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arXiv:1602.08691 · Physical Review Letters

Landau-Zener Bloch Oscillations with Perturbed Flat Bands

Рамаз Хомерики, Sergej Flach A

Published Jun 15, 2016• 111 citations
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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 band, 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 or photonic wave packet is trapped in the original flat band part of the unperturbed spectrum, made possible due to LZ tunneling.

DOI
10.1103/physrevlett.116.245301

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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 band, 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 or photonic wave packet is trapped in the original flat band part of the unperturbed spectrum, made possible due to LZ tunneling.
The effect of an additional high frequency alternating field on the Bloch-Zener oscillation of a quantum particle is investigated theoretically. The effective magnitude of the band gap is reduced by the ac field, and even collapsed to zero by appropriately tuning the amplitude and the frequency of the oscillation. This results in the enhancement of the Zener tunneling with dramatic changes of the Bloch-Zener oscillation. The temporal behavior of the wave packet is clarified as due to the interplay of the Landau-Zener interference in the repeated level crossings with two different time scales, namely, the period of the Bloch oscillation, and the period of the high frequency ac field.
Landau–Zener (LZ) tunneling, i.e., the nonadiabatic level transition under strong parameter driving, is a fundamental concept in modern quantum mechanics. With the advent of non-Hermitian physics, research interest has been paid to the LZ tunneling involving level dissipations. However, experimental demonstrations of such an interesting non-Hermitian LZ problem remain yet elusive. By harnessing a synthetic temporal lattice using a fiber-loop circuit, we report on the first real-time measurement of non-Hermitian LZ tunneling in a dissipative two-band lattice model. An innovative approach based on mode interference is developed to measure the transient band occupancies, providing a powerful tool to explore the non-Hermitian LZ tunneling dynamics in non-orthogonal eigenmodes. We find that the loss does not change the final LZ tunneling probability but can highly affect the tunneling process by modifying the typical band occupancies oscillation behaviors. We initiate exploring intriguing LZ physics and measurements beyond the standard Hermitian paradigm, with potential applications in coherent quantum control and quantum technologies.
We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well-depth, Bloch oscillations were observed. Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied. In order to allow in-trap measurements of these phenomena, we dynamically compensated for the intrinsic micromotion of the atoms in our time-orbiting potential trap.
Ultracold gases in optical lattices have proved to be a flexible tool to simulate many different phenomena of solid state physics [1, 2]. Recently, optical lattices with complex geometries have been realized [3, 4, 5, 6, 7], paving the way to simulating more realistic systems. The honeycomb structure has recently become accessible in an optical lattice composed of mutually perpendicular laser beams. This lattice structure exhibits topological features in its band structure – the Dirac points. At these points, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In optical lattices, Bloch oscillations [8] resolved both in time and in quasi-momentum space can be directly observed. We make use of such Bloch-Zener oscillations to probe the vanishing energy gap at the Dirac points as well as their position in the band structure. In small band gap regions, we observe Landau-Zener tunneling [7, 9] to the second band and the regions of maximum transfer can be identified with the position of the Dirac points.
We report on experiments investigating quantum transport and band interferometry of an atomic Bose-Einstein condensate in an optical lattice with a two-band miniband structure, realized with a Fourier-synthesized optical lattice potential. Bloch-Zener oscillations, the coherent superposition of Bloch oscillations and Landau-Zener tunneling between the two bands, are observed. When the relative phase between paths in different bands is varied, an interference signal is observed, demonstrating the coherence of the dynamics in the miniband system. Measured fringe patterns of this Stückelberg interferometer allow us to interferometrically map out the band structure of the optical lattice over the full Brillouin zone.
We report on experiments investigating quantum transport and band interferometry of an atomic Bose-Einstein condensate in an optical lattice with a two-band miniband structure, realized with a Fourier-synthesized optical lattice potential. Bloch-Zener oscillations, the coherent superposition of Bloch oscillations and Landau-Zener tunneling between the two bands are observed. When the relative phase between paths in different bands is varied, an interference signal is observed, demonstrating the coherence of the dynamics in the miniband system. Measured fringe patterns of this Stückelberg interferometer allow to interferometrically map out the band structure of the optical lattice over the full Brillouin zone.