Adiabaticity and Localization in One-Dimensional Incommensurate Lattices

Abstract

We experimentally investigate the role of localization on the adiabaticity of loading a Bose-Einstein condensate into a one-dimensional optical potential comprised of a shallow primary lattice plus one or two perturbing lattice(s) of incommensurate period. We find that even a very weak perturbation causes dramatic changes in the momentum distribution and makes adiabatic loading of the combined lattice much more difficult than for a single period lattice. We interpret our results using a band structure model and the one-dimensional Gross-Pitaevskii equation.Disorder plays an important role in many condensed matter systems, [1,2] with deep connections to quantum chaos [3], but can be difficult to systematically study due to the challenge of creating reproducible and quantifiable disorder. The control available in ultra-cold atom systems [4] makes it an attractive platform to study disorder [5,6,7,8]. To date much of the work adding disorder to ultra-cold atom systems has explored timeindependent properties, but the long timescales associated with cold atoms allows investigation of dynamical properties as well (see [5, 9, 10, 11] and ref. therein). In this work we examine the ability of a quasi-disordered system to adiabatically follow changes in the Hamiltonian. The presence of disorder produces a complicated eigenvalue spectrum, which greatly affects the adiabaticity criteria. The physics of localization phenomena also has a significant impact on time-dependent processes, such as adiabaticity. Small perturbations to the Hamiltonian can cause large changes to the ground state wavefunction over large length scales, making it difficult for the system to adiabatically follow changes. One recent theoretical study shows that adiabaticity in gapless systems is non-trivial, particularly in lower dimensions [12]. Here we show that even in a gapped system such as ours, adiabaticity is complicated by the presence of disorder.We study adiabaticity in a quasi-disordered system by adding one or two weak incommensurate lattices to a one-dimensional optical lattice loaded with a BoseEinstein condensate (BEC). Localization occurs in both disordered and strictly incommensurate potentials [8,13,14,15] although with distinct differences, which tend to disappear in finite-sized systems such as ours. We observe a complex momentum distribution of the atoms due to the presence of weak perturbing lattices following a ramped loading process that would be nearly adiabatic for a single lattice. We gain insight into the distributions from single-particle band structure, and observe that the effects of the perturbations disappear as interactions increase, as they suppress the long wavelength density modulation of the wavefunction.We form a BEC of ∼10 4 87 Rb atoms in the state |F = 2, m f = 2 in a magnetic trap with ω x ≈ ω z ≈ 2π×410 Hz and ω y ≈ 2π×120 Hz. To reduce the effects of interactions, the trap is subsequently weakened giving final frequencies ω x ≈ 2π×40 Hz, ω y ≈ 2π×20 Hz, and ω z ≈ 2π×30 Hz. We load the BEC into a 1D optical pot...

Strongly Interacting Quantum Systems out of Equilibrium

“…One central aspect for bosonic systems [111] is the competition between disorder, which tends to localize particles [12], and weak repulsive interactions, which instead have a delocalizing effect. Joint theoretical [73,234,238,237] and experimental efforts [183,61,246,89] has been made and recently Anderson localization has been observed in one and two-dimensional systems of ultracold atoms [168,35,247]. It is impossible to completely eliminate it in real physical systems, but its effect on the microscopic components of matter is not as negative as it was previously thought.…”

Matter-wave localization in a random potential

“…Experimental studies employed the bichromatic optical lattice [2,3], shaken optical lattice [4], cold atom lattice [5], and speckle potentials [1]. (The effect of a repulsive atomic interaction on localization has also been studied [6].) Theoretical studies employed the bichromatic optical lattice [7][8][9], cold atom lattice [10,11], and random [12][13][14] potentials among others.…”

Dimensional Reduction and Localization of a Bose-Einstein Condensate in a Quasi-1D Bichromatic Optical Lattice

“…In the last twenty years the phenomenon of localization due to disorder was experimentally observed in electromagnetic waves [2,3], in sound waves [4], and also in quantum matter waves [5][6][7][8].…”