The cold atom Hubbard toolbox

Jaksch, Dieter; Zoller, P.

doi:10.1016/j.aop.2004.09.010

Cited by 994 publications

(1,226 citation statements)

References 77 publications

(114 reference statements)

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“…Here c (1) and c (2) are chosen to enable the calculation of both thermal and charge diffusion constant as well as the cross terms. The remaining terms, c (3) and c (4) , on the other hand, are essential to correctly describe the low temperature limit: For a low density of particles or holes, the conductivity, and therefore the diffusion constant, grows exponentially for low T due to an exponential suppression of Umklapp scattering processes [39].…”

Section: B Boltzmann Equationmentioning

confidence: 99%

“…These complications render an experimental investigation in a clean and well controlled ultracold atom system highly desirable. While the last years have seen dramatic progress in the control of quantum gases in optical lattices [1][2][3], a thorough understanding of the dynamics in these systems is still lacking. Genuine dynamical experiments can not only uncover new dynamic phenomena but are also essential to gain insight into the timescales needed to achieve equilibrium in the lattice [4,5] or to adiabatically load into the lattice [6,7].…”

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Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

et al. 2012

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Transport properties are among the defining characteristics of many important phases in condensed matter physics. In the presence of strong correlations they are difficult to predict even for model systems like the Hubbard model. In real materials they are in general obscured by additional complications including impurities, lattice defects or multi-band effects. Ultracold atoms in contrast offer the possibility to study transport and out-of-equilibrium phenomena in a clean and well-controlled environment and can therefore act as a quantum simulator for condensed matter systems. Here we studied the expansion of an initially confined fermionic quantum gas in the lowest band of a homogeneous optical lattice. While we observe ballistic transport for non-interacting atoms, even small interactions render the expansion almost bimodal with a dramatically reduced expansion velocity. The dynamics is independent of the sign of the interaction, revealing a novel, dynamic symmetry of the Hubbard model.In solid state physics, transport properties are among the key observables, the most prominent example being the electrical conductivity, which e.g. allows to distinguish normal conductors from insulators or superconductors. Furthermore, many of today's most intriguing solid state phenomena manifest themselves in transport properties, examples including high-temperature superconductivity, giant magnetoresistance, quantum hall physics, topological insulators and disorder phenomena. Especially in strongly correlated systems, where the interactions between the conductance electrons are important, transport properties are difficult to calculate beyond the linear response regime. In general, predicting out-of-equilibrium fermionic dynamics represents an even harder problem than the prediction of static properties like the nature of the ground state. In real solids further complications arise due to the effects of e.g. impurities, lattice defects and phonons. These complications render an experimental investigation in a clean and well controlled ultracold atom system highly desirable. While the last years have seen dramatic progress in the control of quantum gases in optical lattices [1-3], a thorough understanding of the dynamics in these systems is still lacking. Genuine dynamical experiments can not only uncover new dynamic phenomena but are also essential to gain insight into the timescales needed to achieve equilibrium in the lattice [4,5] or to adiabatically load into the lattice [6,7].Using both bosonic and fermionic [8-10] atoms, it has become possible to simulate models of strongly interacting quantum particles, for which the Hubbard model [11] * ulrich.schneider@lmu.de is probably the most important example. A major advantage of these systems compared to real solids is the possibility to change all relevant parameters in real-time by e.g. varying laser intensities or magnetic fields. While first studies of dynamical properties of both bosonic and fermionic quantum gases [12][13][14] have already been performed, a remaining...

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Section: B Boltzmann Equationmentioning

confidence: 99%

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confidence: 99%

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

et al. 2012

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“…One of the interesting topics in this field is an optical lattice system [2][3][4][5], which is formed by loading the ultracold atoms in a periodic potential. This gives us clean correlated bosonic systems on various lattices with controllable parameters.…”

Section: Introductionmentioning

confidence: 99%

Supersolid States in a Hard-Core Bose–Hubbard Model on a Layered Triangular Lattice

Suzuki

Koga

2014

J. Phys. Soc. Jpn.

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We study ground-state properties in a hard-core Bose-Hubbard model on a layered triangular lattice. Combining cluster mean-field theory with the density matrix renormalization group method, we discuss the effect of the interlayer coupling on the supersolid states realized in a single layered model. By examining the distributions for the particle density and superfluid order parameter, the rich phase diagram of the system is obtained. We find that the supersolid states are widely stabilized at a commensurate filling, in contrast to the case of the single layered model. The nature of the supersolid states is also addressed.

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“…(16) given by f rj,s1 = e −iφj,s1 g rj ,s1 where the phase φ j,s1 is provided in Eq. (17). By combining Eq.…”

Section: The C Momentum Band and C Fermion Energy Dispersionmentioning

confidence: 99%

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Carmelo

2010

Nuclear Physics B

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The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one-and two-electron subspace are studied. The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global SO(3)×SO(3)×U (1) symmetry. For the model in the oneand two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid. For the Hubbard model on a square lattice in the one-and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it. In the U/4t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field Bs1 ex 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N/2 degenerate one-s1 fermion states of the two-dimensional quantum Hall effect. In turn, for U/4t finite the degeneracy of the N/2 one-s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by Bs1 L 2 /Φ0 and the s1 effective lattice spacing by as1 = ls1/ √ 2π where ls1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ0 = 1. Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors. This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.

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The cold atom Hubbard toolbox

Cited by 994 publications

References 77 publications

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

Supersolid States in a Hard-Core Bose–Hubbard Model on a Layered Triangular Lattice

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

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