%0 Journal Article
%J Physical Review Letters
%D 2014
%T Kitaev chains with long-range pairing
%A Davide Vodola
%A Luca Lepori
%A Elisa Ercolessi
%A Alexey V. Gorshkov
%A Guido Pupillo
%X We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions.
%B Physical Review Letters
%V 113
%8 2014/10/9
%G eng
%U http://arxiv.org/abs/1405.5440v2
%N 15
%! Phys. Rev. Lett.
%R 10.1103/PhysRevLett.113.156402
%0 Journal Article
%J Physical Review A
%D 2006
%T Effects of finite temperature on the Mott insulator state
%A Guido Pupillo
%A Carl J. Williams
%A Nikolay V. Prokof'ev
%X We investigate the effects of finite temperature on ultracold Bose atoms confined in an optical lattice plus a parabolic potential in the Mott insulator state. In particular, we analyze the temperature dependence of the density distribution of atomic pairs in the lattice, by means of exact Monte-Carlo simulations. We introduce a simple model that quantitatively accounts for the computed pair density distributions at low enough temperatures. We suggest that the temperature dependence of the atomic pair statistics may be used to estimate the system's temperature at energies of the order of the atoms' interaction energy.
%B Physical Review A
%V 73
%8 2006/1/20
%G eng
%U http://arxiv.org/abs/cond-mat/0407075v3
%N 1
%! Phys. Rev. A
%R 10.1103/PhysRevA.73.013408
%0 Journal Article
%J Physical Review A
%D 2006
%T Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice
%A Julio Gea-Banacloche
%A Ana Maria Rey
%A Guido Pupillo
%A Carl J. Williams
%A Charles W. Clark
%X We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.
%B Physical Review A
%V 73
%8 2006/1/9
%G eng
%U http://arxiv.org/abs/cond-mat/0410677v4
%N 1
%! Phys. Rev. A
%R 10.1103/PhysRevA.73.013605
%0 Journal Article
%J New Journal of Physics
%D 2006
%T Pseudo-fermionization of 1-D bosons in optical lattices
%A Guido Pupillo
%A Ana Maria Rey
%A Carl J. Williams
%A Charles W. Clark
%X We present a model that generalizes the Bose-Fermi mapping for strongly correlated 1D bosons in an optical lattice, to cases in which the average number of atoms per site is larger than one. This model gives an accurate account of equilibrium properties of such systems, in parameter regimes relevant to current experiments. The application of this model to non-equilibrium phenomena is explored by a study of the dynamics of an atom cloud subject to a sudden displacement of the confining potential. Good agreement is found with results of recent experiments. The simplicity and intuitive appeal of this model make it attractive as a general tool for understanding bosonic systems in the strongly correlated regime.
%B New Journal of Physics
%V 8
%P 161 - 161
%8 2006/08/30
%G eng
%U http://arxiv.org/abs/cond-mat/0505325v2
%N 8
%! New J. Phys.
%R 10.1088/1367-2630/8/8/161
%0 Journal Article
%J Physical Review A
%D 2005
%T Bragg Spectroscopy of ultracold atoms loaded in an optical lattice
%A Ana Maria Rey
%A P. Blair Blakie
%A Guido Pupillo
%A Carl J. Williams
%A Charles W. Clark
%X We study Bragg spectroscopy of ultra-cold atoms in one-dimensional optical lattices as a method for probing the excitation spectrum in the Mott insulator phase, in particular the one particle-hole excitation band. Within the framework of perturbation theory we obtain an analytical expression for the dynamic structure factor $S(q,\omega)$ and use it to calculate the imparted energy which has shown to be a relevant observable in recent experiments. We test the accuracy of our approximations by comparing them with numerically exact solutions of the Bose-Hubbard model in restricted cases and establish the limits of validity of our linear response analysis. Finally we show that when the system is deep in the Mott insulator regime, its response to the Bragg perturbation is temperature dependent. We suggest that this dependence might be used as a tool to probe temperatures of order of the Mott gap.
%B Physical Review A
%V 72
%8 2005/8/12
%G eng
%U http://arxiv.org/abs/cond-mat/0406552v2
%N 2
%! Phys. Rev. A
%R 10.1103/PhysRevA.72.023407
%0 Journal Article
%J Journal of Physics B: Atomic, Molecular and Optical Physics
%D 2005
%T Scalable register initialization for quantum computing in an optical lattice
%A Gavin K. Brennen
%A Guido Pupillo
%A Ana Maria Rey
%A Charles W. Clark
%A Carl J. Williams
%X The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation.
%B Journal of Physics B: Atomic, Molecular and Optical Physics
%V 38
%P 1687 - 1694
%8 2005/06/14
%G eng
%U http://arxiv.org/abs/quant-ph/0312069v1
%N 11
%! J. Phys. B: At. Mol. Opt. Phys.
%R 10.1088/0953-4075/38/11/010
%0 Journal Article
%J Physical Review A
%D 2005
%T Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach
%A Ana Maria Rey
%A Guido Pupillo
%A Charles W. Clark
%A Carl J. Williams
%X We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime.
%B Physical Review A
%V 72
%8 2005/9/22
%G eng
%U http://arxiv.org/abs/cond-mat/0503477v2
%N 3
%! Phys. Rev. A
%R 10.1103/PhysRevA.72.033616
%0 Journal Article
%J Journal of Modern Optics
%D 2004
%T Scalable quantum computation in systems with Bose-Hubbard dynamics
%A Guido Pupillo
%A Ana Maria Rey
%A Gavin Brennen
%A Carl J. Williams
%A Charles W. Clark
%X Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.
%B Journal of Modern Optics
%V 51
%P 2395 - 2404
%8 2004/02/15
%G eng
%U http://arxiv.org/abs/quant-ph/0403052v2
%N 16-18
%! Journal of Modern Optics
%R 10.1080/09500340408231798