01319nas a2200169 4500008004100000245004200041210004100083260001400124490000800138520086500146100001901011700001701030700002101047700002501068700001901093856003701112 2014 eng d00aKitaev chains with long-range pairing0 aKitaev chains with longrange pairing c2014/10/90 v1133 a 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.
1 aVodola, Davide1 aLepori, Luca1 aErcolessi, Elisa1 aGorshkov, Alexey, V.1 aPupillo, Guido uhttp://arxiv.org/abs/1405.5440v201078nas a2200145 4500008004100000245006200041210006200103260001400165490000700179520063300186100001900819700002300838700002700861856004400888 2006 eng d00aEffects of finite temperature on the Mott insulator state0 aEffects of finite temperature on the Mott insulator state c2006/1/200 v733 a 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.
1 aPupillo, Guido1 aWilliams, Carl, J.1 aProkof'ev, Nikolay, V. uhttp://arxiv.org/abs/cond-mat/0407075v301812nas a2200169 4500008004100000245010200041210006900143260001300212490000700225520125500232100002601487700002001513700001901533700002301552700002301575856004401598 2006 eng d00aMean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice
0 aMeanfield treatment of the damping of the oscillations of a 1D B c2006/1/90 v733 a 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.
1 aGea-Banacloche, Julio1 aRey, Ana, Maria1 aPupillo, Guido1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/cond-mat/0410677v401217nas a2200169 4500008004100000245006000041210005800101260001500159300001400174490000600188520072400194100001900918700002000937700002300957700002300980856004401003 2006 eng d00aPseudo-fermionization of 1-D bosons in optical lattices0 aPseudofermionization of 1D bosons in optical lattices c2006/08/30 a161 - 1610 v83 a 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.
1 aPupillo, Guido1 aRey, Ana, Maria1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/cond-mat/0505325v201431nas a2200169 4500008004100000245007100041210006900112260001400181490000700195520091200202100002001114700001801134700001901152700002301171700002301194856004401217 2005 eng d00aBragg Spectroscopy of ultracold atoms loaded in an optical lattice0 aBragg Spectroscopy of ultracold atoms loaded in an optical latti c2005/8/120 v723 a 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.
1 aRey, Ana, Maria1 aBlakie, Blair1 aPupillo, Guido1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/cond-mat/0406552v201428nas a2200181 4500008004100000245008400041210006900125260001500194300001600209490000700225520086200232100002301094700001901117700002001136700002301156700002301179856004401202 2005 eng d00aScalable register initialization for quantum computing in an optical lattice
0 aScalable register initialization for quantum computing in an opt c2005/06/14 a1687 - 16940 v383 a 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.
1 aBrennen, Gavin, K.1 aPupillo, Guido1 aRey, Ana, Maria1 aClark, Charles, W.1 aWilliams, Carl, J. uhttp://arxiv.org/abs/quant-ph/0312069v101494nas a2200157 4500008004100000245010300041210006900144260001400213490000700227520097300234100002001207700001901227700002301246700002301269856004401292 2005 eng d00aUltracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach
0 aUltracold atoms confined in an optical lattice plus parabolic po c2005/9/220 v723 a 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.
1 aRey, Ana, Maria1 aPupillo, Guido1 aClark, Charles, W.1 aWilliams, Carl, J. uhttp://arxiv.org/abs/cond-mat/0503477v201546nas a2200181 4500008004100000245007100041210006900112260001500181300001600196490000700212520099700219100001901216700002001235700001901255700002301274700002301297856004401320 2004 eng d00aScalable quantum computation in systems with Bose-Hubbard dynamics0 aScalable quantum computation in systems with BoseHubbard dynamic c2004/02/15 a2395 - 24040 v513 a 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.
1 aPupillo, Guido1 aRey, Ana, Maria1 aBrennen, Gavin1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/quant-ph/0403052v2