Synthetic Spin–Orbit Coupling and Topological Polaritons in Janeys–Cummings Lattices
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Dynamical Control of Matter Waves in Optical Lattices Sune Schøtt
Aarhus University Faculty of Science Department of Physics and Astronomy PhD Thesis Dynamical Control of Matter Waves in Optical Lattices by Sune Schøtt Mai November 2010 This thesis has been submitted to the Faculty of Science at Aarhus Uni- versity in order to fulfill the requirements for obtaining a PhD degree in physics. The work has been carried out under the supervision of profes- sor Klaus Mølmer and associate professor Jan Arlt at the Department of Physics and Astronomy. Contents Contents i 1 Introduction 3 1.1 Thesis Outline .......................... 3 1.2 Bose-Einstein Condensation .................. 4 2 Experimental Setup and Methods 9 2.1 Overview ............................. 9 2.2 Magneto-Optic Trap and Optical Pumping .......... 9 2.3 Transport with Movable Quadrupole Traps . 13 2.4 Evaporative Cooling ...................... 14 2.5 Absorption Imaging ....................... 15 3 Optical Lattices 17 3.1 Introduction ........................... 17 3.2 AC Stark-shift Induced Potentials . 18 3.2.1 Classical and Semi-Classical Approaches . 18 3.2.2 Dressed State Picture . 20 3.3 Lattice Band Structure ..................... 22 3.3.1 Reciprocal Space Bloch Theorem . 23 3.3.2 The 1D Lattice Band-Structure . 23 4 Lattice Calibration Techniques 27 4.1 Introduction ........................... 27 4.2 Kapitza-Dirac Scattering .................... 28 4.3 Bloch Oscillation and LZ-Tunneling . 30 4.3.1 Bloch Oscillation .................... 31 4.3.2 Landau-Zener Theory . 31 i ii CONTENTS 4.3.3 Experimental Verification of the Landau-Zener Model 32 4.4 Lattice Modulation ....................... 35 4.5 Summary ............................ 35 5 Dynamically Controlled Lattices 39 5.1 Introduction ........................... 39 5.2 Overview ............................. 39 5.3 Controlled Matter Wave Beam Splitter . -
Mott Insulators Atomic Limit - View Electrons in Real Space
Mott insulators Atomic limit - view electrons in real space Virtual system: lattice of H-Atoms: aB << d 2aB d H Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer - H H + -t ionization energy H delocalization localization kinetic energy charge excitation energy metal Mott insulator Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer ionization energy H -t S = 1/2 Mott isolator effective low-energy model low-energy physics no charge fluctuation only spin fluctuation Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 „ground state“ t = 0 E charge excitation U h d Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 t > 0 „ground state“ E W = 4d t U charge excitation h d metal-insulator transition: Uc = 4dt Mott insulators Metal-insulator transition from the metallic side h d tight-binding model density empty sites h = 1/4 doubly occupied sites d = 1/4 half-filled singly occupied sites s = 1/2 conduction band reducing mobility Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side Gutzwiller-approach: variational diminish double-occupancy uncorrelated state variational groundstate density of doubly occupied sites renormalized hopping Mott insulators Gutzwiller approximation Metal-insulator -
Scalability and High-Efficiency of an $(N+ 1) $-Qubit Toffoli Gate Sphere
Scalability and high-efficiency of an (n + 1)-qubit Toffoli gate sphere via blockaded Rydberg atoms Dongmin Yu1, Yichun Gao1, Weiping Zhang2,3, Jinming Liu1 and Jing Qian1,3,† 1State Key Laboratory of Precision Spectroscopy, Department of Physics, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China 2Department of Physics and Astronomy, Shanghai Jiaotong University and Tsung-Dao Lee Institute, Shanghai 200240, China and 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China∗ The Toffoli gate serving as a basic building block for reversible quantum computation, has man- ifested its great potentials in improving the error-tolerant rate in quantum communication. While current route to the creation of Toffoli gate requires implementing sequential single- and two-qubit gates, limited by longer operation time and lower average fidelity. We develop a new theoretical protocol to construct a universal (n + 1)-qubit Toffoli gate sphere based on the Rydberg blockade mechanism, by constraining the behavior of one central target atom with n surrounding control atoms. Its merit lies in the use of only five π pulses independent of the control atom number n which leads to the overall gate time as fast as 125ns and the average fidelity closing to 0.999. The maximal filling number of control atoms can be∼ up to n = 46, determined by the spherical diame- ter which is equal to the blockade radius, as well as by the nearest neighbor spacing between two trapped-atom lattices. Taking n = 2, 3, 4 as examples we comparably show the gate performance with experimentally accessible parameters, and confirm that the gate errors mainly attribute to the imperfect blockade strength, the spontaneous atomic loss and the imperfect ground-state prepa- ration. -
9 Quantum Phases and Phase Transitions of Mott Insulators
9 Quantum Phases and Phase Transitions of Mott Insulators Subir Sachdev Department of Physics, Yale University, P.O. Box 208120, New Haven CT 06520-8120, USA, [email protected] Abstract. This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. Mott insulators in the simplest class have an even number of S =1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S =1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S =1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations. 9.1 Introduction The physics of Mott insulators in two and higher dimensions has enjoyed much attention since the discovery of cuprate superconductors. While a quan- titative synthesis of theory and experiment in the superconducting materials remains elusive, much progress has been made in describing a number of antiferromagnetic Mott insulators. -
Structural Superfluid-Mott Insulator Transition for a Bose Gas in Multi
Structural Superfluid-Mott Insulator Transition for a Bose Gas in Multi-Rods Omar Abel Rodríguez-López,1, ∗ M. A. Solís,1, y and J. Boronat2, z 1Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000 Ciudad de México, México 2Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, España (Dated: Modified: January 12, 2021/ Compiled: January 12, 2021) We report on a novel structural Superfluid-Mott Insulator (SF-MI) quantum phase transition for an interacting one-dimensional Bose gas within permeable multi-rod lattices, where the rod lengths are varied from zero to the lattice period length. We use the ab-initio diffusion Monte Carlo method to calculate the static structure factor, the insulation gap, and the Luttinger parameter, which we use to determine if the gas is a superfluid or a Mott insulator. For the Bose gas within a square Kronig-Penney (KP) potential, where barrier and well widths are equal, the SF-MI coexistence curve shows the same qualitative and quantitative behavior as that of a typical optical lattice with equal periodicity but slightly larger height. When we vary the width of the barriers from zero to the length of the potential period, keeping the height of the KP barriers, we observe a new way to induce the SF-MI phase transition. Our results are of significant interest, given the recent progress on the realization of optical lattices with a subwavelength structure that would facilitate their experimental observation. I. INTRODUCTION close experimental realization of a sequence of Dirac-δ functions, forming the well-known Dirac comb poten- Phase transitions are ubiquitous in condensed matter tial [13], and could be useful to test many mean-field physics. -
Arxiv:2002.00554V2 [Cond-Mat.Str-El] 28 Jul 2020
Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices Zhihao Xu1, 2, 3, 4, ∗ and Shu Chen2, 5, 6, y 1Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China 2Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, P.R.China 4State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, P.R.China 5School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China 6Yangtze River Delta Physics Research Center, Liyang, Jiangsu 213300, China We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by the strong repulsion results in a stable topological Bose-Mott insulator which has shares features similar to the Hermitian case. However, for the non-Hermitian model related to the one-body loss, we find the non-Hermitian topological Mott insulators are unstable with a finite imaginary excitation gap. Finally, we also discuss the stability of the Mott phase in the presence of two-body loss by solving the Lindblad master equation. -
Chapter 5. Atoms in Optical Lattices
Strongly correlated systems in atomic and condensed matter physics Lecture notes for Physics 284 by Eugene Demler Harvard University September 18, 2014 2 Chapter 5 Atoms in optical lattices Optical lattices provide a powerful tool for creating strongly correlated many- body systems of ultracold atoms. By choosing different lattice geometries one can obtain very different single particle dispersions. The ratio of the interaction and kinetic energies can be controlled by tuning the depth of the lattice. 5.1 Noninteracting particles in optical lattices The simplest possible periodic optical potential is formed by overlapping two counter-propagating beams. Electric field in the resulting standing wave is E(z) = E0 sin(kz + θ) cos !t (5.1) Here k = 2π/λ is the wavevector of the laser light. Following the general recipe for AC Stark effects, we calculate electric dipolar moments induced by this field in the atoms, calculate interaction between dipolar moments and the electric field, and average over fast optical oscillations (see chapter ??). The result is the potential 2 V (z) = −V0 sin (kz + θ) (5.2) 2 where V0 = α(!)E0 =2, with α(!) being polarizability. It is common to express 2 2 V0 in units of the recoil energy Er = ~ k =2m. In real experiments one also needs to take into account the transverse profile of the beam. Hence V (r?; z) = exp{−2r2=w2(z)g×V (z). In most experiments the main effect of the transverse profile is only to renormalize the parabolic confining potentia. Combining three perpendicular sets of standing waves we get a simple cubic lattice V (r) = −Vx 0 cosqxx − Vy 0 cosqyy − Vz 0 cosqzz (5.3) 3 4 CHAPTER 5. -
Veselago Lensing with Ultracold Atoms in an Optical Lattice
ARTICLE Received 9 Dec 2013 | Accepted 27 Jan 2014 | Published 14 Feb 2014 DOI: 10.1038/ncomms4327 Veselago lensing with ultracold atoms in an optical lattice Martin Leder1, Christopher Grossert1 & Martin Weitz1 Veselago pointed out that electromagnetic wave theory allows for materials with a negative index of refraction, in which most known optical phenomena would be reversed. A slab of such a material can focus light by negative refraction, an imaging technique strikingly different from conventional positive refractive index optics, where curved surfaces bend the rays to form an image of an object. Here we demonstrate Veselago lensing for matter waves, using ultracold atoms in an optical lattice. A relativistic, that is, photon-like, dispersion relation for rubidium atoms is realized with a bichromatic optical lattice potential. We rely on a Raman p-pulse technique to transfer atoms between two different branches of the dispersion relation, resulting in a focusing that is completely analogous to the effect described by Veselago for light waves. Future prospects of the demonstrated effects include novel sub-de Broglie wavelength imaging applications. 1 Institut fu¨r Angewandte Physik der Universita¨t Bonn, Wegelerstrae 8, 53115 Bonn, Germany. Correspondence and requests for materials should be addressed to M.W. (email: [email protected]). NATURE COMMUNICATIONS | 5:3327 | DOI: 10.1038/ncomms4327 | www.nature.com/naturecommunications 1 & 2014 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4327 eselago lensing is a concept based on negative of spatial periodicity l/4, generated by the dispersion of multi- refraction1–3, where a spatially diverging pencil of rays photon Raman transitions17. -
Ultracold Atoms in a Disordered Optical Lattice
ULTRACOLD ATOMS IN A DISORDERED OPTICAL LATTICE BY MATTHEW ROBERT WHITE B.S., University of California, Santa Barbara, 2003 DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate College of the University of Illinois at Urbana-Champaign, 2009 Urbana, Illinois Doctoral Committee: Professor Paul Kwiat, Chair Assistant Professor Brian DeMarco, Director of Research Assistant Professor Raffi Budakian Professor David Ceperley Acknowledgments This work would not have been possible without the support of my advisor Brian DeMarco and coworkers Matt Pasienski, David McKay, Hong Gao, Stanimir Kondov, David Chen, William McGehee, Matt Brinkley, Lauren Aycock, Cecilia Borries, Soheil Baharian, Sarah Gossett, Minsu Kim, and Yutaka Miyagawa. Generous funding was provided by the Uni- versity of Illinois, NSF, ARO, and ONR. ii Table of Contents List of Figures..................................... v Chapter 1 Introduction .............................. 1 1.1 Strongly-interacting Boson Systems.......................1 1.2 Bose-Hubbard Model...............................2 1.3 Disordered Bose-Hubbard Model with Cold Atoms..............3 1.4 Observations...................................4 1.5 Future Work on the DBH Model........................5 1.6 Quantum Simulation...............................5 1.7 Outline......................................6 Chapter 2 BEC Apparatus............................ 8 2.1 Introduction....................................8 2.2 Atomic Properties................................8 -
Polariton Panorama (QED) with Atomic Systems
Nanophotonics 2020; ▪▪▪(▪▪▪): 20200449 Review D. N. Basov*, Ana Asenjo-Garcia, P. James Schuck, Xiaoyang Zhu and Angel Rubio Polariton panorama https://doi.org/10.1515/nanoph-2020-0449 (QED) with atomic systems. Here, we attempt to summarize Received August 5, 2020; accepted October 2, 2020; (in alphabetical order) some of the polaritonic nomenclature published online November 11, 2020 in the two subfields. We hope this summary will help readers to navigate through the vast literature in both of Abstract: In this brief review, we summarize and elaborate these fields [1–520]. Apart from its utilitarian role, this on some of the nomenclature of polaritonic phenomena summary presents a broad panorama of the physics and and systems as they appear in the literature on quantum technology of polaritons transcending the specifics of materials and quantum optics. Our summary includes at particular polaritonic platforms (Boxes 1 and 2). We invite least 70 different types of polaritonic light–matter dres- readers to consult with reviews covering many important sing effects. This summary also unravels a broad pano- aspects of the physics of polaritons in QMs [1–3], atomic and rama of the physics and applications of polaritons. A molecular systems [4], and in circuit QED [5, 6], as well as constantly updated version of this review is available at general reviews of the closely related topic of strong light– https://infrared.cni.columbia.edu. matter interaction [7–11, 394]. A constantly updated version Keywords: portions; quantum electrodynamics; quantum is available at https://infrared.cni.columbia.edu. materials; quantum optics. Anderson–Higgs polaritons [12, 13]. -
Mott Insulators
Quick and Dirty Introduction to Mott Insulators Branislav K. Nikoli ć Department of Physics and Astronomy, University of Delaware, U.S.A. PHYS 624: Introduction to Solid State Physics http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html Weakly correlated electron liquid: Coulomb interaction effects When local perturbation δ U ( r ) potential is switched on, some electrons will leave this region in order to ensure ε≃ µ constant F (chemical potential is a thermodynamic potential; therefore, in equilibrium it must be homogeneous throughout the crystal). δ= ε δ n()r eD ()F U () r δ≪ ε assume:e U (r ) F ε→ = θεε − f( , T 0) (F ) PHYS 624: Quick and Dirty Introduction to Mott Insulators Thomas –Fermi Screening Except in the immediate vicinity of the perturbation charge, assume thatδ U ( r ) is caused eδ n (r ) by the induced space charge → Poisson equation: ∇2δU(r ) = − ε − 0 1 ∂ ∂ αe r/ r TF ∇2 = r 2 ⇒ δ U (r ) = 2 −1/ 6 ∂ ∂ 2 rrr r 1 n 4πℏ ε ≃ = 0 rTF , a 0 ε 2 a3 me 2 r = 0 0 TF 2 ε = ⋅23− 3 Cu = e D (F ) nCu8.510 cm , r TF 0.55Å q in vacuum:D (ε )= 0, δ U (r ) = = α F πε 4 0 2 1/3 312n m 2/3ℏ 2/3− 4 1/3 n D()ε= =() 3,3 πεπ2 n = () 222 nr⇒ = () 3 π F ε π2ℏ 2 F TF π 2F 2 2 m a 0 PHYS 624: Quick and Dirty Introduction to Mott Insulators Mott Metal-Insulator Transition 1 a r2≃0 ≫ a 2 TF 4 n1/3 0 −1/3 ≫ n4 a 0 Below the critical electron concentration, the potential well of the screened field extends far enough for a bound state to be formed → screening length increases so that free electrons become localized → Mott Insulators Examples: transition metal oxides, glasses, amorphous semiconductors PHYS 624: Quick and Dirty Introduction to Mott Insulators Metal vs. -
Dynamics of Hubbard Hamiltonians with the Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles Axel Lode, Christoph Bruder
Dynamics of Hubbard Hamiltonians with the multiconfigurational time-dependent Hartree method for indistinguishable particles Axel Lode, Christoph Bruder To cite this version: Axel Lode, Christoph Bruder. Dynamics of Hubbard Hamiltonians with the multiconfigurational time-dependent Hartree method for indistinguishable particles. Physical Review A, American Physical Society 2016, 94, pp.013616. 10.1103/PhysRevA.94.013616. hal-02369999 HAL Id: hal-02369999 https://hal.archives-ouvertes.fr/hal-02369999 Submitted on 19 Nov 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. PHYSICAL REVIEW A 94, 013616 (2016) Dynamics of Hubbard Hamiltonians with the multiconfigurational time-dependent Hartree method for indistinguishable particles Axel U. J. Lode* and Christoph Bruder Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland (Received 29 April 2016; published 22 July 2016) We apply the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) to systems of bosons or fermions in lattices described by Hubbard-type Hamiltonians with long-range or short-range interparticle interactions. The wave function is expanded in a variationally optimized time-dependent many-body basis generated by a set of effective creation operators that are related to the original particle creation operators by a time-dependent unitary transform.