Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1012.4167

Robust states of ultra-cold bosons in tilted optical lattices

Moritz Hiller, Hannah Venzl, Tobias Zech, Bartłomiej Oleś, Florian Mintert, Andreas Buchleitner

Published Dec 19, 2010• 0 citations
arXivHTMLPDF

Abstract

We identify regular structures in the globally chaotic spectra of an interacting bosonic quantum gas in tilted periodic potentials. The associated eigenstates exhibit strong localization properties on the lattice, and are dynamically robust against external perturbations.
DOI
10.48550/arxiv.1012.4167

Related papers

Robust states of ultracold bosons in tilted optical lattices

Moritz Hiller, Hannah Venzl, Tobias Zech +3 more

We identify regular structures in the globally chaotic spectra of an interacting bosonic quantum gas in tilted periodic potentials. The associated eigenstates exhibit strong localization properties on the lattice and are dynamically robust against external perturbations.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 19, 2012•10 citations

Many-body localization of bosons in an optical lattice: Dynamics in disorder-free potentials

Ruixiao Yao, Jakub Zakrzewski

The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.

arXiv:2007.04745•Physical review. B./Physical review. B•Sep 23, 2020•52 citations

Ultrakalte Bosonen in optischen Gittern - der Einfluss spektraler Statistik auf Simulierbarkeit, Stabilität und Dynamik

Hannah Venzl

In this thesis, we study interacting ultracold bosons in tilted optical lattices, a paradigm for complex many-body quantum systems. Our analysis is based on the tilted Bose-Hubbard Hamiltonian which incorporates inter-site tunneling, inter-particle interaction, and a static field. The competition between the three contributions induces the system’s complexity which, on the spectral level, is reflected in chaotic level statistics. We address the question how this spectral chaos influences the dynamical behavior of the system and, vice versa, which information we can infer from the system’s dynamics on its many-body spectrum. Employing methods from random matrix theory, we first perform a detailed analysis of the Hamiltonian’s regular and chaotic spectral regimes and determine their borders by means of a scaling analysis. In the main part of the thesis, we tackle the question raised above from three different perspectives: Firstly, we investigate how the Hamiltonian’s level statistics affects the simulability of the system and find a breakdown of the simulation efficiency at the crossover from the regular to the chaotic regime. Secondly, we analyze the stability of the Hamiltonian’s eigenstates within the chaotic spectral regime and identify robust states that are dynamically stable against perturbations. Thirdly, we study the fast and irreversible decay of the Bloch oscillations in the chaotic regime. We develop an approach that is based on a statistical analysis of the velocity operator and find a characteristic crossover in the Bloch oscillations’ decay, once again right at the transition from regular to chaotic level statistics.

•Jan 1, 2011•0 citations

Quantum chaos for cold atoms in an optical lattice with a tilted harmonic trap

T. M. Fromhold, Christopher R. Tench, Sylwia Bujkiewicz +2 more

We show how ultracold (sub-µK temperature) atoms in a one-dimensional periodic optical potential with a harmonic trap can provide a new quantum chaotic system that is accessible to experiment. Provided that the harmonic potential varies slowly over a lattice period, the optical lattice has well defined energy bands. The energy-wavevector dispersion curves define an effective Hamiltonian that can be used to calculate classical orbits for atoms confined to a single band. We show that tilting the harmonic trap relative to the optical lattice induces a controllable transition from stable regular motion to classical chaos. The onset of chaos strongly delocalizes the atom orbits and should be manifest in both the classical and quantum properties of the trapped atoms. We also consider how the transition to chaos might affect the collective time-dependent dynamics of interacting atoms in Bose-Einstein condensates.

Journal of Optics B Quantum and Semiclassical Optics•Oct 1, 2000•11 citations

Characterization of the chaotic phase in the tilted Bose-Hubbard model

Pilar Martín Clavero, Alberto Rodríguez

The chaotic phase of the tilted Bose-Hubbard model is identified as a function of energy, tilt strength, and particle interaction, from the eigenstate structure and the statistical features of the energy spectrum. Our analysis reveals that the chaotic phase of the bare Bose-Hubbard Hamiltonian can be enhanced by the presence of a moderate tilt. We further unveil the development and scaling of the chaotic regime from the perspective of a homogeneous density configuration typically used in cold atom experiments, providing a valuable phase diagram for future theoretical and experimental studies of this system.

arXiv:2504.01462•Physical review. E•Jun 6, 2025•1 citation

Many-body localization in a quantum gas with long-range interactions and linear external potential

I. V. Lukin, Yu. V. Slyusarenko, Andrii Sotnikov

We study theoretical transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria characterizing localization, we construct effective phase diagrams for several types of lattice systems with variable amplitude of the external linear tilt and interaction strength. By means of exact diagonalization and time-dependent variational principle numerical approaches we analyze system dynamics after quenches. Our results reveal that the Stark localization without any artificial source of disorder remains stable upon inclusion of long-range interactions.

arXiv:2201.13090•Physical review. B./Physical review. B•May 31, 2022•5 citations
The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.
In this thesis, we study interacting ultracold bosons in tilted optical lattices, a paradigm for complex many-body quantum systems. Our analysis is based on the tilted Bose-Hubbard Hamiltonian which incorporates inter-site tunneling, inter-particle interaction, and a static field. The competition between the three contributions induces the system’s complexity which, on the spectral level, is reflected in chaotic level statistics. We address the question how this spectral chaos influences the dynamical behavior of the system and, vice versa, which information we can infer from the system’s dynamics on its many-body spectrum. Employing methods from random matrix theory, we first perform a detailed analysis of the Hamiltonian’s regular and chaotic spectral regimes and determine their borders by means of a scaling analysis. In the main part of the thesis, we tackle the question raised above from three different perspectives: Firstly, we investigate how the Hamiltonian’s level statistics affects the simulability of the system and find a breakdown of the simulation efficiency at the crossover from the regular to the chaotic regime. Secondly, we analyze the stability of the Hamiltonian’s eigenstates within the chaotic spectral regime and identify robust states that are dynamically stable against perturbations. Thirdly, we study the fast and irreversible decay of the Bloch oscillations in the chaotic regime. We develop an approach that is based on a statistical analysis of the velocity operator and find a characteristic crossover in the Bloch oscillations’ decay, once again right at the transition from regular to chaotic level statistics.
We show how ultracold (sub-µK temperature) atoms in a one-dimensional periodic optical potential with a harmonic trap can provide a new quantum chaotic system that is accessible to experiment. Provided that the harmonic potential varies slowly over a lattice period, the optical lattice has well defined energy bands. The energy-wavevector dispersion curves define an effective Hamiltonian that can be used to calculate classical orbits for atoms confined to a single band. We show that tilting the harmonic trap relative to the optical lattice induces a controllable transition from stable regular motion to classical chaos. The onset of chaos strongly delocalizes the atom orbits and should be manifest in both the classical and quantum properties of the trapped atoms. We also consider how the transition to chaos might affect the collective time-dependent dynamics of interacting atoms in Bose-Einstein condensates.
The chaotic phase of the tilted Bose-Hubbard model is identified as a function of energy, tilt strength, and particle interaction, from the eigenstate structure and the statistical features of the energy spectrum. Our analysis reveals that the chaotic phase of the bare Bose-Hubbard Hamiltonian can be enhanced by the presence of a moderate tilt. We further unveil the development and scaling of the chaotic regime from the perspective of a homogeneous density configuration typically used in cold atom experiments, providing a valuable phase diagram for future theoretical and experimental studies of this system.
We study theoretical transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria characterizing localization, we construct effective phase diagrams for several types of lattice systems with variable amplitude of the external linear tilt and interaction strength. By means of exact diagonalization and time-dependent variational principle numerical approaches we analyze system dynamics after quenches. Our results reveal that the Stark localization without any artificial source of disorder remains stable upon inclusion of long-range interactions.