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Chinese Physics Letters

Light-Induced Hofstadter's Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagomé Lattice

Jing-Min Hou

Published Dec 1, 2009• 10 citations
Publisher

Abstract

We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations from the Schrödinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations. We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.

DOI
10.1088/0256-307x/26/12/123701

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We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations from the Schrödinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations. We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.
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.
Viewed as an ideal quantum simulator, the optical lattice system with trapped ultracold atoms has been developed into a powerful tool to investigate unusual physical properties due to its considerable tunability. In this paper, we propose to construct a feasible two-dimensional optical lattice which can be continuously transformed from a square lattice to a Lieb lattice by tuning laser intensity. In these transformations, accompanied with the crossover between nonrelativistic particles and relativistic Dirac fermions, the topological and transport properties are varied under artificial gauge potentials. It is found that the fractal energy spectrum in an effective magnetic field splits and reassembles from a traditional Hofstadter butterfly to multiple ones with flat band, characterized by different Chern numbers. In a specific case of half a pseudomagnetic flux quantum, the spectrum has a transition from individual Dirac cones to double-layer Dirac cones, then to the Dirac cones with a flat band, the pseudospin of particles changes from 1/2 to 3/2, then to 1. In the structural evolution, a remarkable birefringent tunneling across a potential barrier is demonstrated. The adjustable lattice structure replenished with synthetic gauge fields for cold atoms offers more opportunities to observe intriguing physical properties.