Berry and Pancharatnam Topological Phases of Atomic and Optical Systems

Abstract

Theoretical and experimental studies of Berry and Pancharatnam phases are reviewed. Basic elements of differential geometry are presented for understanding the topological nature of these phases. The basic theory analyzed by Berry in relation to magnetic monopoles is presented. The theory is generalized to nonadiabatic processes and to noncyclic Pancharatnam phases. Different systems are discussed including polarization optics, n-level atomic systems, neutron interferometry and molecular topological phases.

Review article,72 pages, 186 references

References in corpus (10)

• An experimental observation of geometric phases for mixed states using NMR interferometry
• Geometric phases for non-degenerate and degenerate mixed states
• Generalization of geometric phase to completely positive maps
• Off-diagonal geometric phase for mixed states
• Topological phase for entangled two-qubit states
• Relation between geometric phases of entangled bi-partite systems and their subsystems
• Uhlmann's geometric phase in presence of isotropic decoherence
• Geometric Phase and Helicity Inversion of Photons Propagating inside a Noncoplanarly Curved Optical Fiber
• Noncyclic mixed state phase in SU(2) polarimetry
• Pancharatnam and Berry Phases in Three-Level Photonic Systems

Cited by in corpus (17)

• Spin-orbit interactions of light
• Goos-Hänchen and Imbert-Fedorov beam shifts: An overview
• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
• Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects
• Berry phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material from a Classical Electromagnetics Perspective
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• The Parity Operator: applications in quantum metrology
• Vortices and chirality of magnetostatic modes in quasi-2D ferrite disk particles
• Geometric phase for an adiabatically evolving open quantum system
• Geometric Thermoelectric Pump: Energy Harvesting beyond Seebeck and Pyroelectric Effects
• Berry phase in superconducting charge qubits interacting with a cavity field
• Geometric phase at graphene edge
• Self-Induced Quasistationary Magnetic Fields
• Nonadiabatic geometric phase induced by a counterpart of the Stark shift
• Local and Tunable Geometric Phase of Dirac Fermions in a Topological Junction
• Interplay between geometric and dynamic phases in a single spin system
• Interferometric and Uhlmann phases of mixed polarization states