Exploring complex phenomena using ultracold atoms in bichromatic lattices

Abstract

With an underlying common theme of competing length scales, we study the many-body Schrödinger equation in a quasiperiodic potential and discuss its connection with the Kolmogorov-Arnold-Moser (KAM) problem of classical mechanics. We propose a possible visualization of such connection in experimentally accessible many-body observables. Those 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 non-linear phenomena such as Arnold tongues, bifurcations and devil's staircases. Our numerical treatment is complemented with a perturbative analysis which provides insight on the underlying physics. The perturbation 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.

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• A Mott insulator of fermionic atoms in an optical lattice
• Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice
• Bosons in one-dimensional incommensurate superlattices
• Noise correlation spectroscopy of the broken order of a Mott insulating phase
• Hanbury Brown-Twiss Interferometry for Fractional and Integer Mott Phases

Cited by in corpus (5)

• Fibonacci optical lattices for tunable quantum quasicrystals
• Wave interactions in localizing media - a coin with many faces
• Noise Correlation Scalings: Revisiting the Quantum Phase Transition in Incommensurate Lattices with Hard-Core Bosons
• Devil's staircases without particle-hole symmetry
• Quantum Brownian motion in a quasiperiodic potential