Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms

By D. Jaksch, Peter Zoller. 2003

567 citations recorded by the source corpus.

We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non-vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This set-up is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields—which is not experimentally accessible for electrons in metals—where a fractal band structure, the Hofstadter butterfly, characterizes the system.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7ff100cdad0b43dbb8c5546cf96ebe5b0e995e27

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Citations in the corpus

Topological quantum matter with ultracold gases in optical lattices (2016, methodology): “This method was proposed to simulate synthetic magnetic fields [33, 70] and spin-orbit coupling [62, 71, 72] in optical lattices, in view of creating topological insulators and superfluids in atomic gases.”
Exploring topological phases with quantum walks (2010, methodology): “[35] Jaksch,D & Zoller, P.”
Quantum matter built from nanoscopic lattices of atoms and photons (2018, result): “Similar to the Raman-addressing schemes already developed in cold atoms and trapped ions (Jaksch and Zoller, 2003; Bermudez, Schaetz, and Porras, 2011; Kolovsky, 2011; Aidelsburger et al., 2013; Miyake et al., 2013), here the interaction coefficients Jjl can also acquire a complex phase Jjl ¼…”
Gauge fields for ultracold atoms in optical superlattices (2009, methodology): “Following Jaksch and Zoller [8], we calculate the effective g − e hopping matrix element between two neighboring sites located at rg = (2n,m) and re = rg + b = (2n+ 1, m) as”
Rotating trapped Bose-Einstein condensates (2008, background): “In the context of optical lattices, Jaksch and Zoller (2003) propose inducing various terms in the single-particle Hamiltonian that mimic the effect of 34 an external magnetic field.”