Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a mott insulator as the lattice potential depth is increased. Lattice geometry the simplest possible lattice is a one dimensional lattice 1d lattice. It makes a route through the physics of cold atoms in periodic potentials starting from the simple noninteracting system and going into the manybody physics that describes the strongly correlated mott insulator regime. A quantum theory of cold bosonic atoms in optical lattices. We demonstrate a novel experimental arrangement which can rotate a 2d optical lattice at frequencies up to several kilohertz. This chapter describes basic methods to realise optical potentials and optical lattices, listing in detail what can be controlled in ultracold atomic systems. The resulting periodic potential may trap neutral atoms via the stark shift. It revisits the properties of noninteracting particles in periodic lattices.
Simulating quantum manybody systems, by maciej lewenstein, anna sanpera and veronica ahufinger. Ultracold atoms in optical lattices hardcover maciej. Particles can be released from the trapping potential and their density distribution imaged after a suitable timeofflight period. Some condensed matter much of this chapter is familiar. Ultracold atoms in optical lattices derevianko group. In the limit of very low temperatures, cavity field and atomic dynamics require a quantum description. Quantum degenerate gases of magnetic lanthanide atoms in optical lattices offer an avenue to access the physics of strongly correlated systems for both bosonic and fermionic hubbard dynamics in the presence of dipolar interactions, while building on the welldeveloped toolbox to prepare ultracold dense samples and to manipulate and measure.
It makes a route through the physics of cold atoms. Here, we demonstrate how quantized dynamical gauge. Review quantum simulations with ultracold atoms in optical lattices christian gross1 and immanuel bloch1,2 quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Vexandvgx are external trapping potentials for the atom in the excited and the. Collective electronic excitations excitons in planar optical lattices exhibit strong modifications of the radiative damping rate and directional emission pattern as compared to a single excited atom. The physics of ultracold atoms, ions, and molecules offers unprecedented possibilities of control of quantum many systems, and novel possibilities of applications for quantum information and quantum metrology. This masterpiece is a unique opportunity to learn about the frontiers of quantum manybody physics, and how they can be explored with ultracold atoms in optical lattices. In order to investigate the quantum phase transitions and the timeofflight absorption pictures analytically in a systematic way for ultracold bose gases in bipartite optical lattices, we present a generalized greens function method. Quantum computers, although not yet available on the market, will revolutionise the future of information processing. They provide a clean, tuneable system which can be engineered to.
Maciej lewenstein, anna sanpera, and veronica ahufinger. Ultracold atoms in optical lattices with long range interactions and periodic driving. Controlling spin exchange interactions of ultracold atoms in optical lattices l. Ultracold atoms in optical lattices paperback maciej. Utilizing this method, we study the quantum phase transitions of ultracold bose gases in two types of bipartite optical lattices, i. The theory is based on a change of variables in which the boson coherent state. Pdf ultracold atoms in optical lattices pedro duarte. The optical lattices are formed by standing waves of laser light.
Particularly fascinating is the possibility of using ultracold atoms in lattices to. Probing quantum phases of ultracold atoms in optical. Spatial quantum noise interferometry in expanding ultracold atom clouds. We study an ultracold gas of neutral atoms subject to the periodic optical potential generated by a highq cavity mode.
Whilst normally the atoms are manipulated using classical light beams there is a. In general, two detection methods are used to reveal the quantum phases of ultracold gases in optical lattices. Ultracold atoms and molecules have opened a new field for studying strong correlation effects in manybody quantum systems in a highly controllable setting. Lukin2 1institute for quantum information, california institute of technology, mc 10781, pasadena, california 91125, usa 2physics department, harvard university, cambridge, massachusetts 028, usa received 25 october 2002.
Mitchell quantum gauge theories and ultracold atoms. Specifically, there have been intense theoretical efforts involving large samples of cold neutral atoms for coherent control of light. Ultracold gases trapped in optical lattices is a very successful and interdisciplinary field of research 1,2. Particularly fascinating is the possibility of using ultracold atoms in lattices to simulate condensed matter or even high energy physics. Relativistic simulations with cold atoms 2d and 3d refocusing of atomic wavepackets imaging of e. Topological manybody phases of matter exhibit remarkable electronic properties and ultracold atoms in optical lattices constitute promising candidates to study them in a wellcontrolled environment.
Studies of ultracold gases in optical lattices provide a means for testing fundamental and applicationoriented quantum manybody concepts of condensedmatter physics in. Laserassisted tunneling between atoms in different internal states along y axis with recoil along x. Realization of the hofstadter hamiltonian with ultracold atoms in optical lattices m. In twodimensional 2d electron gases topological phases may emerge in the presence of strong magnetic fields. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. Quantum simulation using ultracold atoms in twodimensional optical lattices sarah alassam, balliol college, oxford d. Ultracold dipolar gases in optical lattices christian trefzger.
The nook book ebook of the ultracold atoms in optical lattices. The scattering length is a single number that describes the lowenergy physics of collisions between ultracold atoms. A versatile system to explore few and manybody physics in periodic potentials david petrosyan iesl forth, greece fastquast, 250909 p. Some of the most talented theorists in the field guide the readers through the fascinating interplay of atomic, optical. Lightinduced gauge potentials and optical flux lattices. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum hall effect. Alternatively, one can image the intrap density distribution of atoms. This book provides a complete and comprehensive overview of ultracold lattice gases as quantum simulators. Optical potentials and in particular optical lattices have proven to be a powerful tool for manipulating ultracold atomic systems and are used in a wide range of experiments 7, 8,9.
The chapter derives the hubbard model in the tight binding approximation, and discusses boseeinstein. Veselago lensing with ultracold atoms in an optical lattice. Realization of the hofstadter hamiltonian with ultracold. Quantum coherence and entanglement with ultracold atoms in. Simulations of nonabelian gauge theories with optical lattices, l. In this paper i construct the naive lattice dirac hamiltonian describing the propagation of fermions in a generic 2d optical metric for different lattice and fluxlattice geometries. Controlling and detecting spin correlations of ultracold. However, there are some new ideas about lowdimensional systems that i didnt know beforehand. Manipulation of light using atoms plays a fundamental and important role in emerging technologies such as integrated photonics, information storage, and quantum sensors. Trapped atoms experience a harmonic potential, vr 1 2. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation. This thesis covers most of my work in the field of ultracold atoms loaded in optical lattices. Although most of such gases in the nanokelvin regime are first prepared in a continuum phase, a lattice structure can be superimposed onto the particles by using optical standing wave laser fields. First comprehensive book on ultracold gases in optical lattices.
Artificial gauge fields and topology with ultracold atoms. Maschler et al ultracold atoms in optical lattices generated by quantized light. Ultracold atoms in optical lattices with long range interactions and. First, i apply a topdown constructive approach that we first proposed in boada et al. Notes on lewenstein, sanpera, and ahu ngers ultracold atoms in optical lattices. We study the continuous zero temperature quantum phase transition from the superfluid to the mott insulator phase induced by varying the depth of the optical potential, where the mott. Ultracold atoms in optical lattices simulating quantum manybody systems maciej lewenstein, anna sanpera, and veronica ahufinger. Ultracold atoms in optical lattices generated by quantized. Review quantum simulations with ultracold atoms in optical. Effective magnetic fields without rotation optical square lattices d. In the case of cavity pumping, all atoms are simultane ously coupled to the same mode.
Here we present a theoretical scheme that enables efficient computation of collective. Atoms are cooled and congregate in the locations of potential minima. Such ultracold atoms in optical lattices form a completely novel and highly promising. For large detunings the conservative part of the optical potential dominates and can be used to trap the atoms. An individual user may print out a pdf of a single chapter of a monograph in oso for personal use.
Boseeinstein condensates in optical lattices and optical potentials, including the work of greiner et al. Topological phase transitions in the nonabelian honeycomb lattice a bermudez, n goldman, a kubasiak et al. An optical lattice is formed by the interference of counterpropagating laser beams, creating a spatially periodic polarization pattern. In this chapter we introduce the reader to the physics of ultracold atoms trapped in crystals made of light. The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a bosehubbard model where the system parameters are controlled by laser light. What makes optical lattices so useful is the nearly complete control it gives us over the system. Ultracold ferromagnetism the theoretical work described in chapter4arose from discussions with arun paramekanti and joseph thywissen regarding possible observable signatures of itinerant ferromagnetism in a trapped ultracold fermi gas. Outline the hubbard model for atoms optical dipole potential cold bosonic atoms in a tightbinding periodic potential. Optical lattices are an ideal platform for atomic experimentation.
Neutral atoms can be trapped in the intensity maxima or minima of these standing waves due to the optical dipole force see e. Request pdf on apr 1, 20, maciej lewenstein and others published ultracold atoms in optical lattices. Osa light reflection and transmission in planar lattices. Phil thesis, michaelmas 2010 ultracold atoms in optical lattices can be used to model condensed matter systems. Simulating quantum manybody systems kindle edition by maciej lewenstein, anna sanpera, veronica ahufinger. Extended bosehubbard models with ultracold magnetic atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a nonabelian gauge potential, which are depicted by nonabelian aah models. Quantum simulations based on ultracold atoms in optical lattices provide a promising avenue to study these complex systems and unravel the underlying manybody physics. Studies of ultracold gases in optical lattices provide a means for testing fundamental and applicationoriented quantum manybody concepts of condensedmatter physics in well controllable atomic systems. Simulating quantum manybody systems jimmy qin fall 2019 ch 2. Pdf this thesis covers most of my work in the field of ultracold atoms loaded 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.
Quantum coherence and entanglement with ultracold atoms in optical lattices immanuel bloch 1 at nanokelvin temperatures, ultracold quantum. Castelldefels, spain, where he leads the quantum optics theory group. From the standard model of particle physics to strongly correlated electrons, various physical settings are formulated in terms of matter coupled to gauge fields. Excitons for long wave numbers and polarizations orthogonal to the lattice plane exhibit superradiance with a very short life time and a tightly confined emission direction. Ultracold molecules and atom pairs in optical lattice. Quantum simulations of lattice gauge theories using. Gauge fields for ultracold atoms in optical superlattices. Notes on lewenstein, sanpera, and ahu ngers ultracold. Controlling spin exchange interactions of ultracold atoms. Optical lattices have seen utilization in such diverse.
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