Review Letters (2026). DOI: 10.1103/6msd-mdw4

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