Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

Abstract

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

Motto:

There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy 1

Keywords:

• Ultracold atomic and molecular gases
• Hubbard Models
• Disordered systems
• Frustrated systems
• Spinor gases
• Quantum information

Acknowledgements

This review is to a great extent based on ideas and discussions that we shared with our long lasting friends, close collaborators, and colleagues: Jan Arlt, Alain Aspect, Nuri Barberan, Michael Baranov, Indrani Bose, Immanuel Bloch, Kai Bongs, Sibylle Braungardt, Dagmar Bruß, Ignacio Cirac, Eugene Demler, Kai Eckert, Wolfgang Ertmer, Uli Everts, Henning Fehrmann, Massimo Inguscio, Jarosław Korbicz, Anna Kubasiak, Jonas Larson, Mikko Juhani Leskinen, Alem Mebrahtu, Chiara Menotti, Armand Niederberger, Belen Paredes, Eugene Polzik, Andreas Osterloh, Klaus Osterloh, Carles Rodó, Oriol Romero-Isart, Robert Roth, Kazimierz Rzazewski, Krzysztof Sacha, Laurent Sanchez-Palencia, Luis Santos, Klaus Sengstock, Gora Shlyapnikov, Christian Trefzger, Janek Wehr, Jakub Zakrzewski, Łukasz Zawitkowski, and Peter Zoller.

We acknowledge support from the Deutsche Forschungsgemeinschaft (SFB 407, SPP1078 and SPP1116), the Spanish Ministerio de Ciencia y Tecnología grants BFM-2002-02588, FIS2005-04627, FIS2005-01497, FIS2005-01369, Consolider Ingenio 2010 CSD2006-00019 and Ramón y Cajal, the Alexander von Humboldt Foundation, the ESF Program QUDEDIS, the EU IP SCALA, and the U.S. Department of Energy.

Notes

†This statement has to be revised when the lattice is created inside of an optical cavity. As we discuss later, the presence of atoms may affect the cavity field.

‡Some authors go beyond this assumption. See for instance Ref. 156.

†The studies of trapped FB gases concerned in particular FB phase separation 211, 212, the phase diagram 213, novel types of collective modes 212, 214, Fermi-Fermi interactions mediated by bosons 212, 215, the collapse of the Fermi cloud in the presence of attractive FB interactions 216, or the effects characteristic for the 1D FB mixtures 217.

†The Majumdar-Ghosh model is one of the few frustrated spin models for which the exact ground states are known. See also, e.g. 452–455.

†Since the submission of an earlier version of this review, the distributed case has also been considered 776, 783.