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arXiv:1103.4293

Dynamic Localization in Optical Lattices

Stephan Arlinghaus, Matthias Langemeyer, Martin Holthaus

Published Mar 22, 2011• 0 citations
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Abstract

We recapitulate the principle enabling the phenomenon of dynamic localization, and provide model calculations for ultracold atoms in driven optical lattices which indicate that the localization effect remains almost unaffected by interband transitions if the parameters are chosen carefully. In addition, we suggest to exploit the underlying quasienergy band collapse for coherently controlling the metal-insulator transition that occurs in the Harper model, as realized with quasiperiodic optical lattices.

DOI
10.48550/arxiv.1103.4293

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We recapitulate the principle enabling the phenomenon of dynamic localization, and provide model calculations for ultracold atoms in driven optical lattices which indicate that the localization effect remains almost unaffected by interband transitions if the parameters are chosen carefully. In addition, we suggest to exploit the underlying quasienergy band collapse for coherently controlling the metal-insulator transition that occurs in the Harper model, as realized with quasiperiodic optical lattices.
We suggest the possibility to realize an optical quasicrystal with ultracold atoms in far-detuned, bichromatic standing light waves. If the optical potentials created by the individual light waves have sufficiently different strength, one obtains an atom-optical realization of Harper's model. This model exhibits a metal-insulator transition at a certain value of the site-to-site hopping integral. Since this hopping integral is effectively renormalized by an additional oscillating force, one can switch from the regime of extended states to the regime of localized states by varying the amplitude of that force.
We show that ultracold atoms can be controlled in multi-band optical lattices through spatially periodic Raman pulses for investigation of a class of strongly correlated physics related to the Kondo problem. The underlying dynamics of this system is described by a spin-dependent fermionic or bosonic Kondo-Hubbard lattice model even if we have only spin-independent atomic collision interaction. We solve the bosonic Kondo-Hubbard lattice model through a mean-field approximation, and the result shows a clear phase transition from the ferromagnetic superfluid to the Kondo-singlet insulator at the integer filling.
We investigate the localization transition in a one-dimensional extended Aubry–André–Harper (AAH) model, emphasizing its implementation as a quantum simulator in ultracold atomic optical lattices. In the single-particle case, quasi-periodic hopping modulation allows the localization transition point to be clearly observed even for small system sizes. By driving the system into strongly Anderson localized states immediately after the transition, we observe a sharp many-body localization (MBL) transition upon introducing interactions, with the MBL transition point closely approaching that of Anderson localization. To demonstrate the effects of interactions, we map out a global phase diagram and find that critical states in this model are easily thermalized. Contrary to previous studies where enhanced interactions significantly promoted thermalization, we find that increasing interactions does not notably shift the MBL transition point. Importantly, our setup offers a practical and experimentally accessible platform for studying sharp MBL transitions using ultracold atoms in optical lattices, bridging MBL physics with advances in quantum optics and cold-atom technologies.
We study the dynamics of ultracold atoms in an optical lattice under constant bias. After recapitulating the ideas underlying Bloch oscillations and Zener's formula for interband transitions, the Bloch-Zener scenario is tested by means of accurate numerical solutions to the time-dependent Schrödinger equation. It is shown how two shortcomings of the traditional Zener formula can be removed: the common weak-binding approximation can be circumvented by combining Kohn's insight into the structure of complex energy bands with the Dykhne-Davis-Pechukas description of transitions in terms of adiabatic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against the condensate's nonlinear self-interaction. Yet, under appropriate conditions a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic signatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggested that such experimentally detectable signatures will play an important role in future high-precision experiments aiming at the exploration of many-body dynamics in periodic potentials with condensates in optical lattices.
An optical lattice is the periodic potential that atoms experience via the ac-Stark shift when they are illuminated by counter-propagating laser beams that form a standing-wave pattern. Optical lattices have been widely used as a versatile platform in cooling, trapping, controlling atoms, and also for the study of a variety of problems in physics. The many-body states of ultracold atoms in optical lattices can be characterized by the quantum-correlations encoded in time-of-flight images. In this thesis, we mainly discuss the use of correlations function as a natural framework for characterizing quantum states in optical lattices.\nThe outline of the thesis is as follows. Chapter 1 gives a brief introduction to optical lattice potentials and ways for describing particles moving in a periodic potential. Chapter 2 explains the importance of correlations and discusses common methods to detect them in cold atom experiments.\nChapter 3 presents work done to study the many-body Schrödinger equation in a quasiperiodic potential and discusses its connection with the Kolmogorov-Arnold-Moser (KAM) problem of classical mechanics. We posed a possible visualization of such a connection in experimentally accessible many-body observables. These observables are useful probes for the three characteristic phases of the problem: the metallic, Anderson, and band-insulator phases. In addition, they exhibit fingerprints of nonlinear phenomena such as bifurcations and devil's staircases. Our numerical treatment is complemented with a perturbative analysis that provides insight on the underlying physics. The perturbative-theory approach is particularly useful in illuminating the distinction between the Anderson-insulator and the band-insulator phases in terms of paired sets of dimerized states.\nChapter 4 discusses several theoretical procedures developed to understand a recent experiment on macroscopic quantum self-trapping (ST) performed in a 2D optical lattice. Mean field and truncated-Wigner-approximation (TWA) calculations are performed trying to reproduce the experimental observations. The discrepancy between the theory and the experiment lead to the hypothesis of a new type of ST caused by strong correlations. We analyze toy models to support it.