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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

A glimpse of quantum phenomena in optical lattices

Smitha Vishveshwara

Published May 21, 2012• 4 citations
Publisher

Abstract

Optical lattices in cold atomic systems offer an excellent setting for realizing quantum condensed matter phenomena. Here, a glimpse of such a setting is provided for the non-specialist. Some basic aspects of cold atomic gases and optical lattices are reviewed. Quantum many-body physics is explored in the case of interacting bosons on a lattice. Quantum behaviour in the presence of a potential landscape is examined for three different cases: a hexagonal lattice potential, a quasi-periodic potential and a disorder potential.

DOI
10.1098/rsta.2011.0248

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Optical lattices in cold atomic systems offer an excellent setting for realizing quantum condensed matter phenomena. Here, a glimpse of such a setting is provided for the non-specialist. Some basic aspects of cold atomic gases and optical lattices are reviewed. Quantum many-body physics is explored in the case of interacting bosons on a lattice. Quantum behaviour in the presence of a potential landscape is examined for three different cases: a hexagonal lattice potential, a quasi-periodic potential and a disorder potential.
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. 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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 87 Rb 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
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.
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 Citation1
Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular periodic lattices are presented. A special attention is paid to the discussion of Bose-atom properties in the frame of the boson Hubbard model. Optical lattices with arbitrary strong disorder, induced by random potentials, are treated. Possible applications of cold atoms in optical lattices are discussed, with an emphasis of their usefulness for quantum information processing and quantum computing. An important feature of the present review article, distinguishing it from other review works, is that theoretical fundamentals here are not just mentioned in brief, but are thoroughly explained. This makes it easy for the reader to follow the principal points without the immediate necessity of resorting to numerous publications in the field.
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.