Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices

Abstract

We study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system is captured by a two-species Bose-Hubbard model, but realizes in a certain parameter regime actually the physics of a spin-1/2 Heisenberg magnet, describing the second order hopping processes. Tuning of the superlattice allows for controlling the effect of fast first order processes versus the slower second order ones. Using the density-matrix renormalization-group method, we provide the evolution of typical experimentally available observables. The validity of the description via the Heisenberg model, depending on the parameters of the Hubbard model, is studied numerically and analytically. The analysis is also motivated by recent experiments [S. Foelling et al., Nature 448, 1029 (2007); S. Trotzky et al., Sience 319, 295 (2008)] where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were realized. We provide theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. Contrary to the case of isolated double wells, relaxation of local observables can be observed. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and Bethe ansatz integrable models. We show that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models. We discuss the preparation of magnetic groundstates by adiabatic tuning of the superlattice parameters.

20 pages, 24 figures; minor changes, published version

References in corpus (18)

• Many-Body Physics with Ultracold Gases
• Real time evolution using the density matrix renormalization group
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Spatial quantum noise interferometry in expanding ultracold atom clouds
• The Luttinger model following a sudden interaction switch-on
• Interaction Quench in the Hubbard model
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• A lattice of double wells for manipulating pairs of cold atoms
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• Strongly correlated fermions after a quantum quench
• Implementation of Spin Hamiltonians in Optical Lattices
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Correlations in an expanding gas of hard-core bosons
• d-wave resonating valence bond states of fermionic atoms in optical lattices
• Quantum Many-Body Dynamics of Coupled Double-Well Superlattices

Cited by in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Characterization of Bose-Hubbard Models with Quantum Non-demolition Measurements
• Temporal decay of Neel order in the one-dimensional Fermi-Hubbard model
• Preparation of two-particle total hyperfine spin singlet states via spin-changing dynamics
• Emergence of Topological Fermi Liquid from a Strongly Correlated Bosonic System in Optical Superlattices