# The cold atom Hubbard toolbox

@article{Jaksch2005TheCA, title={The cold atom Hubbard toolbox}, author={Dieter Jaksch and Peter Zoller}, journal={Annals of Physics}, year={2005}, volume={315}, pages={52-79} }

Abstract We review recent theoretical advances in cold atom physics concentrating on strongly correlated cold atoms in optical lattices. We discuss recently developed quantum optical tools for manipulating atoms and show how they can be used to realize a wide range of many body Hamiltonians. Then, we describe connections and differences to condensed matter physics and present applications in the fields of quantum computing and quantum simulations. Finally, we explain how defects and atomic… Expand

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#### References

SHOWING 1-10 OF 125 REFERENCES

Spin-dependent Hubbard model and a quantum phase transition in cold atoms

- Physics
- 2004

We describe an experimental protocol for introducing spin-dependent lattice structure in a cold atomic Fermi gas using lasers. It can be used to realize Hubbard models whose hopping parameters depend… Expand

Controlling spin exchange interactions of ultracold atoms in optical lattices.

- Physics, Medicine
- Physical review letters
- 2003

It is illustrated how this technique can be used to efficiently "engineer" quantum spin systems with desired properties, for specific examples ranging from scalable quantum computation to probing a model with complex topological order that supports exotic anyonic excitations. Expand

Defect-suppressed atomic crystals in an optical lattice.

- Physics, Medicine
- Physical review letters
- 2003

We present a coherent filtering scheme which dramatically reduces the site occupation number defects for atoms in an optical lattice by transferring a chosen number of atoms to a different internal… Expand

Cold Bosonic Atoms in Optical Lattices

- Physics
- 1998

The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the… Expand

From Cooper pairs to Luttinger liquids with bosonic atoms in optical lattices.

- Physics, Medicine
- Physical review letters
- 2003

This work identifies the range of parameters where fermionic phenomena with bosonic atoms in optical lattices appear, illustrates the predictions with numerical calculations, and shows how to detect the presence of pairing. Expand

High-temperature superfluidity of fermionic atoms in optical lattices.

- Physics, Medicine
- Physical review letters
- 2002

An atomic physics experiment is described that can provide critical insight into the origin of high-temperature superconductivity in cuprates. Expand

Atomic quantum gases in Kagomé lattices.

- Physics, Medicine
- Physical review letters
- 2004

The possibility of creating and controlling an ideal and trimerized optical Kagomé lattice is demonstrated, and the low temperature physics of various atomic gases in such lattices are studied. Expand

Quantum computations with atoms in optical lattices: marker qubits and molecular interactions

- Physics
- 2004

We develop a scheme for quantum computation with neutral atoms, based on the concept of ``marker'' atoms, i.e., auxiliary atoms that can be efficiently transported in state-independent periodic… Expand

QUANTUM LOGIC GATES IN OPTICAL LATTICES

- Physics
- 1999

We propose a new system for implementing quantum logic gates: neutral atoms trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to occupy the same well by varying the… Expand

Atomic Bose-Fermi mixtures in an optical lattice.

- Physics, Medicine
- Physical review letters
- 2004

The phase diagram at low temperatures, and in the limit of strong atom-atom interactions, is discussed, and the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes are predicted. Expand