28 research outputs found
Quantum gases in optical lattices
The experimental realization of correlated quantum phases with ultracold
gases in optical lattices and their theoretical understanding has witnessed
remarkable progress during the last decade. In this review we introduce basic
concepts and tools to describe the many-body physics of quantum gases in
optical lattices. This includes the derivation of effective lattice
Hamiltonians from first principles and an overview of the emerging quantum
phases. Additionally, state-of-the-art numerical tools to quantitatively treat
bosons or fermions on different lattices are introduced.Comment: 29 pages, 3 figures. This article will be published as Chapter 2 in
"Quantum gas experiments - exploring many-body states", edited by P. Torma
and K. Sengstock, Imperial College Press, London, to be published 201
Finite temperature dynamical correlations for the dimerized spin-1/2 chain
We use the density matrix renormalization group method (DMRG) to compute the
frequency and momentum resolved spin-spin correlation functions of a dimerized
spin-1/2 chain under a magnetic field at finite temperature. The spectral
features strongly depend on the regime of the magnetic field. For increasing
magnetic fields, the transitions from a gapped spin liquid phase to a
Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be
identified in the spectra. Compared to the zero temperature case, the finite
temperature excitations give rise to additional spectral features that we
compute numerically and identify analytically as transitions from thermally
excited states. We compute quantitatively the broadening of the dispersion of a
single spin-flip excitation due to the temperature and find a strong asymmetric
broadening. We discuss the consequences of these findings for neutron
experiments on dimerized one dimensional quantum chains.Comment: 13 pages, 14 figure
Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
We study the unitary time evolution of antiferromagnetic order in anisotropic
Heisenberg chains that are initially prepared in a pure quantum state far from
equilibrium. Our analysis indicates that the antiferromagnetic order imprinted
in the initial state vanishes exponentially. Depending on the anisotropy
parameter, oscillatory or non-oscillatory relaxation dynamics is observed.
Furthermore, the corresponding relaxation time exhibits a at the critical
point, in contrast to the usual notion of critical slowing down, from which a
maximum is expected.Comment: 4 pages, 4 figure
Propagation front of correlations in an interacting Bose gas
We analyze the quench dynamics of a one-dimensional bosonic Mott insulator
and focus on the time evolution of density correlations. For these we identify
a pronounced propagation front, the velocity of which, once correctly
extrapolated at large distances, can serve as a quantitative characteristic of
the many-body Hamiltonian. In particular, the velocity allows the weakly
interacting regime, which is qualitatively well described by free bosons, to be
distinguished from the strongly interacting one, in which pairs of distinct
quasiparticles dominate the dynamics. In order to describe the latter case
analytically, we introduce a general approximation to solve the Bose-Hubbard
Hamiltonian based on the Jordan-Wigner fermionization of auxiliary particles.
This approach can also be used to determine the ground-state properties. As a
complement to the fermionization approach, we derive explicitly the
time-dependent many-body state in the noninteracting limit and compare our
results to numerical simulations in the whole range of interactions of the
Bose-Hubbard model.Comment: 16 pages, 7 figure
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Scaling Approach to Quantum Non-equilibrium Dynamics of Many-body Systems
Understanding non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of non-equilibrium dynamics of many-body systems, which allow reliable theoretical analysis, are few and far between. In this paper we discuss a broad class of time-dependent interacting systems subject to external linear and parabolic potentials, for which the many-body Schrodinger equation can be solved using a scaling transformation. We demonstrate that scaling solutions exist for both local and nonlocal interactions and derive appropriate self-consistency equations. We apply this approach to several specific experimentally relevant examples of interacting bosons in one and two dimensions. As an intriguing result we find that weakly and strongly interacting Bose-gases expanding from a parabolic trap can exhibit very similar dynamics.Physic
Controllable manipulation and detection of local densities and bipartite entanglement in a quantum gas by a dissipative defect
We study the complex dynamics of a one-dimensional Bose gas subjected to a
dissipative local defect which induces one-body atom losses. In experiments
these atom losses occur, for example, when a focused electron or light beam or
a single trapped ion is brought into contact with a quantum gas. We discuss how
within such setups one can measure or manipulate densities locally and specify
the excitations that are induced by the defect. In certain situations the
defect can be used to generate entanglement in a controlled way despite its
dissipative nature. The careful examination of the interplay between hole
excitations and the collapse of the wave function due to nondetection of loss
is crucial for the understanding of the dynamics we observe.Comment: 4+ pages, 3 figure
Slow quench dynamics of Mott-insulating regions in a trapped Bose gas
We investigate the dynamics of Mott-insulating regions of a trapped bosonic
gas as the interaction strength is changed linearly with time. The bosonic gas
considered is loaded into an optical lattice and confined to a parabolic
trapping potential. Two situations are addressed: the formation of Mott domains
in a superfluid gas as the interaction is increased, and their melting as the
interaction strength is lowered. In the first case, depending on the local
filling, Mott-insulating barriers can develop and hinder the density and energy
transport throughout the system. In the second case, the density and local
energy adjust rapidly whereas long range correlations require longer time to
settle. For both cases, we consider the time evolution of various observables:
the local density and energy, and their respective currents, the local
compressibility, the local excess energy, the heat and single particle
correlators. The evolution of these observables is obtained using the
time-dependent density-matrix renormalization group technique and comparisons
with time-evolutions done within the Gutzwiller approximation are provided.Comment: 15 pages, 13 figure
Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
We propose a method for controllable generation of non-local entangled pairs
using spinor atoms loaded in an optical superlattice. Our scheme iteratively
increases the distance between entangled atoms by controlling the coupling
between the double wells. When implemented in a finite linear chain of 2N
atoms, it creates a triplet valence bond state with large persistency of
entanglement (of the order of N). We also study the non-equilibrium dynamics of
the one-dimensional ferromagnetic Heisenberg Hamiltonian and show that the time
evolution of a state of decoupled triplets on each double well leads to the
formation of a highly entangled state where short-distance antiferromagnetic
correlations coexist with longer-distance ferromagnetic ones. We present
methods for detection and characterization of the various dynamically generated
states. These ideas are a step forward towards the use of atoms trapped by
light as quantum information processors and quantum simulators.Comment: 13 pages, 10 figures, references adde
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Quantum quenches in the anisotropic spin-\frac{1}{2} Heisenberg chain: different approaches to many-body dynamics far from equilibrium
Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties usually relevant in solid-state many-body systems. In this paper we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ-model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. This reveals which aspects of non-equilibrium dynamics can as in equilibrium be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.Physic