By Monika Aidelsburger
ISBN-10: 3319258273
ISBN-13: 9783319258270
ISBN-10: 331925829X
ISBN-13: 9783319258294
This paintings studies at the new release of man-made magnetic fields with ultracold atoms in optical lattices utilizing laser-assisted tunneling, in addition to at the first Chern-number size in a non-electronic system.
It starts off with an advent to the Hofstadter version, which describes the dynamics of charged debris on a sq. lattice subjected to robust magnetic fields. This version shows power bands with non-zero topological invariants referred to as Chern numbers, a estate that's on the starting place of the quantum corridor impact. the most a part of the paintings discusses the belief of analog platforms with ultracold impartial atoms utilizing laser-assisted-tunneling innovations either from a theoretical and experimental standpoint. Staggered, homogeneous and spin-dependent flux distributions are generated and characterised utilizing two-dimensional optical super-lattice potentials. also their topological houses are studied through the remark of bulk topological currents.
The experimental options provided the following provide a special environment for learning topologically non-trivial structures with ultracold atoms.
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Additional resources for Artificial Gauge Fields with Ultracold Atoms in Optical Lattices
Sample text
64) =: −η0 sin ωt + 2 Using the equations above we study the micro-motion for different on-site potentials ˆ m , which is fully determined by the unitary operator R(t) in Eq. 62) as shown above (Sect. 4). 1 Micro-motion Staggered Superlattice Potential The staggered superlattice potential illustrated in Fig. 1a consists of two nonequivalent lattice sites (two sectors α) with on-site potential energies that alternate 42 3 Artificial Gauge Fields with Laser-Assisted Tunneling in sign along the direction of the staggered potential micro-motion operator is determined by ˆ stagg (t) = M − m m = (−1)m /2.
Y. Hatsugai, Chern number and edge states in the integer quantum Hall effect. Phys. Rev. Lett. 71, 3697–3700 (1993) 27. Y. Hatsugai, Edge states in the integer quantum Hall effect and the Riemann surface of the Bloch function. Phys. Rev. B 48, 11851–11862 (1993) 28. -L. -S. -C. Zhang, General theorem relating the bulk topological number to edge states in two-dimensional insulators. Phys. Rev. B 74, 045125 (2006) 29. M. Aidelsburger, M. Lohse, C. Schweizer, M. T. Barreiro, S. R. Cooper, I. Bloch, N.
It has been shown that the quantization of the Hall conductance discovered by Klaus von Klitzing et al. in 1980 [23] is directly related to an integer topological invariant known as the Chern number [24]. In solid-state experiments the quantization of the Hall conductance σ H is observed by sending a constant current through the sample and measuring the voltage difference in the transverse direction. At low temperatures all energy bands below the Fermi energy E F are filled. 45) E μ Artificial Gauge Fields with Ultracold Atoms in Optical Lattices by Monika Aidelsburger
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