2007/12/31 by N. Goldman, Nathan Goldman, A. Kubasiak +4
Mathematics · Physics and Astronomy · #Abelian group #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Coupling constant #Electron #Fermi energy #Gauge (firearms) #Gauge theory #Mathematics #Phase (matter) #Phase diagram #Physics #Quantum #Quantum Hall effect #Quantum electrodynamics #Quantum mechanics #Theoretical and Computational Physics #Topological Materials and Phenomena #Ultracold atom #cond-mat.mes-hall #hep-th #quant-ph
paper · pdf · doi:10.1103/physreva.79.023624
published as Phys. Rev. A. 79, 023624 (2009) · 6 pages, 5 figures
arxiv created 2008/09/09 · openalex publication_date 2009/02/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties of an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a constant Wilson loop. Under this specific condition, the energy spectrum exhibits a robust band structure with large gaps and reveals a new fractal figure. The transverse conductivity is related to topological invariants and is shown to be quantized when the Fermi energy lies inside a gap of the spectrum. We demonstrate that the analog of the integer quantum Hall effect for neutral atoms survives the non-Abelian coupling and leads to a striking fractal phase diagram. Moreover, this coupling induces an anomalous Hall effect as observed in graphene.