Related Experiment Video
Updated: Jun 19, 2026
06:24
High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
Published on: October 31, 2019
Bloch oscillations in complex crystals with PT symmetry
1Dipartimento di Fisica and Istituto di Fotonica e Nanotecnologie del CNR, Politecnico di Milano, I-20133 Milano, Italy.
Physical Review Letters
|October 2, 2009
Summary
Bloch oscillations in complex lattices with parity-time (PT) symmetry exhibit unique behaviors, including nonreciprocal oscillations not seen in standard lattices. This study explores these novel dynamics in photonic systems with gain or loss.
Area of Science:
- Physics
- Optics
- Condensed Matter Physics
Background:
- Bloch oscillations describe particle motion in a crystal lattice under an external electric field.
- Parity-time (PT) symmetry offers unique properties to complex systems, including non-Hermitian Hamiltonians.
- Photonic lattices with gain or loss regions are crucial for studying light propagation in complex optical potentials.
Purpose of the Study:
- To theoretically investigate Bloch oscillations in complex lattices exhibiting PT symmetry.
- To explore optical Bloch oscillations in photonic lattices with engineered gain or loss.
- To identify and highlight novel dynamical phenomena absent in ordinary lattices.
Main Methods:
- Theoretical analysis of Bloch oscillations within complex lattice potentials.
- Modeling of optical Bloch oscillations in PT-symmetric photonic lattices.
- Investigation of phenomena related to the violation of Friedel's law in complex potentials.
Main Results:
- Demonstration of nonreciprocal Bloch oscillations in PT-symmetric complex lattices.
- Observation of phenomena not present in standard lattices, such as violation of Friedel's law.
- Characterization of unique dynamical behaviors arising from gain and loss regions.
Conclusions:
- Complex lattices with PT symmetry host novel Bloch oscillation dynamics.
- Nonreciprocal Bloch oscillations and Friedel's law violation are key features in these systems.
- The findings offer new insights into light propagation and control in complex photonic structures.
Related Concept Videos
01:27Symmetry Elements in a Crystal
Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
01:29Crystallographic Point Groups
Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
01:04Oscillations about an Equilibrium Position
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
01:24The Seven Crystal Systems: Overview
Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
02:58Crystal Field Theory - Octahedral Complexes
Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...