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Optical Lattices: Theory

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Book cover Emergent Nonlinear Phenomena in Bose-Einstein Condensates

Part of the book series: Atomic, Optical, and Plasma Physics ((SSAOPP,volume 45))

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This chapter presents an overview of the properties of a Bose-Einstein condensate (BEC) trapped in a periodic potential. This system has attracted a wide interest in the last years, and a few excellent reviews of the field have already appeared in the literature (see, for instance, [1–3] and references therein). For this reason, and because of the huge amount of published results, we do not pretend here to be comprehensive, but we will be content to provide a flavor of the richness of this subject, together with some useful references. On the other hand, there are good reasons for our effort. Probably, the most significant is that BEC in periodic potentials is a truly interdisciplinary problem, with obvious connections with electrons in crystal lattices, polarons and photons in optical fibers. Moreover, the BEC experimentalists have reached such a high level of accuracy to create in the lab, so to speak, paradigmatic Hamiltonians, which were first introduced as idealized theoretical models to study, among others, dynamical instabilities or quantum phase transitions.

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Author information

Authors and Affiliations

  1. Universita’ di Trento, I-38050, Povo, Italy

    A. Smerzi

  2. Int. School for Advanced Studies, I-34104, Trieste, Italy

    A. Trombettoni

Authors
  1. A. Smerzi
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  2. A. Trombettoni
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Editor information

Editors and Affiliations

  1. University of Massachusetts, Amherst, MA, 01003-4515, USA

    Panayotis G. Kevrekidis

  2. University of Athens, Athens, 15784, Greece

    Dimitri J. Frantzeskakis

  3. San Diego State University, San Diego, CA, 92182-7720, USA

    Ricardo Carretero-González

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Smerzi, A., Trombettoni, A. (2008). Optical Lattices: Theory. In: Kevrekidis, P.G., Frantzeskakis, D.J., Carretero-González, R. (eds) Emergent Nonlinear Phenomena in Bose-Einstein Condensates. Atomic, Optical, and Plasma Physics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73591-5_13

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