Landau-Zener Bloch oscillations with perturbed flat bands

Abstract

Sinusoidal Bloch oscillations appear in band structures exposed to external fields. Landau-Zener (LZ) tunneling between different bands is usually a counteracting effect limiting Bloch oscillations. Here we consider a flat band network with two dispersive and one flat bands, e.g. for ultracold atoms and optical waveguide networks. Using external synthetic gauge and gravitational fields we obtain a perturbed yet gapless band structure with almost flat parts. The resulting Bloch oscillations consist of two parts - a fast scan through the nonflat part of the dispersion structure, and an almost complete halt for substantial time when the atomic wave packet is trapped in the original flat band part of the unperturbed spectrum, made possible due to LZ tunneling.

5 pages, 6 figures

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• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
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• Designer Flat Bands in Quasi-One-Dimensional Atomic Lattices
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• Flat bands and nontrivial topological properties in an extended Lieb lattice
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• Flat band in two-dimensional non-Hermitian optical lattices
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• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• Compact Discrete Breathers on Flat Band Networks
• Flat-band localization and self-collimation of light in photonic crystals
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• Topological inverse Anderson insulator
• Necessary and sufficient conditions for flat bands in $M$-dimensional $N$-band lattices with complex-valued nearest-neighbour hopping
• Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric flat band lattice
• Anti-$\mathcal{P}\mathcal{T}$ flatbands
• Dynamical quantum phase transitions on cross-stitch flat band networks
• Andreev reflection of massive pseudospin-1 fermions
• Compact localised states in magnonic Lieb lattices
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
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• Thermal Transport Properties of Magnons on the $\alpha$-T${}_3$ Lattice
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• Irregular Bloch Zener oscillations in two-dimensional flat-band Dirac materials
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• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Quantum Metric-induced Oscillations in Flat Bands
• Non-Hermitian Aharonov-Bohm Cage
• Resonant cavity-QED with chiral flat bands
• Compact localized currents in flat bands with broken time-reversal symmetry
• Quantum transport in the flux rhombic lattice