Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Anderson Localization and Mobility Edges in Ruby

J. Koo, L. R. Walker, Stanley Geschwind

Published Dec 15, 1975• 72 citations
Publisher

Abstract

When the ${R}_{1}$ line in ruby is swept with a tunable laser from the center to the wings, the ratio of trap emission to ${R}_{1}$ emission remains constant up to a point in the line where it suddenly drops to a lower constant value out to the wings. We suggest that this break corresponds to mobility edges separating delocalized states in the central region from "localized" states beyond this break.

DOI
10.1103/physrevlett.35.1669

Related papers

Search for the Anderson transition in ruby

Paul E. Jessop, A. Szabó

A new diagnostic to detect the occurrence of an Anderson transition, using photon echoes, is proposed and experimentally tested for the ${R}_{1}$ line in ruby. A search for mobility edges in samples up to 0.1 wt.% ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ concentration was unsuccessful.

Physical review. B, Condensed matter•Jul 1, 1982•7 citations

Multiple Quantum Transitions and Simultaneous Laser Action of R1 and R2 Lines in Ruby

幹郎 片山, 鉄也 菅井, 啓三 林 +3 more

•Dec 8, 1963•0 citations

Measurement of the mobility edge for 3D Anderson localization

Giulia Semeghini, Manuele Landini, P. C. M. Castilho +6 more

arXiv:1404.3528•Nature Physics•May 30, 2015•251 citations

Laser-Induced Fluorescence-Line Narrowing in Ruby

Arthur G. Szabo

Using resonance ruby-laser excitation, narrowing of the ruby ${R}_{1}$ fluorescence line to width 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 4.2\ifmmode^\circ\else\textdegree\fi{}K is observed. Absence of spectral diffusion indicates that a short-range interaction rather than earlier postulated multipolar interactions is responsible for energy transfer in concentrated ruby.

Physical Review Letters•Oct 5, 1970•241 citations

Fluorescence-line-narrowing and energy-transfer studies in ruby

Peter M. Selzer, David L. Huber, B. B. Barnett +1 more

Fluorescence-line-narrowing and time-resolved studies have been conducted in ruby crystals and powders, in concentrations varying from 0.025 to 0.9 at.%. The resonance fluorescence component of the ${R}_{1}$ line at low temperatures is observed to increase dramatically as the laser is tuned from line center toward the low-energy wing of the inhomogeneously broadened absorption. This is presumed to indicate the presence of weakly coupled pairs in the wings of the line. Intraline and interline (${R}_{1}\ensuremath{\rightarrow}{N}_{1,2}$) energy transfer have also been studied, and an elaboration of earlier work is given. Time-resolved selective-excitation scans have revealed numerous channels in the vicinity of the $R$ lines by which the different pairs can be directly excited. These are assumed to be Cr ions near enough to a pair to be in a highly perturbed environment. Various experimental results are shown to be consistent with a model of rapid transfer between resonant Cr ions which feeds the pairs via a weak, nonresonant coupling to these perturbed ions. Macroscopic strain broadening is also shown to be favored over microscopic broadening, and the implications for Anderson localization in ruby are discussed.

Physical review. B, Condensed matter•Jun 15, 1978•91 citations

Limitations of Avila-inspired theory in the diamond chain with quasiperiodic disorder

Manish Kumar, Ivan M. Khaymovich, Auditya Sharma

The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic frequencies on the mobility edge formation. We focus on the example of the addition of a constant offset to the quasiperiodic potential of the one-dimensional all-bands-flat diamond chain. We show that this additional offset can transform the anomalous mobility edges (AMEs), i.e. the energies, separating localized and multifractal states, into conventional mobility edges, separating localized from delocalized states. Also this appears to be the first example which shows the inability of Avila's global theory to analytically predict the ME location. We observe this both quantitatively, through the ME location mismatch, and qualitatively, via the formation of multiple MEs, not predicted by the theory.

cond-mat.str-elCross-listedarXiv:2603.12362•Mar 16, 2026
When the R1{R}_{1}R1​ line in ruby is swept with a tunable laser from the center to the wings, the ratio of trap emission to R1{R}_{1}R1​ emission remains constant up to a point in the line where it suddenly drops to a lower constant value out to the wings. We suggest that this break corresponds to mobility edges separating delocalized states in the central region from "localized" states beyond this break.
A new diagnostic to detect the occurrence of an Anderson transition, using photon echoes, is proposed and experimentally tested for the R1{R}_{1}R1​ line in ruby. A search for mobility edges in samples up to 0.1 wt.% Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ concentration was unsuccessful.
Using resonance ruby-laser excitation, narrowing of the ruby R1{R}_{1}R1​ fluorescence line to width 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 4.2\ifmmode^\circ\else\textdegree\fi{}K is observed. Absence of spectral diffusion indicates that a short-range interaction rather than earlier postulated multipolar interactions is responsible for energy transfer in concentrated ruby.
Fluorescence-line-narrowing and time-resolved studies have been conducted in ruby crystals and powders, in concentrations varying from 0.025 to 0.9 at.%. The resonance fluorescence component of the R1{R}_{1}R1​ line at low temperatures is observed to increase dramatically as the laser is tuned from line center toward the low-energy wing of the inhomogeneously broadened absorption. This is presumed to indicate the presence of weakly coupled pairs in the wings of the line. Intraline and interline (${R}_{1}\ensuremath{\rightarrow}{N}_{1,2}$) energy transfer have also been studied, and an elaboration of earlier work is given. Time-resolved selective-excitation scans have revealed numerous channels in the vicinity of the RRR lines by which the different pairs can be directly excited. These are assumed to be Cr ions near enough to a pair to be in a highly perturbed environment. Various experimental results are shown to be consistent with a model of rapid transfer between resonant Cr ions which feeds the pairs via a weak, nonresonant coupling to these perturbed ions. Macroscopic strain broadening is also shown to be favored over microscopic broadening, and the implications for Anderson localization in ruby are discussed.
The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic frequencies on the mobility edge formation. We focus on the example of the addition of a constant offset to the quasiperiodic potential of the one-dimensional all-bands-flat diamond chain. We show that this additional offset can transform the anomalous mobility edges (AMEs), i.e. the energies, separating localized and multifractal states, into conventional mobility edges, separating localized from delocalized states. Also this appears to be the first example which shows the inability of Avila's global theory to analytically predict the ME location. We observe this both quantitatively, through the ME location mismatch, and qualitatively, via the formation of multiple MEs, not predicted by the theory.