The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.Comment: 13 pages, 10 figure

Quantum entanglement of spin-1 bosons with coupled ground states in optical lattices

We examine particle entanglement, characterized by pseudo-spin squeezing, of spin-1 bosonic atoms with coupled ground states in a one-dimensional optical lattice. Both the superfluid and Mott-insulator phases are investigated separately for ferromagnetic and antiferromagnetic interactions. Mode entanglement is also discussed in the Mott insulating phase. The role of a small but nonzero angle between the polarization vectors of counter-propagating lasers forming the optical lattice on quantum correlations is investigated as well.Comment: 18 pages, 8 figures. To be published in Journal of Physics

Model Hierarchies for Understanding Atmospheric Circulation

This is the final version. Available from Wiley via the DOI in this record.In this review, we highlight the complementary relationship between simple and comprehensive models in addressing key scientific questions to describe Earth’s atmospheric circulation. The systematic representation of models in steps, or hierarchies, connects our understanding from idealized systems to comprehensive models, and ultimately the observed atmosphere. We define three interconnected principles that can be used to characterize the model hierarchies of the atmosphere. We explore the rich diversity within the governing equations in the dynamical hierarchy, the ability to isolate and understand atmospheric processes in the process hierarchy, and the importance of the physical domain and resolution in the hierarchy of scale. We center our discussion on the large scale circulation of the atmosphere and its interaction with clouds and convection, focusing on areas where simple models have had a significant impact. Our confidence in climate model projections of the future is based on our efforts to ground the climate predictions in fundamental physical understanding. This understanding is, in part, possible due to the hierarchies of idealized models that afford the simplicity required for understanding complex systems.Natural Environment Research Council (NERC)US National Science FoundationUS Department of Energy Office of Biological and Environmental ResearchNatural Science and Engineering Research Council of CanadaAustralian Research CouncilSimons FoundationGerman Ministry of Education and Research (BMBF)FONA: Research for Sustainable DevelopmentState Research Agency of Spai

Thermometry with spin-dependent lattices

We propose a method for measuring the temperature of strongly correlated phases of ultracold atom gases confined in spin-dependent optical lattices. In this technique, a small number of "impurity" atoms--trapped in a state that does not experience the lattice potential--are in thermal contact with atoms bound to the lattice. The impurity serves as a thermometer for the system because its temperature can be straightforwardly measured using time-of-flight expansion velocity. This technique may be useful for resolving many open questions regarding thermalization in these isolated systems. We discuss the theory behind this method and demonstrate proof-of-principle experiments, including the first realization of a 3D spin-dependent lattice in the strongly correlated regime.Comment: 22 pages, 8 figures v2: Several references added; Section on heating rates updated to include dipole fluctuation terms; Section added on the limitations of the proposed method. To appear in New Journal of Physic

Mean-field phase diagram of disordered bosons in a lattice at non-zero temperature

Bosons in a periodic lattice with on-site disorder at low but non-zero temperature are considered within a mean-field theory. The criteria used for the definition of the superfluid, Mott insulator and Bose glass are analysed. Since the compressibility does never vanish at non-zero temperature, it can not be used as a general criterium. We show that the phases are unambiguously distinguished by the superfluid density and the density of states of the low-energy exitations. The phase diagram of the system is calculated. It is shown that even a tiny temperature leads to a significant shift of the boundary between the Bose glass and superfluid

Phase diagram of two-component bosons on an optical lattice

We present a theoretical analysis of the phase diagram of two--component bosons on an optical lattice. A new formalism is developed which treats the effective spin interactions in the Mott and superfluid phases on the same footing. Using the new approach we chart the phase boundaries of the broken spin symmetry states up to the Mott to superfluid transition and beyond. Near the transition point, the magnitude of spin exchange can be very large, which facilitates the experimental realization of spin-ordered states. We find that spin and quantum fluctuations have a dramatic effect on the transition making it first order in extended regions of the phase diagram. For Mott states with even occupation we find that the competition between effective Heisenberg exchange and spin-dependent on--site interaction leads to an additional phase transition from a Mott insulator with no broken symmetries into a spin-ordered insulator

Vortex Pinning and the Non-Hermitian Mott Transition

The boson Hubbard model has been extensively studied as a model of the zero temperature superfluid/insulator transition in Helium-4 on periodic substrates. It can also serve as a model for vortex lines in superconductors with a magnetic field parallel to a periodic array of columnar pins, due to a formal analogy between the vortex lines and the statistical mechanics of quantum bosons. When the magnetic field has a component perpendicular to the pins, this analogy yields a non-Hermitian boson Hubbard model. At integer filling, we find that for small transverse fields, the insulating phase is preserved, and the transverse field is exponentially screened away from the boundaries of the superconductor. At larger transverse fields, a ``superfluid'' phase of tilted, entangled vortices appears. The universality class of the transition is found to be that of vortex lines entering the Meissner phase at H_{c1}, with the additional feature that the direction of the tilted vortices at the transition bears a non-trivial relationship to the direction of the applied magnetic field. The properties of the Mott Insulator and flux liquid phases with tilt are also discussed.Comment: 20 pages, 12 figures included in text; to appear in Physical Review

Mixtures of Bosonic and Fermionic Atoms in Optical Lattices

We discuss the theory of mixtures of Bosonic and Fermionic atoms in periodic potentials at zero temperature. We derive a general Bose--Fermi Hubbard Hamiltonian in a one--dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean field criterion for the onset of a Bosonic superfluid transition. We investigate the ground state properties of the mixture in the Gutzwiller formulation of mean field theory, and present numerical studies of finite systems. The Bosonic and Fermionic density distributions and the onset of quantum phase transitions to demixing and to a Bosonic Mott--insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasi--degenerate ground states is related to a breaking of the mirror symmetry in the lattice.Comment: 11 pages, 8 figures; added discussions; conclusions and references expande