Collective Oscillations of Strongly Correlated One-Dimensional Bosons on a Lattice

We study the dipole oscillations of strongly correlated 1D bosons, in the hard-core limit, on a lattice, by an exact numerical approach. We show that far from the regime where a Mott insulator appears in the system, damping is always present and increases for larger initial displacements of the trap, causing dramatic changes in the momentum distribution, $n_k$. When a Mott insulator sets in the middle of the trap, the center of mass barely moves after an initial displacement, and $n_k$ remains very similar to the one in the ground state. We also study changes introduced by the damping in the natural orbital occupations, and the revival of the center of mass oscillations after long times.Comment: 4 pages, 5 figures, published versio

Phase separation in the bosonic Hubbard model with ring exchange

We show that soft core bosons in two dimensions with a ring exchange term exhibit a tendency for phase separation. This observation suggests that the thermodynamic stability of normal bose liquid phases driven by ring exchange should be carefully examined.Comment: 4 pages, 6 figure

Optimized Confinement of Fermions in Two Dimensions

One of the challenging features of studying model Hamiltonians with cold atoms in optical lattices is the presence of spatial inhomogeneities induced by the confining potential, which results in the coexistence of different phases. This paper presents Quantum Monte Carlo results comparing meth- ods for confining fermions in two dimensions, including conventional diagonal confinement (DC), a recently proposed 'off-diagonal confinement' (ODC), as well as a trap which produces uniform den- sity in the lattice. At constant entropy and for currently accessible temperatures, we show that the current DC method results in the strongest magnetic signature, primarily because of its judicious use of entropy sinks at the lattice edge. For d-wave pairing, we show that a constant density trap has the more robust signal and that ODC can implement a constant density profile. This feature is important to any prospective search for superconductivity in optical lattices

Ring Exchange and Phase Separation in the Two-dimensional Boson Hubbard model

We present Quantum Monte Carlo simulations of the soft-core bosonic Hubbard model with a ring exchange term K. For values of K which exceed roughly half the on-site repulsion U, the density is a non-monotonic function of the chemical potential, indicating that the system has a tendency to phase separate. This behavior is confirmed by an examination of the density-density structure factor and real space images of the boson configurations. Adding a near-neighbor repulsion can compete with phase separation, but still does not give rise to a stable normal Bose liquid.Comment: 12 pages, 23 figure

Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap

Quantum Monte Carlo (QMC) simulations and the Local Density Approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose Hubbard Hamiltonian confined in a harmonic trap onto the $(\mu/U,t/U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator (MI) lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.Comment: New version of figure 1

On the liquid drop model mass formulae and charge radii

ENAM 08International audienceAn adjustment to 782 ground state nuclear charge radii for nuclei with N,Z $\ge$ 8 leads to $R_0=1.2257~A^{1/3}$~fm and $\sigma =0.124$~fm for the charge radius. Assuming such a Coulomb energy $E_c=\frac {3}{5} {e^2Z^2}/{1.2257~A^{\frac {1}{3}}}$, the coefficients of different possible mass formulae derived from the liquid drop model and including the shell and pairing energies have been determined from 2027 masses verifying N,Z $\ge$ 8 and a mass uncertainty $\le$ 150 keV. These formulae take into account or not the diffuseness correction ($Z^2/A$ term), the charge exchange correction term ($Z^{4/3}/A^{1/3}$ term), the curvature energy, the Wigner terms and different powers of $I=(N-Z)/A$. The Coulomb diffuseness correction or the charge exchange correction term plays the main role to improve the accuracy of the mass formulae. The different fits lead to a surface energy coefficient of around 17-18~MeV. A possible more precise formula for the Coulomb radius is $R_0=1.2332A^{1/3}+{2.8961}/{A^{2/3}}-0.18688A^{1/3}I$~fm with $\sigma =0.052$~fm