Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
arXiv:1912.12596 · doi:10.1038/s42254-019-0071-1
Abstract
Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior and later manifestations exist. Though traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized and became increasingly influential in many areas from condensed-matter physics and optics to high energy and particle physics and from fluid mechanics to gravity and cosmology. Interestingly, the geometric phase also offers unique opportunities for quantum information and computation. In this Review we first introduce the Aharonov-Bohm effect as an important realization of the geometric phase. Then we discuss in detail the broader meaning, consequences and realizations of the geometric phase emphasizing the most important mathematical methods and experimental techniques used in the study of geometric phase, in particular those related to recent works in optics and condensed-matter physics.
This is the author's accepted manuscript. The finalized version is available on: https://www.nature.com/articles/s42254-019-0071-1
References in corpus (25)
- Non-Abelian Anyons and Topological Quantum Computation
- Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media
- Universal computation by quantum walk
- Quantum spin Hall effect of light
- Geometrodynamics of Spinning Light
- Observation of Berry's Phase in a Solid State Qubit
- Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices
- Angular Momenta and Spin-Orbit Interaction of Nonparaxial Light in Free Space
- Observation of Dirac Monopoles in a Synthetic Magnetic Field
- Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation
- An Aharonov-Bohm interferometer for determining Bloch band topology
- Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
- Aharonov-Bohm oscillations in disordered topological insulator nanowires
- Quantum walks and wavepacket dynamics on a lattice with twisted photons
- Photonic quantum walk in a single beam with twisted light
- Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
- Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges
- Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
- Geometric nature of the environment-induced Berry phase and geometric dephasing
- Shot Noise in Anyonic Mach-Zehnder Interferometer
- Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
- Aharonov-Bohm effect in the tunnelling of a quantum rotor in a linear Paul trap
- Hanbury-Brown and Twiss interference of anyons
- Spin and Orbital Angular Momenta of Light Reflected from a Cone
- Achromatic orbital angular momentum generator
Cited by in corpus (74)
- Applications of Bound States in the Continuum in Photonics
- Topological quantum materials from the viewpoint of chemistry
- Probing topological quantum matter with scanning tunnelling microscopy
- Non-Hermitian chiral phononics through optomechanically-induced squeezing
- Experimental Observation of Berry Phases in Optical Moebius-strip Microcavities
- Non-Hermitian Photonic Lattices: tutorial
- Geometric phases of light: insights from fibre bundle theory
- Janus Bound States in the Continuum with Asymmetric Topological Charges
- Photonic topological insulators a beginner's introduction
- Introduction to topological defects: from liquid crystals to particle physics
- Switchable X-ray Orbital Angular Momentum from an Artificial Spin Ice
- Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases
- Toward arbitrary spin-orbit flat optics via structured geometric phase gratings
- Dynamic transition and Galilean relativity of current-driven skyrmions
- Finite-temperature topological phase transitions of spin- systems in Uhlmann processes: General formalism and experimental protocols
- Geometric phases and the Sagnac effect: Foundational aspects and sensing applications
- Complex Berry phase and imperfect non-Hermitian phase transitions
- Deciphering Pancharatnam's discovery of geometric phase
- Manifestation of the Berry phase in the atomic nucleus Pb
- Investigation of the Aharonov-Bohm and Aharonov-Casher Topological Phases for Quantum Entangled States in 2+1 Dimensions
- Coherence and realism in the Aharonov-Bohm effect
- Geometric Induction in Chiral Superfluids
- Universal perspective on nonadiabatic quantum control
- Topological transitions of the generalized Pancharatnam-Berry phase
- Massive scalar perturbations in Kerr Black Holes: near extremal analysis
- Structured Light Modal Interface via Liquid-Crystal Planar Optics
- Local diabatic representation of conical intersection quantum dynamics
- Spin angular momentum and optical chirality of Poincaré vector vortex beams
- Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
- Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases
- Waveguiding driven by the Pancharatnam-Berry phase
- Uhlmann quench and geometric dynamic quantum phase transition of mixed states
- Berry phase in the rigid rotor: the emergent physics of odd antiferromagnets
- Electrodynamic Aharonov-Bohm effect
- Machine-learning-inspired quantum optimal control of nonadiabatic geometric quantum computation via reverse engineering
- Geometric and Majorana phases in neutrino oscillations
- On the Geometric Phase and Majorana Neutrinos
- Spin-texture topology in curved circuits driven by spin-orbit interactions
- Effect of Energy Conservation Law, Space Dimension, and Problem Symmetry on the Poynting Vector Field Singularities
- Orthonormal bases of extreme quantumness
- The Aharonov-Bohm effect in a closed flux line
- Manifestation of the Berry connection in chiral lattice systems
- On local conservation of information content in Schwarzschild black holes
- On the role of geometric phase in the dynamics of elastic waveguides
- Ternary Logic Design in Topological Quantum Computing
- Curves in quantum state space, geometric phases, and the brachistophase
- Topological photon pumping in quantum optical systems
- Generalizations of Berry phase and differentiation of purified state and thermal vacuum of mixed states
- Geometric phase for twisted light
- Geometric phases of a vortex in a superfluid
- The Poynting vector field singularities: Effects of symmetry and its violation
- The Aharonov-Casher phase is geometrical and not topological
- Spin Vector Potential and Spin Aharonov-Bohm Effect
- Experimental measurement of the geometric phase of non-geodesic circles
- van de Hulst Essay: Geometric-phase portrayal of electromagnetic scattering by a three-dimensional object in free space
- Topological phases in discrete stochastic systems
- Poincaré sphere engineering of dynamical ferroelectric topological solitons
- On the geometric phases in entangled states
- Geometry-induced wavefunction collapse
- Geometric phase and a nonreciprocal spin wave circular polarizer
- The Aharonov Casher phase of a bipartite entanglement pair traversing a quantum square ring
- Mixed-state geometric phases of coherent and squeezed spin states
- Dynamic and Geometric Shifts in Wave Scattering
- Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
- Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
- Geometric phases in neutrino mixing
- Electric-Magnetic Geometric Phase
- Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect
- Partition laser assembling technique
- Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
- Geometric Phase and Nanoscale Architected Morphology of Reusch Piles
- Topology of the Aharonov-Bohm effect in different reference frames
- Ergodic Hysteresis of the Kerr black hole spectrum
- The effects of light-wave nonstaticity on accompanying geometric-phase evolutions