Characteristics of Bose-Einstein condensation in an optical lattice

We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system.Comment: 12 pages, 13 figures; Revised version with new figures; Phys. Rev. A 77, 043626 (2008

A scheme for demonstration of fractional statistics of anyons in an exactly solvable model

We propose a scheme to demonstrate fractional statistics of anyons in an exactly solvable lattice model proposed by Kitaev that involves four-body interactions. The required many-body ground state, as well as the anyon excitations and their braiding operations, can be conveniently realized through \textit{dynamic}laser manipulation of cold atoms in an optical lattice. Due to the perfect localization of anyons in this model, we show that a quantum circuit with only six qubits is enough for demonstration of the basic braiding statistics of anyons. This opens up the immediate possibility of proof-of-principle experiments with trapped ions, photons, or nuclear magnetic resonance systems.Comment: 4 pages, 3 figure

Superfluid shells for trapped fermions with mass and population imbalance

We map out the phase diagram of strongly interacting fermions in a potential trap with mass and population imbalance between the two spin components. As a unique feature distinctively different from the equal-mass case, we show that the superfluid here forms a shell structure which is not simply connected in space. Different types of normal states occupy the trap regions inside and outside this superfluid shell. We calculate the atomic density profiles, which provide an experimental signature for the superfluid shell structure.Comment: 4 pages, 3 figure

Disclination in Lorentz Space-Time

The disclination in Lorentz space-time is studied in detail by means of topological properties of $\phi$-mapping. It is found the space-time disclination can be described in term of a Dirac spinor. The size of the disclination, which is proved to be the difference of two sets of su(2)% -like monopoles expressed by two mixed spinors, is quantized topologically in terms of topological invariants$-$winding number. The projection of space-time disclination density along an antisymmetric tensor field is characterized by Brouwer degree and Hopf index.Comment: Revtex, 7 page

Signal of Bose condensation in an optical lattice at finite temperature

We discuss the experimental signal for the Bose condensation of cold atoms in an optical lattice at finite temperature. Instead of using the visibility of the interference pattern via the time-of-flight imaging, we show that the momentum space density profile in the first Brillouin zone, in particular its bimodal distribution, provides an unambiguous signal for the Bose condensation. We confirm this point with detailed calculation of the change in the atomic momentum distribution across the condensation phase transition, taking into account both the global trapping potential and the atomic interaction effects.Comment: 4 pages, 2 figures, replaced with the published versio

On the Applicability of Temperature and Precipitation Data from CMIP3 for China

Global Circulation Models (GCMs) contributed to the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) and are widely used in global change research. This paper assesses the performance of the AR4 GCMs in simulating precipitation and temperature in China from 1960 to 1999 by comparison with observed data, using system bias (B), root-mean-square error (RMSE), Pearson correlation coefficient (R) and Nash-Sutcliffe model efficiency (E) metrics. Probability density functions (PDFs) are also fitted to the outputs of each model. It is shown that the performance of each GCM varies to different degrees across China. Based on the skill score derived from the four metrics, it is suggested that GCM 15 (ipsl_cm4) and GCM 3 (cccma_cgcm_t63) provide the best representations of temperature and precipitation, respectively, in terms of spatial distribution and trend over 10 years. The results also indicate that users should apply carefully the results of annual precipitation and annual temperature generated by AR4 GCMs in China due to poor performance. At a finer scale, the four metrics are also used to obtain best fit scores for ten river basins covering mainland China. Further research is proposed to improve the simulation accuracy of the AR4 GCMs regarding China

Correlations in interference and diffraction

Quantum formalism of Fraunhofer diffraction is obtained. The state of the diffraction optical field is connected with the state of the incident optical field by a diffraction factor. Based on this formalism, correlations of the diffraction modes are calculated with different kinds of incident optical fields. Influence of correlations of the incident modes on the diffraction pattern is analyzed and an explanation of the ''ghost'' diffraction is proposed.Comment: 16 pages, 2 figures, Latex, to appear in J. Mod. Op

Simulation and detection of Dirac fermions with cold atoms in an optical lattice

We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.Comment: 4 pages; Published versio

Temperature driven structural phase transition for trapped ions and its experimental detection

A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology.Comment: 4 pages, 5 figure