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arXiv:0707.4668 · New Journal of Physics

Atomic lattice excitons: from condensates to crystals

Adrian Kantian, Andrew J. Daley, Päivi Törmä, P Zoller

Published Nov 13, 2007• 11 citations
arXivHTMLPDF

Abstract

We discuss atomic lattice excitons (ALEs), bound particle–hole pairs formed by fermionic atoms in two bands of an optical lattice. Such a system provides a clean set-up, with tunable masses and interactions, to study fundamental properties of excitons including exciton condensation. We also find that for a large effective mass ratio between particles and holes, effective long-range interactions can mediate the formation of an exciton crystal, for which superfluidity is suppressed. Using a combination of mean-field treatments, bosonized theory based on a Born–Oppenheimer approximation, and one-dimensional (1D) numerical computation, we discuss the properties of ALEs under varying conditions, and discuss in particular their preparation and measurement.

DOI
10.1088/1367-2630/9/11/407

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Focus on Cold Atoms in Optical Lattices

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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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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

New Journal of Physics•Aug 30, 2006•16 citations
We discuss atomic lattice excitons (ALEs), bound particle–hole pairs formed by fermionic atoms in two bands of an optical lattice. Such a system provides a clean set-up, with tunable masses and interactions, to study fundamental properties of excitons including exciton condensation. We also find that for a large effective mass ratio between particles and holes, effective long-range interactions can mediate the formation of an exciton crystal, for which superfluidity is suppressed. Using a combination of mean-field treatments, bosonized theory based on a Born–Oppenheimer approximation, and one-dimensional (1D) numerical computation, we discuss the properties of ALEs under varying conditions, and discuss in particular their preparation and measurement.
Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of geometries and dimensionality. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties. Even the formation of molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.
In this thesis, we discuss ultracold quantum gases both in continuum and optical lattices. For the continuum Fermi gases in BCS-BEC crossover, we present an effective field theory study on the recently discovered puzzling damping phenomena on the BCS side of the crossover. We find that in contrast to the previous proposed pair-breaking mechanism of damping, the damping process is due to the interaction between superfluid phonons and thermally excited fermionic quasi particles. Results from our effective field theory are compared quantitatively with experiments, showing a good agreement. For the ultracold fermionic atoms in optical lattices, we propose two novel quantum phases. Firstly, we show that a novel superconducting pairing occurs for spin-imbalanced Fermi gases with the spin up and down Fermi levels lying within the px- and s- orbital bands of a quasi-one-dimensional optical lattice. The pairs condense at a finite momentum equal to the sum of the two Fermi momenta of spin up and down fermions, and form a p-orbital condensate. The phase diagram shows that the p-orbital pair condensate occurs in a wide range of fillings. Secondly, we study instabilities of single-species fermionic atoms in the p-orbital bands in two-dimensional square optical lattices. From the nearly-perfect nesting Fermi surfaces, charge density wave and orbital density wave orderings with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superconducting phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible liquid crystal phases in our system. For bosons, we study ultracold bosonic atoms loaded in a one-dimensional optical lattice of two-fold p-orbital degeneracy at each site, and find an anti-ferro-orbital, a homogeneous px Mott insulator phase and two kinds of superfluid phases distinguished by the orbital ordering.
A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far has been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.
We review our studies on Bose and Fermi superfluids of cold atomic gases in optical lattices at zero temperature. Especially, we focus on superfluid Fermi gases along the crossover between the Bardeen-Cooper-Schrieffer (BCS) and the Bose-Einstein condensate (BEC) states, which enable us to study the Bose and the Fermi superfluids in a unified point of view. We discuss basic static and long-wavelength properties (such as the equation of state, incompressibility, and effective mass), energetic stability, and energy band structures of the superfluid Fermi gases in an optical lattice periodic along one spatial direction. The periodic potential causes pairs of atoms to be strongly bound, and this can affect the static and long-wavelength properties and the stability of the superflow. Regarding the band structure, a peculiar loop structure called “swallowtail” can appear in superfluid Fermi gases and in the Bose case, but the mechanism of emergence in the Fermi case is very different from that in bosonic case. Other quantum phases that the cold atomic gases in optical lattices can show are also briefly discussed based on their roles as quantum simulators of Hubbard models.
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
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 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. 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