Supersolid and pair correlations of the extended Jaynes-Cummings-Hubbard model on triangular lattices

We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to two-dimensional triangular lattices, we present evidence for the emergence of a light supersolid in this case also.Comment: 11 pages, 16 figure

Ultracold quantum gases in triangular optical lattices

Over the last years the exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand for experimental environments with non-cubic lattice geometries. In this paper we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step the superfluid-Mott insulator (SF-MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this we study the physics of spinor Bose-Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF-MI transition. Our results suggest that below the SF-MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly this opens new perspectives for a lattice driven tuning of a spin dynamics resonance occurring through the interplay of quadratic Zeeman effect and spin-dependent interaction. We finally discuss further lattice configurations which can be realized with our setup.Comment: 19 pages, 7 figure

Classification of a supersolid: Trial wavefunctions, Symmetry breakings and Excitation spectra

A state of matter is characterized by its symmetry breaking and elementary excitations. A supersolid is a state which breaks both translational symmetry and internal $U(1)$ symmetry. Here, we review some past and recent works in phenomenological Ginsburg-Landau theories, ground state trial wavefunctions and microscopic numerical calculations. We also write down a new effective supersolid Hamiltonian on a lattice. The eigenstates of the Hamiltonian contains both the ground state wavefunction and all the excited states (supersolidon) wavefunctions. We contrast various kinds of supersolids in both continuous systems and on lattices, both condensed matter and cold atom systems. We provide additional new insights in studying their order parameters, symmetry breaking patterns, the excitation spectra and detection methods.Comment: REVTEX4, 19 pages, 3 figure

Quantum crystal growing: Adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity

We theoretically study the adiabatic preparation of an antiferromagnetic phase in a mixed Mott insulator of two bosonic atom species in a one-dimensional optical lattice. In such a system one can engineer a tunable parabolic inhomogeneity by controlling the difference of the trapping potentials felt by the two species. Using numerical simulations we predict that a finite parabolic potential can assist the adiabatic preparation of the antiferromagnet. The optimal strength of the parabolic inhomogeneity depends sensitively on the number imbalance between the two species. We also find that during the preparation finite size effects will play a crucial role for a system of realistic size. The experiment that we propose can be realized, for example, using atomic mixtures of Rubidium 87 with Potassium 41 or Ytterbium 168 with Ytterbium 174.Comment: 25 pages, 6 figure

Topological Quantum Glassiness

Quantum tunneling often allows pathways to relaxation past energy barriers which are otherwise hard to overcome classically at low temperatures. However, this is not always the case. In this paper we provide simple exactly solvable examples where the barriers each system encounters on its approach to lower and lower energy states become increasingly large and eventually scale with the system size. If the environment couples locally to the physical degrees of freedom in the system, tunnelling under large barriers requires processes whose order in perturbation theory is proportional to the width of the barrier. This results in quantum relaxation rates that are exponentially suppressed in system size: For these quantum systems, no physical bath can provide a mechanism for relaxation that is not dynamically arrested at low temperatures. The examples discussed here are drawn from three dimensional generalizations of Kitaev's toric code, originally devised in the context of topological quantum computing. They are devoid of any local order parameters or symmetry breaking and are thus examples of topological quantum glasses. We construct systems that have slow dynamics similar to either strong or fragile glasses. The example with fragile-like relaxation is interesting in that the topological defects are neither open strings or regular open membranes, but fractal objects with dimension $d^* = ln 3/ ln 2$.Comment: (18 pages, 4 figures, v2: typos and updated figure); Philosophical Magazine (2011

Vacancy diffusion in the triangular lattice dimer model

We study vacancy diffusion on the classical triangular lattice dimer model, sub ject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e. a monomer, in an otherwise fully packed lattice, is always localized in a tree-like structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16 \pm 0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous:Comment: 15 pages, 27 eps figures. submitted to Physical Review

Atomic quantum gases in periodically driven optical lattices

Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent control of many-body systems. In particular, experiments with ultracold quantum gases in optical lattices subjected to periodic driving in the lower kilohertz regime have attracted a lot of attention. Milestones include the observation of dynamic localization, the dynamic control of the quantum phase transition between a bosonic superfluid and a Mott insulator, as well as the dynamic creation of strong artificial magnetic fields and topological band structures. This article reviews these recent experiments and their theoretical description. Moreover, fundamental properties of periodically driven many-body systems are discussed within the framework of Floquet theory, including heating, relaxation dynamics, anomalous topological edge states, and the response to slow parameter variations.Comment: Review, accepted for publication as Colloquium in Reviews of Modern Physic