Introduction

During the last few years the physics of ultracold atomic gases has experienced an extraordinary development, mostly due to the experimental realization of Bose-Einstein condensation (BEC). This development has being certainly interdisciplinary, bridging the gaps among very different areas, including atomic and molecular physics, quantum optics, condensed matter and solid-state physics, nonlinear physics, quantum information theory, etc.

The amazing degree of control of the properties of trapped ultracold atomic gases have allowed for an unprecedented capability of manipulation of the physics of these systems. Nowadays, the temperature of the samples can be reduced down to the nK scale, the atoms can be confined in basically any arbitrary potential (allowing, e.g., for the analysis of low-dimensional systems), and even the atom-atom interactions can be modified by means of the nowadays standard technique of Feshbach resonances.

Among the most relevant possibilities, the confinement of cold atomic gases in periodic potentials has recently generated a huge interest. These periodic potentials can be produced by a standing wave generated by two counterpropagating laser beams, although other alternatives are also possible, as the use of optical or magnetical microtraps.

It is the aim of this Focus Issue of Optics Express to present some of the research lines that have been recently devoted to the physics of atoms in lattices.

The possibility of loading a BEC into an optical lattice has aroused a growing attention from both the cold gases and the nonlinear physics communities. The BEC in different lattice wells allows for the generation of a Josephson-junction array of condensates. Particularly interesting is the interplay between nonlinearity and the periodicity of the laser potential. In this sense, the contribution of Cristiani et al. analyzes the instabilities of a BEC in a periodic potential when the BEC is accelerated across the edge of the Brillouin zone of a 1D optical lattice. The periodicity of the lattice allows for the managing of the dispersion experienced by the BEC. The latter has been analyzed in the contribution of Anker et al.. The existence of localized atomic structures for BEC in optical lattices is analyzed in detail in the paper of E. A. Ostrovskaya and Y. S. Kivshar, where different families of gap solitons are discussed in one- and two-dimensional lattices.

Additionally, the atoms trapped in the different wells of a lattice may be selectively photoassociated, leading to the fascinating possibility of on-site chemistry. The latter is analyzed in detail in the contribution of Search et al., where the authors draw an interesting analogy between the photoassociation of fermionic gases and the maser physics, showing once more the interdisciplinary character of this research field.

Finally, new developments in the control of ultracold gases allow for the analysis of systems that depart from the fruitful but limited mean-field frame. A new research field has rapidly developed, namely that of strongly-correlated atomic gases, which includes low-dimensional gases (Luttinger liquids), rapidly rotating gases (with physics similar to that of fractional Quantum Hall effect), gases with large scattering length, and of course also gases in optical lattices (recent observation of the superfluid to Mott-insulator transition). Two contributions in this special issue are devoted to the analysis of strongly-correlated gases in optical lattices. Garcia-Ripoll et al. develop in their paper a variational Ansatz for the superfluid to Mott-insulator transition in optical lattices. The contribution of Fehrmann et al. is devoted to the analysis of the rich physics appearing when Bose-Fermi mixtures are confined in periodic potentials.

In summary, the physics of atoms in optical lattices is nowadays one of the most fruitful research areas among those devoted to the properties of ultracold gases. The constant improvement of the experimental techniques allows to foresee a brilliant future for this particular field.

I hope, that the present Focus Issue may serve not only as a summary of the different research lines, but also may encourage further experimental and theoretical work in this exciting field.

I would like to thank all the authors who have contributed to this issue. I would also like to thank Optics Express Associate Editor Kazimierz Rząẑewski for supporting this project, and Managing Editor Jennifer Martin for her continuous help during the preparation of this Focus Issue.

Luis Santos

Universität Hannover