Quantum Mechanics with a Momentum-Space Artificial Magnetic Field
arXiv:1403.6041 · doi:10.1103/PhysRevLett.113.190403
Abstract
The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly relevant to ultracold gases and photonics. Given the exchanged roles of momentum and position, we demonstrate that the global topology of momentum space is crucially important. We propose an experiment to study the Harper-Hofstadter Hamiltonian with a harmonic trap that will illustrate the advantages of this approach and that will also constitute the first realization of magnetism on a torus.
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- Experimental observation of one-dimensional superradiance lattices in ultracold atoms
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- Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
- Lattice dynamics with molecular Berry curvature: chiral optical phonons
- Steady-state Hall response and quantum geometry of driven-dissipative lattices
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- Light-matter interactions near photonic Weyl points
- Momentum-space Harper-Hofstadter model
- Band geometry from position-momentum duality at topological band crossings
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- Momentum-space Landau levels in driven-dissipative cavity arrays
- What is measured when measuring a thermoelectric coefficient?
- Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled Systems
- Chiral Wigner crystal phases induced by Berry curvature
- Phase space curvature in spin-orbit coupled ultracold atom systems
- Monopole Antimonopole Instability in Non-Hermitian Coupled Waveguides