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Physics

Disorder Induces Delocalization

Charles Day

Published Sep 19, 2024• 0 citations
Publisher

Abstract

A one-dimensional Bose-Einstein condensate's superfluid state is surprisingly robust if the atoms are trapped in a quasiperiodic lattice. By Charles Day ABose-Einstein condensate of cold atoms occupying a periodic lattice can flow like a superfluid.But if the atoms' mutual repulsion is strengthened and the lattice potential deepened, the atoms can become immobilized in a state known as a Mott insulator.Now Hepeng Yao of the University of Geneva and his collaborators have examined the Mott transition of cold atoms trapped in a lattice that is quasiperiodic rather than periodic [1].Given that quasiperiodicity and other kinds of disorder tend to trap particles, the researchers were surprised to discover that their quasiperiodic lattice sustained the superfluid state rather than weakening it.

DOI
10.1103/physics.17.s112

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A one-dimensional Bose-Einstein condensate's superfluid state is surprisingly robust if the atoms are trapped in a quasiperiodic lattice. By Charles Day ABose-Einstein condensate of cold atoms occupying a periodic lattice can flow like a superfluid.But if the atoms' mutual repulsion is strengthened and the lattice potential deepened, the atoms can become immobilized in a state known as a Mott insulator.Now Hepeng Yao of the University of Geneva and his collaborators have examined the Mott transition of cold atoms trapped in a lattice that is quasiperiodic rather than periodic [1].Given that quasiperiodicity and other kinds of disorder tend to trap particles, the researchers were surprised to discover that their quasiperiodic lattice sustained the superfluid state rather than weakening it.
Disorder or quasidisorder is known to favor localization in many-body Bose systems. Here, in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Switching from periodic to quasiperiodic potential with the same amplitude, we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum Monte Carlo calculations, showing this anomalous delocalization induced by the interplay between the disorder and interaction.
We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.
We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasiperiodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical lattice in the presence of a superlattice potential whose wavelength is incommensurate with the main lattice wavelength. After discussing the conditions under which the model can be realized experimentally, the study of the density vs the chemical potential curves for a nontrapped system unveils the existence of gapped phases at incommensurate densities interpreted as incommensurate charge-density-wave phases. Furthermore, a localization transition is known to occur above a critical value of the potential depth V2{V}_{2}V2​ in the case of free and hard-core bosons. We extend these results to soft-core bosons for which the phase diagrams at fixed densities display new features compared with the phase diagrams known for random box distribution disorder. In particular, a direct transition from the superfluid phase to the Mott-insulating phase is found at finite V2{V}_{2}V2​. Evidence for reentrances of the superfluid phase upon increasing interactions is presented. We finally comment on different ways to probe the emergent quantum phases and most importantly, the existence of a critical value for the localization transition. The latter feature can be investigated by looking at the expansion of the cloud after releasing the trap.
Quasiperiodic potentials and dipolar interactions each impose long-range order in quantum systems, but their interplay unlocks a rich landscape of unexplored quantum phases. In this work, we investigate how dipolar bosonic crystals respond to correlated disorder in the form of quasiperiodic potentials. Using exact numerical simulations and a suite of observables—including order parameters, energy, density distributions, and two-body coherence measures—we explore one-dimensional dipolar bosons in quasiperiodic lattices at both commensurate and incommensurate fillings. Our results reveal a complex competition between superfluid, Mott-insulator, density-wave, and crystalline phases, governed by the intricate balance of dipolar interactions, kinetic energy, and disorder strength. Crucially, we identify mechanisms that influence dipolar crystals, showing their surprising robustness even in the presence of strong quasiperiodic disorder. Strikingly, we challenge previous claims by demonstrating that a crystal phase—expected to precede full crystallization—does not emerge in the ground state. Instead, its traits appear only under moderate disorder, but never fully develop, giving way to a direct transition from a charge density wave to a crystal state. These findings provide new insights into the resilience of many-body quantum phases in complex environments and pave the way for engineering exotic quantum states in ultracold atomic systems.
Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.
The superfluid to one-dimensional Mott-insulator transition of a 87Rb Bose-Einstein condensate is demonstrated. In the experiment, we apply a one-dimensional optical lattice, formed by two laser beams with a wavelength of 852 nm, to a three dimensional BEC in a shallow trap. We use Kapitza-Dirac scattering to determine the depth of the optical lattice without knowledge of its exact geometry. We further study the dynamics of the transition as well as steady-state phase behavior specific to the one-dimensional case.