Imagine you could produce an artificial crystal for quantum matter, defect free and with complete control over the periodic crystal potential. The shape of the periodic potential, its depth and the interactions between the underlying particles could be changed at will and the particles could be moved around in a highly controlled way, at essentially zero temperature. This sounds almost too good to be true, but it is in fact what optical lattices have made possible for cold and ultracold atoms.

How does this work? Neutral atoms can be trapped in the periodic intensity pattern of light, which is formed when two laser beams interfere. The varying light intensity creates a periodic potential landscape – the optical lattice – for the atoms via an AC-Stark shift interaction. Such optical lattices have recently turned into a major research field, especially with the advent of degenerate bosonic and fermionic quantum gases. There, the artificial crystal of light is used to create and investigate fundamental quantum phases of bosonic and fermionic many-body systems.

One of the great advantages of these systems is that the physical behaviour of the atoms is usually perfectly described by a simple underlying Hamiltonian. They can thus can be used as a testbed for modern condensed matter theories with unique manipulation and control possibilities. Furthermore, novel and exotic many body quantum phases have also been predicted to be realizable in such 'quantum simulators as Richard P Feynman might have called them. Some of the most famous Hamiltonians that have been proposed in this respect include the Bose–Hubbard and Hubbard Hamiltonians for interacting bosons and fermions in periodic potentials, respectively. The physics within the Hubbard Hamiltonian is believed to contain an explanation for the origin of High-T_c superconductivity, but so far even the exact phase diagram of this basic Hamiltonian is still under discussion after decades of theoretical research on this problem. Another research focus in this respect has been to use ultracold atoms in optical lattices for the investigation of quantum magnetism. Here the spin state of an atom does not have to be restricted to two possible values, as for electrons, but can cover several possible magnetic substates, yielding rich and novel quantum phases. In the latest proposals, it has also been shown how quantum spin models could be robustly and efficiently simulated with polar molecules trapped in optical lattices.

Next to exploring the fundamental behaviour of quantum matter in periodic potentials, optical lattices have also shown to be very useful for the generation of ultracold molecules. Imagine for example having two atoms at each lattice site of an optical lattice. Then photoassociation or Feshbach resonances can be used to convert these atom pairs into stable molecules in a defined rotational-vibrational quantum state. One might consider such a coherent conversion of atoms into molecules to be the ultimate quantum limit that we can reach in the control over a 'chemical reaction'.

Next to being micro-laboratories for molecular physics, optical lattices also play an important role in quantum information processing. Atoms localized in the nodes of the optical potential can be seen as a natural quantum register that opens powerful possibilities for quantum computing. In this Focus Issue, it is shown, for example, how atoms can be sorted with an arrangement of two crossed optical standing waves.

The topics covered by the articles in this Focus Issue of New Journal of Physics reflect almost the whole breadth of topics discussed above and in fact the great interest in this field has required us to split off some of the articles to be published at a later date (still as part of this focus issue). We hope that you will find detailed new research results in this collection that are of interest to you and furthermore hope that the issue can increase the interest of the non-expert for this exciting and interdisciplinary research field.

The articles below represent the first contributions and further additions will appear.

Focus on Cold Atoms in Otical Lattices Contents

Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp
J E Williams, Nicolai Nygaard and Charles W Clark

Dressed molecules in an optical lattice
K B Gubbels, D B M Dickersheid and Henk T C Stoof

Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 ⁸⁷Rb atoms
Artur Widera, Fabrice Gerbier, Simon Folling, Tatjana Gericke, Olaf Mandel and Immanuel Bloch

The Fermi–Hubbard model at unitarity
Evgeni Burovski, Nikolay Prokof'ev, B Svistunov and M Troyer

Interaction broadening of wannier functions and mott transitions in atomic BEC
Jinbin Li, Yue Yu, A M Dudarev and Qian Niu

Hanbury Brown–Twiss interferometry for fractional and integer Mott phases
Ana Maria Rey, I I Satija and Charles W Clark

Quantum random walk with Rydberg atoms in an optical lattice
Robin Cote, Alexander Russell, Edward E. Eyler and Phillip Gould

Raman Spectroscopy of Mott insulator states in optical lattices
P Blair Blakie

Interacting Bose gases in quasi-one dimensional optical lattices
M A Cazalilla, A F Ho and Thierry Giamarchi

Long distance transport of ultracold atoms using a 1D optical lattice
Stefan Schmid, Gregor Thalhammer, Klaus Winkler, Florian Lang and J H Denschlag

Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms
S R Clark and Dieter Jaksch

Extended fermionization of 1D bosons in optical lattices
Guido Pupillo, Ana Maria Rey, Carl J Williams and Charles W Clark

One-dimensional description of a Bose–Einstein condensate in a rotating closed-loop waveguide
Sylvain Schwartz, Marco Cozzini, Chiara Menotti, I Carusotto, Philippe Bouyer and Sandro Stringari

Photo-ionization in far-off resonant optical lattices
R M Potvliege and Charles S Adams

Cooling toolbox for atoms in optical lattices
Markus Popp, J J Garcia-Ripoll, K G Vollbrecht and J I Cirac

Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle
David Clement, A F Varon, J A Retter, L Sanchez-Palencia, Alain Aspect and P Bouyer

Quantum dynamics, particle localization and instability of Mott states: the effect of fermion-boson conversion on Mott states
Fei Zhou and Congjun Wu

Off-diagonal correlations of lattice impenetrable bosons in one dimension
D M Gangardt and Gora V Shlyapnikov

Collective mode damping and viscosity in a 1D unitary Fermi gas
Matthias Punk and W Zwerger

Coherent matter waves emerging from Mott-insulators
K Rodriguez, S R Manmana, Madrazo Marcos Rigol, R M Noack and A Muramatsu

Phase-matched matter wave collisions in periodic potentials
Klaus Moelmer

Fermion pairing with spin-density imbalance in an optical lattice
T Koponen, J Kinnunen, J-P Martikainen, L M Jensen and P Törmä

Macroscopic superpositions of superfluid flows
David W Hallwood, Keith Burnett and Jacob Dunningham

Mean-field phase diagram of disordered bosons in a lattice at nonzero temperature
K V Krutitsky, A Pelster and R Graham

A primary noise thermometer for ultracold Bose gases
R Gati, J Esteve, B Hemmerling, T B Ottenstein, J Appmeier, A Weller and M K Oberthaler

Precision preparation of strings of trapped neutral atoms
Y Miroshnychenko, W Alt, I Dotsenko, L Förster, M Khudaverdyan, A Rauschenbeutel and D Meschede

Cold Fermi gases: a new perspective on spin-charge separation
Corinna Kollath and Ulrich Schollwöck

Analysis of localization phenomena in weakly interacting disordered lattice gases
T Schulte, S Drenkelforth, J Kruse, R Tiemeyer, K Sacha, J Zakrzewski, M Lewenstein, W Ertmer and J J Arlt

Localization and anomalous transport in a 1D soft boson optical lattice
A K Tuchman, W Li, H Chien, S Dettmer and M A Kasevich

Quantum switches and quantum memories for matter-wave lattice solitons
V Ahufinger, A Mebrahtu, R Corbalán and A Sanpera

Quantum noise analysis of spin systems realized with cold atoms
Robert W Cherng and Eugene Demler

Effective-range description of a Bose gas under strong one- or two-dimensional confinement
Pascal Naidon, Eite Tiesinga, William F Mitchell and Paul S Julienne

Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: dark state cooling of atoms within a Bloch band of an optical lattice
A Griessner, A J Daley, S R Clark, D Jaksch and P Zoller

Inhomogeneous broadening of a Mott insulator spectrum
V Guarrera, L Fallani, J E Lye, C Fort and M Inguscio

Immanuel Bloch, Johannes Gutenberg-Universität, Mainz, Germany
Peter Zoller, Universität Innsbruck, Austria