Topological Bandstructures for Ultracold Atoms
|
|
- Christina Sims
- 5 years ago
- Views:
Transcription
1 Topological Bandstructures for Ultracold Atoms Nigel Cooper Cavendish Laboratory, University of Cambridge New quantum states of matter in and out of equilibrium GGI, Florence, 12 April 2012 NRC, PRL 106, (2011) Benjamin Béri & NRC, PRL 107, (2011) NRC & Jean Dalibard, EPL 95, (2011)
2 Motivation: fractional quantum Hall regime Rotating BECs n φ = 2MΩ h [K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806 (2000)] FQH states of bosons for n 2D n φ < 6 [NRC, Wilkin & Gunn, PRL (2001)] [Laughlin, composite fermion, Moore-Read and Read-Rezayi] Ω 2π 100Hz n φ < cm 2
3 Optically Induced Gauge Fields [Y.-J. Lin, R.L. Compton, K. Jiménez-García, J.V. Porto and I.B. Spielman, Nature 462, 628 (2009)]
4 [NRC, PRL 106, (2011); NRC & Jean Dalibard, EPL 95, (2011)] Ĥ = p2 2M Î + ˆV (r) Landau levels: Narrow bands with unit Chern number n φ 10 9 cm 2 FQH states at high particle densities Distinct from previous tight-binding proposals [Jaksch & Zoller (2003); Mueller (2004); Sørensen, Demler & Lukin (2005); Gerbier & Dalibard (2010)] Generalizes to Z 2 topological invariant [Benjamin Béri & NRC, PRL 107, (2011)] Nearly free electron approach to topological bands
5 Outline Optically Induced Gauge Fields
6 Optically Induced Gauge Fields [J. Dalibard, F. Gerbier, G. Juzeliūnas, P. Öhberg, RMP 83, 1523 (2011)] Ĥ = p2 2M Î + ˆV (r) ˆV (r): optical coupling of N internal states 3P 0 e.g. 1 S 0 and 3 P 0 for Yb or alkaline earth atom [F. Gerbier & J. Dalibard, NJP 12, (2010)] Ω R 1S 0 ω
7 3P 0 e.g. 1 S 0 and 3 P 0 for Yb or alkaline earth atom [F. Gerbier & J. Dalibard, NJP 12, (2010)] Ω R ω ( ˆV = ( ( ΩR e iωt + Ω R e iωt) ) 1 ( 0 2 Ω R e iωt + Ω R e iωt) ω ( Ω R + Ω R e 2iωt) ( ΩR + Ω R e 2iωt) 2 ( ΩR (r) ) ) 1S 0 RWA ω, Ω R ˆV 2 Ω R (r)
8 [J. Dalibard, F. Gerbier, G. Juzeliūnas, P. Öhberg, RMP 83, 1523 (2011)] Ĥ = p2 2M Î + ˆV (r) ˆV (r) local spectrum E n (r) and dressed states n r ψ(r) = n ψ n (r) n r Adiabatic motion H n ψ n = n r Ĥψ n n r H n = (p qa)2 2M + V n (r) qa = i n r n r
9 Maximum flux density: Back of the envelope Vector potential qa = i 0 r 0 r qa < Cloud of radius R λ N φ n φ d 2 r = q h n φ N φ πr 2 < h λ A ds = q h 1 Rλ cm 2 A dr < 1 λ (2πR) [R 10µm λ 0.5µm]
10 Maximum flux density: Carefully this time! Optical wavelength λ qa < A can have singularities if the optical fields have vortices. h λ e.g. Ω R (r) (x + iy) Vanishing net flux. Can be removed by a gauge transformation. [cf. Dirac strings ]
11 Gauge-independent approach (two-level system) Bloch vector n(r) = 0 r ˆ σ 0 r r n φ = 1 8π ɛ ijkɛ µν n i µ n j ν n k Region A n n φ < Solid Angle Ω 1 λ 2 area A n φ d 2 r = Ω 4π The number of flux quanta in region A is the number of times the Bloch vector wraps over the sphere.
12 Optical flux lattices [NRC, Phys. Rev. Lett. 106, (2011)] Spatially periodic light fields which cause the Bloch vector to wrap the sphere a nonzero integer number, N φ, times in each unit cell. n φ = N φ A cell 1 λ cm 2 vectors (n x, n y ) contours n z N φ = 2 a contours n φ. (a) a (b)
13 Optical Flux Lattice: One-Photon Implementation Ĥ = p2 2M Î + V ˆM(r) ˆM = M(r) ˆ σ 3P 0 e.g. 1 S 0 and 3 P 0 for Yb or alkaline earth atom [Gerbier & Dalibard, New Journal of Physics 12, (2010)] Ω R ω M x, M y : Rabi coupling, ω ω 0 M z : standing waves at anti-magic frequency, ω am ( VM = 2 V Ω(r) am(r) 2 Ω (r) V am(r) ) 1S 0
14 Square Lattice ( sin(κx) sin(κy) cos(κx) i cos(κy) ˆM sq = cos(κx) + i cos(κy) sin(κx) sin(κy) where κ 2π/a. ) vectors (n x, n y ) contours n z N φ = 2 a contours n φ (a) a (b)
15 Triangular lattice ( ˆM tri = cos[r (κ 1 + κ 2 )] cos(r κ 1 ) i cos(r κ 2 ) cos(r κ 1 ) + i cos(r κ 2 ) cos[r (κ 1 + κ 2 )] ) κ κ 1 + κ 2 2 (a) (b) θ κ 1 θ 2π/3 vectors: (n x, n y ) contours: n z N φ = 2 a a
16 Bandstructure (Triangular Lattice) Ĥ = p2 2M Î + V [c 1ˆσ x + c 2ˆσ y + c 12ˆσ z ] Tight-binding limit V > E R 2 κ 2 2M c i cos(κ i r), c 12 cos[(κ 1 + κ 2 ) r] 2Π Π E tb Π 2Π k ya k a x Lowest energy band has narrow width and Chern number of 1.
17 Two-Photon Dressed States J e = 1/2 [NRC & Jean Dalibard, EPL 95, (2011)] Light at two frequencies: ω L with Rabi freqs. κ m (m = 0, ±1) ω L + δ with Rabi freq. E in σ g g + ω L ω L ω L ω L + δ σ pol.
18 Triangular lattice with N φ = 1 per unit cell.
19 Bandstructure, J g = 1/2 DoS (arb.) x 1/10 V = 2E R, θ = π/4, ɛ = E/E R Narrow lowest energy band, with Chern number of 1 Can also be applied to bosons J g = 1 (e.g. 87 Rb)
20 Experimental Consequences Non-interacting fermions (IQHE) Filled band has chiral edge state: Precession of collective modes Bloch oscillations [Hannah Price & NRC, PRA 85, (2012)] Interacting fermions/bosons Strongly correlated phases if interactions large compared to bandwidth: likely candidates for FQHE states. Incompressible states (density plateaus) Chiral edge modes
21 Outline Optically Induced Gauge Fields
22 Topological Insulators [Hasan & Kane, RMP 82, 3045 (2010); Qi & Zhang, RMP 83, 1057 (2011)] TI: Band insulator with gapless surface states. IQHE: 2D, broken time reversal symmetry (TRS) Chern number number of chiral edge states Z 2 TI: fermions (S = 1 2, 3 2,...) with TRS (Kramers deg.) Band insulators are: trivial; or non-trivial (metallic surface) 2D: counterpropagating edge channels of opposite spin; Spin up Spin down 3D: relativistic (Dirac) 2D surface state.
23 Ĥ = p2 2M ÎN + V ˆM(r) [Benjamin Béri & NRC, PRL 107, (2011)] Time-reversal ˆθ = i ˆσ y ˆK TRS: ˆM = ˆθ 1 ˆM ˆθ N = 4 ( (A + B)Î ˆM = 2 CÎ 2 i ˆ σ D ) CÎ 2 + i ˆ σ D (A B)Î 2 = AÎ 4 + B ˆΣ 3 + C ˆΣ 1 + D ˆΣ 2ˆ σ [A, B, C, D = (D x, D y, D z ) real] Dressed states are Kramers doublets non-abelian gauge field.
24 171 Yb has nuclear spin I = 1/2 3P 0 V ˆM = ( ( 2 + V am) Î2 i ˆ σ Ed ) r i ˆ σ E ( d r 2 + V ) am Î2 1S 0 I = 1/2 +1/2 z TRS preserved if all components of E have a common phase.
25 Two Dimensions d r E = V (δ, cos(r κ1 ), cos(r κ 2 )) κ 1 = (1, 0, 0)κ κ 2 = (cos θ, sin θ, 0)κ κ 2 E z θ Ey κ 1 E x κ 3 =z 2 + V am(r) = V cos[r (κ 1 + κ 2 )] For Yb, θ 2π/3
26 Û = 2 1/2 (Î 4 i ˆΣ 3ˆσ 2 ) ˆM = Û ˆMÛ = c 1 ˆΣ 1 + c 2 ˆΣ 2ˆσ 3 + c 12 ˆΣ 3 + δ ˆΣ 2ˆσ 1. c i cos(κ i r), c 12 cos[(κ 1 + κ 2 ) r] (i) Decoupled spins, δ = 0 ˆM = c 1 ˆΣ 1 ± c 2 ˆΣ 2 + c 12 ˆΣ 3 OFLs of opposite flux for spin σ 3 = ±1. σ 3 = ±1 bands are degenerate, but with opposite Chern numbers. quantum spin Hall system [e.g. Levin & Stern, PRL (2009)]
27 (ii) Spin-orbit coupling, δ E/E R _ -0.4 (1,1) _ + + (0,1) (0,0) (1,0) (1,1) _ Γ nm = 1 2 (nκ 1 + mκ 2 ) Inversion symmetry [Fu & Kane, PRB (2007)] n,m=0,1 α filled ξ (α) nm = 1
28 Three Dimensions This nearly-free electron viewpoint leads to a general method to construct Z 2 non-trivial bands in 3D. [Benjamin Béri & NRC, PRL 107, (2011)] e.g. δ δ 0 cos(κ 3 r) c 12 c 12 + δ 0 (µ + c 13 + c 23 ) -0.6 E/E R V = 0.9E R δ 0 = 1, µ = k 1
29 Summary Simple forms of optical dressing lead to optical flux lattices : periodic magnetic flux with high mean density, n φ 1/λ 2. The low energy bands are analogous to the lowest Landau level of a charged particle in a uniform magnetic field. The approach can be generalized to generate Z 2 nontrivial bandstructures in 2D and 3D. Ultracold atomic gases can readily be used to explore strong correlation phenomena in topological bands.
Optical Flux Lattices for Cold Atom Gases
for Cold Atom Gases Nigel Cooper Cavendish Laboratory, University of Cambridge Artificial Magnetism for Cold Atom Gases Collège de France, 11 June 2014 Jean Dalibard (Collège de France) Roderich Moessner
More informationMapping the Berry Curvature of Optical Lattices
Mapping the Berry Curvature of Optical Lattices Nigel Cooper Cavendish Laboratory, University of Cambridge Quantum Simulations with Ultracold Atoms ICTP, Trieste, 16 July 2012 Hannah Price & NRC, PRA 85,
More informationQuantum Quenches in Chern Insulators
Quantum Quenches in Chern Insulators Nigel Cooper Cavendish Laboratory, University of Cambridge CUA Seminar M.I.T., November 10th, 2015 Marcello Caio & Joe Bhaseen (KCL), Stefan Baur (Cambridge) M.D. Caio,
More informationLaboratoire Kastler Brossel Collège de France, ENS, UPMC, CNRS. Artificial gauge potentials for neutral atoms
Laboratoire Kastler Brossel Collège de France, ENS, UPMC, CNRS Artificial gauge potentials for neutral atoms Fabrice Gerbier Workshop Hadrons and Nuclear Physics meet ultracold atoms, IHP, Paris January
More informationTopological Phases of Matter Out of Equilibrium
Topological Phases of Matter Out of Equilibrium Nigel Cooper T.C.M. Group, Cavendish Laboratory, University of Cambridge Solvay Workshop on Quantum Simulation ULB, Brussels, 18 February 2019 Max McGinley
More informationTopological Kondo Insulator SmB 6. Tetsuya Takimoto
Topological Kondo Insulator SmB 6 J. Phys. Soc. Jpn. 80 123720, (2011). Tetsuya Takimoto Department of Physics, Hanyang University Collaborator: Ki-Hoon Lee (POSTECH) Content 1. Introduction of SmB 6 in-gap
More informationMagnetic Crystals and Helical Liquids in Alkaline-Earth 1D Fermionic Gases
Magnetic Crystals and Helical Liquids in Alkaline-Earth 1D Fermionic Gases Leonardo Mazza Scuola Normale Superiore, Pisa Seattle March 24, 2015 Leonardo Mazza (SNS) Exotic Phases in Alkaline-Earth Fermi
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son (University of Chicago) Cold atoms meet QFT, 2015 Ref.: 1502.03446 Plan Plan Composite fermion: quasiparticle of Fractional Quantum Hall Effect (FQHE)
More informationArtificial magnetism and optical flux lattices for ultra cold atoms
Artificial magnetism and optical flux lattices for ultra cold atoms Gediminas Juzeliūnas Institute of Theoretical Physics and Astronomy,Vilnius University, Vilnius, Lithuania Kraków, QTC, 31 August 2011
More informationLoop current order in optical lattices
JQI Summer School June 13, 2014 Loop current order in optical lattices Xiaopeng Li JQI/CMTC Outline Ultracold atoms confined in optical lattices 1. Why we care about lattice? 2. Band structures and Berry
More informationAdiabatic trap deformation for preparing Quantum Hall states
Marco Roncaglia, Matteo Rizzi, and Jean Dalibard Adiabatic trap deformation for preparing Quantum Hall states Max-Planck Institut für Quantenoptik, München, Germany Dipartimento di Fisica del Politecnico,
More informationField Theory Description of Topological States of Matter. Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti)
Field Theory Description of Topological States of Matter Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti) Topological States of Matter System with bulk gap but non-trivial at energies below
More informationCorrelated Phases of Bosons in the Flat Lowest Band of the Dice Lattice
Correlated Phases of Bosons in the Flat Lowest Band of the Dice Lattice Gunnar Möller & Nigel R Cooper Cavendish Laboratory, University of Cambridge Physical Review Letters 108, 043506 (2012) LPTHE / LPTMC
More informationThe Quantum Spin Hall Effect
The Quantum Spin Hall Effect Shou-Cheng Zhang Stanford University with Andrei Bernevig, Taylor Hughes Science, 314,1757 2006 Molenamp et al, Science, 318, 766 2007 XL Qi, T. Hughes, SCZ preprint The quantum
More informationDisordered topological insulators with time-reversal symmetry: Z 2 invariants
Keio Topo. Science (2016/11/18) Disordered topological insulators with time-reversal symmetry: Z 2 invariants Hosho Katsura Department of Physics, UTokyo Collaborators: Yutaka Akagi (UTokyo) Tohru Koma
More informationIntroductory lecture on topological insulators. Reza Asgari
Introductory lecture on topological insulators Reza Asgari Workshop on graphene and topological insulators, IPM. 19-20 Oct. 2011 Outlines -Introduction New phases of materials, Insulators -Theory quantum
More informationTopological Insulators
Topological Insulators Aira Furusai (Condensed Matter Theory Lab.) = topological insulators (3d and 2d) Outline Introduction: band theory Example of topological insulators: integer quantum Hall effect
More informationConference on Research Frontiers in Ultra-Cold Atoms. 4-8 May Generation of a synthetic vector potential in ultracold neutral Rubidium
3-8 Conference on Research Frontiers in Ultra-Cold Atoms 4-8 May 9 Generation of a synthetic vector potential in ultracold neutral Rubidium SPIELMAN Ian National Institute of Standards and Technology Laser
More informationTopological Kondo Insulators!
Topological Kondo Insulators! Maxim Dzero, University of Maryland Collaborators: Kai Sun, University of Maryland Victor Galitski, University of Maryland Piers Coleman, Rutgers University Main idea Kondo
More informationTopological Photonics with Heavy-Photon Bands
Topological Photonics with Heavy-Photon Bands Vassilios Yannopapas Dept. of Physics, National Technical University of Athens (NTUA) Quantum simulations and many-body physics with light, 4-11/6/2016, Hania,
More informationVortex States in a Non-Abelian Magnetic Field
Vortex States in a Non-Abelian Magnetic Field Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University SESAPS November 10, 2016 Acknowledgments Collin Broholm IQM
More informationArtificial Gauge Fields for Neutral Atoms
Artificial Gauge Fields for Neutral Atoms Simon Ristok University of Stuttgart 07/16/2013, Hauptseminar Physik der kalten Gase 1 / 29 Outline 1 2 3 4 5 2 / 29 Outline 1 2 3 4 5 3 / 29 What are artificial
More informationDrag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas
/ 6 Drag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas Giovanni Italo Martone with G. V. Shlyapnikov Worhshop on Exploring Nuclear Physics with Ultracold Atoms
More informationTopological Insulators and Superconductors
Topological Insulators and Superconductors Lecture #1: Topology and Band Theory Lecture #: Topological Insulators in and 3 dimensions Lecture #3: Topological Superconductors, Majorana Fermions an Topological
More informationMeasuring many-body topological invariants using polarons
1 Anyon workshop, Kaiserslautern, 12/15/2014 Measuring many-body topological invariants using polarons Fabian Grusdt Physics Department and Research Center OPTIMAS, University of Kaiserslautern, Germany
More informationExploring Topological Phases With Quantum Walks
Exploring Topological Phases With Quantum Walks Tk Takuya Kitagawa, Erez Berg, Mark Rudner Eugene Demler Harvard University References: PRA 82:33429 and PRB 82:235114 (2010) Collaboration with A. White
More informationTopological Insulators in 3D and Bosonization
Topological Insulators in 3D and Bosonization Andrea Cappelli, INFN Florence (w. E. Randellini, J. Sisti) Outline Topological states of matter: bulk and edge Fermions and bosons on the (1+1)-dimensional
More informationYtterbium quantum gases in Florence
Ytterbium quantum gases in Florence Leonardo Fallani University of Florence & LENS Credits Marco Mancini Giacomo Cappellini Guido Pagano Florian Schäfer Jacopo Catani Leonardo Fallani Massimo Inguscio
More informationDesign and realization of exotic quantum phases in atomic gases
Design and realization of exotic quantum phases in atomic gases H.P. Büchler and P. Zoller Theoretische Physik, Universität Innsbruck, Austria Institut für Quantenoptik und Quanteninformation der Österreichischen
More informationPhases of strongly-interacting bosons on a two-leg ladder
Phases of strongly-interacting bosons on a two-leg ladder Marie Piraud Arnold Sommerfeld Center for Theoretical Physics, LMU, Munich April 20, 2015 M. Piraud Phases of strongly-interacting bosons on a
More informationBraid Group, Gauge Invariance and Topological Order
Braid Group, Gauge Invariance and Topological Order Yong-Shi Wu Department of Physics University of Utah Topological Quantum Computing IPAM, UCLA; March 2, 2007 Outline Motivation: Topological Matter (Phases)
More informationComposite Dirac liquids
Composite Dirac liquids Composite Fermi liquid non-interacting 3D TI surface Interactions Composite Dirac liquid ~ Jason Alicea, Caltech David Mross, Andrew Essin, & JA, Physical Review X 5, 011011 (2015)
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son GGI conference Gauge/gravity duality 2015 Ref.: 1502.03446 Plan Plan Fractional quantum Hall effect Plan Fractional quantum Hall effect Composite fermion
More informationEffective Field Theories of Topological Insulators
Effective Field Theories of Topological Insulators Eduardo Fradkin University of Illinois at Urbana-Champaign Workshop on Field Theoretic Computer Simulations for Particle Physics and Condensed Matter
More informationInteger quantum Hall effect for bosons: A physical realization
Integer quantum Hall effect for bosons: A physical realization T. Senthil (MIT) and Michael Levin (UMCP). (arxiv:1206.1604) Thanks: Xie Chen, Zhengchen Liu, Zhengcheng Gu, Xiao-gang Wen, and Ashvin Vishwanath.
More informationFloquet theory of photo-induced topological phase transitions: Application to graphene
Floquet theory of photo-induced topological phase transitions: Application to graphene Takashi Oka (University of Tokyo) T. Kitagawa (Harvard) L. Fu (Harvard) E. Demler (Harvard) A. Brataas (Norweigian
More informationUniversal phase transitions in Topological lattice models
Universal phase transitions in Topological lattice models F. J. Burnell Collaborators: J. Slingerland S. H. Simon September 2, 2010 Overview Matter: classified by orders Symmetry Breaking (Ferromagnet)
More informationTime Reversal Invariant Ζ 2 Topological Insulator
Time Reversal Invariant Ζ Topological Insulator D Bloch Hamiltonians subject to the T constraint 1 ( ) ΘH Θ = H( ) with Θ = 1 are classified by a Ζ topological invariant (ν =,1) Understand via Bul-Boundary
More informationGeometric responses of Quantum Hall systems
Geometric responses of Quantum Hall systems Alexander Abanov December 14, 2015 Cologne Geometric Aspects of the Quantum Hall Effect Fractional Quantum Hall state exotic fluid Two-dimensional electron gas
More informationKonstantin Y. Bliokh, Daria Smirnova, Franco Nori. Center for Emergent Matter Science, RIKEN, Japan. Science 348, 1448 (2015)
Konstantin Y. Bliokh, Daria Smirnova, Franco Nori Center for Emergent Matter Science, RIKEN, Japan Science 348, 1448 (2015) QSHE and topological insulators The quantum spin Hall effect means the presence
More informationTopological insulator with time-reversal symmetry
Phys620.nb 101 7 Topological insulator with time-reversal symmetry Q: Can we get a topological insulator that preserves the time-reversal symmetry? A: Yes, with the help of the spin degree of freedom.
More informationSymmetric Surfaces of Topological Superconductor
Symmetric Surfaces of Topological Superconductor Sharmistha Sahoo Zhao Zhang Jeffrey Teo Outline Introduction Brief description of time reversal symmetric topological superconductor. Coupled wire model
More informationAdiabatic Control of Atomic Dressed States for Transport and Sensing
Adiabatic Control of Atomic Dressed States for Transport and Sensing N. R. Cooper T.C.M. Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 HE, United Kingdom A.
More informationField Theory Description of Topological States of Matter
Field Theory Description of Topological States of Matter Andrea Cappelli, INFN Florence (w. E. Randellini, J. Sisti) Outline Topological states of matter Quantum Hall effect: bulk and edge Effective field
More informationEnergy Spectrum and Broken spin-surface locking in Topological Insulator quantum dots
Energy Spectrum and Broken spin-surface locking in Topological Insulator quantum dots A. Kundu 1 1 Heinrich-Heine Universität Düsseldorf, Germany The Capri Spring School on Transport in Nanostructures
More informationTopological Properties of Quantum States of Condensed Matter: some recent surprises.
Topological Properties of Quantum States of Condensed Matter: some recent surprises. F. D. M. Haldane Princeton University and Instituut Lorentz 1. Berry phases, zero-field Hall effect, and one-way light
More informationteam Hans Peter Büchler Nicolai Lang Mikhail Lukin Norman Yao Sebastian Huber
title 1 team 2 Hans Peter Büchler Nicolai Lang Mikhail Lukin Norman Yao Sebastian Huber motivation: topological states of matter 3 fermions non-interacting, filled band (single particle physics) topological
More informationFirst-Principles Calculation of Topological Invariants (Wannier Functions Approach) Alexey A. Soluyanov
First-Principles Calculation of Topological Invariants (Wannier Functions Approach) Alexey A. Soluyanov ES'12, WFU, June 8, 212 The present work was done in collaboration with David Vanderbilt Outline:
More informationSpontaneous Loop Currents and Emergent Gauge Fields in Optical Lattices
IASTU Condensed Matter Seminar July, 2015 Spontaneous Loop Currents and Emergent Gauge Fields in Optical Lattices Xiaopeng Li ( 李晓鹏 ) CMTC/JQI University of Maryland [Figure from JQI website] Gauge fields
More informationTopological Physics in Band Insulators II
Topological Physics in Band Insulators II Gene Mele University of Pennsylvania Topological Insulators in Two and Three Dimensions The canonical list of electric forms of matter is actually incomplete Conductor
More informationCreating novel quantum phases by artificial magnetic fields
Creating novel quantum phases by artificial magnetic fields Gunnar Möller Cavendish Laboratory, University of Cambridge Theory of Condensed Matter Group Cavendish Laboratory Outline A brief introduction
More informationFloquet Topological Insulator:
Floquet Topological Insulator: Understanding Floquet topological insulator in semiconductor quantum wells by Lindner et al. Condensed Matter Journal Club Caltech February 12 2014 Motivation Motivation
More informationTOPOLOGICAL SUPERFLUIDS IN OPTICAL LATTICES
TOPOLOGICAL SUPERFLUIDS IN OPTICAL LATTICES Pietro Massignan Quantum Optics Theory Institute of Photonic Sciences Barcelona QuaGATUA (Lewenstein) 1 in collaboration with Maciej Lewenstein Anna Kubasiak
More informationBasics of topological insulator
011/11/18 @ NTU Basics of topological insulator Ming-Che Chang Dept of Physics, NTNU A brief history of insulators Band insulator (Wilson, Bloch) Mott insulator Anderson insulator Quantum Hall insulator
More informationManipulation of Artificial Gauge Fields for Ultra-cold Atoms
Manipulation of Artificial Gauge Fields for Ultra-cold Atoms Shi-Liang Zhu ( 朱诗亮 ) slzhu@scnu.edu.cn Laboratory of Quantum Information Technology and School of Physics South China Normal University, Guangzhou,
More informationExperimental Reconstruction of the Berry Curvature in a Floquet Bloch Band
Experimental Reconstruction of the Berry Curvature in a Floquet Bloch Band Christof Weitenberg with: Nick Fläschner, Benno Rem, Matthias Tarnowski, Dominik Vogel, Dirk-Sören Lühmann, Klaus Sengstock Rice
More informationExperimental reconstruction of the Berry curvature in a topological Bloch band
Experimental reconstruction of the Berry curvature in a topological Bloch band Christof Weitenberg Workshop Geometry and Quantum Dynamics Natal 29.10.2015 arxiv:1509.05763 (2015) Topological Insulators
More informationArtificial electromagnetism and spin-orbit coupling for ultracold atoms
Artificial electromagnetism and spin-orbit coupling for ultracold atoms Gediminas Juzeliūnas Institute of Theoretical Physics and Astronomy,Vilnius University, Vilnius, Lithuania *******************************************************************
More informationTopological insulators. Pavel Buividovich (Regensburg)
Topological insulators Pavel Buividovich (Regensburg) Hall effect Classical treatment Dissipative motion for point-like particles (Drude theory) Steady motion Classical Hall effect Cyclotron frequency
More informationSymmetry, Topology and Phases of Matter
Symmetry, Topology and Phases of Matter E E k=λ a k=λ b k=λ a k=λ b Topological Phases of Matter Many examples of topological band phenomena States adiabatically connected to independent electrons: - Quantum
More informationTopological insulators
http://www.physik.uni-regensburg.de/forschung/fabian Topological insulators Jaroslav Fabian Institute for Theoretical Physics University of Regensburg Stara Lesna, 21.8.212 DFG SFB 689 what are topological
More informationOrganizing Principles for Understanding Matter
Organizing Principles for Understanding Matter Symmetry Conceptual simplification Conservation laws Distinguish phases of matter by pattern of broken symmetries Topology Properties insensitive to smooth
More informationTopological Defects inside a Topological Band Insulator
Topological Defects inside a Topological Band Insulator Ashvin Vishwanath UC Berkeley Refs: Ran, Zhang A.V., Nature Physics 5, 289 (2009). Hosur, Ryu, AV arxiv: 0908.2691 Part 1: Outline A toy model of
More informationarxiv: v1 [cond-mat.str-el] 6 May 2010
MIT-CTP/4147 Correlated Topological Insulators and the Fractional Magnetoelectric Effect B. Swingle, M. Barkeshli, J. McGreevy, and T. Senthil Department of Physics, Massachusetts Institute of Technology,
More informationKouki Nakata. University of Basel. KN, S. K. Kim (UCLA), J. Klinovaja, D. Loss (2017) arxiv:
Magnon Transport Both in Ferromagnetic and Antiferromagnetic Insulating Magnets Kouki Nakata University of Basel KN, S. K. Kim (UCLA), J. Klinovaja, D. Loss (2017) arxiv:1707.07427 See also review article
More informationThe Half-Filled Landau Level
Nigel Cooper Department of Physics, University of Cambridge Celebration for Bert Halperin s 75th January 31, 2017 Chong Wang, Bert Halperin & Ady Stern. [C. Wang, NRC, B. I. Halperin & A. Stern, arxiv:1701.00007].
More informationCharacterization of Topological States on a Lattice with Chern Number
Characterization of Topological States on a Lattice with Chern Number The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation
More informationWiring Topological Phases
1 Wiring Topological Phases Quantum Condensed Matter Journal Club Adhip Agarwala Department of Physics Indian Institute of Science adhip@physics.iisc.ernet.in February 4, 2016 So you are interested in
More informationSpin-injection Spectroscopy of a Spin-orbit coupled Fermi Gas
Spin-injection Spectroscopy of a Spin-orbit coupled Fermi Gas Tarik Yefsah Lawrence Cheuk, Ariel Sommer, Zoran Hadzibabic, Waseem Bakr and Martin Zwierlein July 20, 2012 ENS Why spin-orbit coupling? A
More informationTopological Electromagnetic and Thermal Responses of Time-Reversal Invariant Superconductors and Chiral-Symmetric band insulators
Topological Electromagnetic and Thermal Responses of Time-Reversal Invariant Superconductors and Chiral-Symmetric band insulators Satoshi Fujimoto Dept. Phys., Kyoto University Collaborator: Ken Shiozaki
More informationWhat is a topological insulator? Ming-Che Chang Dept of Physics, NTNU
What is a topological insulator? Ming-Che Chang Dept of Physics, NTNU A mini course on topology extrinsic curvature K vs intrinsic (Gaussian) curvature G K 0 G 0 G>0 G=0 K 0 G=0 G
More informationDensity Waves and Supersolidity in Rapidly Rotating Atomic Fermi Gases
Density Waves and Supersolidity in Rapidly Rotating Atomic Fermi Gases Nigel Cooper T.C.M. Group, Cavendish Laboratory, University of Cambridge Quantum Gases Conference, Paris, 30 June 2007. Gunnar Möller
More informationBuilding Frac-onal Topological Insulators. Collaborators: Michael Levin Maciej Kosh- Janusz Ady Stern
Building Frac-onal Topological Insulators Collaborators: Michael Levin Maciej Kosh- Janusz Ady Stern The program Background: Topological insulators Frac-onaliza-on Exactly solvable Hamiltonians for frac-onal
More informationVortices and other topological defects in ultracold atomic gases
Vortices and other topological defects in ultracold atomic gases Michikazu Kobayashi (Kyoto Univ.) 1. Introduction of topological defects in ultracold atoms 2. Kosterlitz-Thouless transition in spinor
More informationShuichi Murakami Department of Physics, Tokyo Institute of Technology
EQPCM, ISSP, U. Tokyo June, 2013 Berry curvature and topological phases for magnons Shuichi Murakami Department of Physics, Tokyo Institute of Technology Collaborators: R. Shindou (Tokyo Tech. Peking Univ.)
More informationKai Sun. University of Michigan, Ann Arbor. Collaborators: Krishna Kumar and Eduardo Fradkin (UIUC)
Kai Sun University of Michigan, Ann Arbor Collaborators: Krishna Kumar and Eduardo Fradkin (UIUC) Outline How to construct a discretized Chern-Simons gauge theory A necessary and sufficient condition for
More informationTopology and many-body physics in synthetic lattices
Topology and many-body physics in synthetic lattices Alessio Celi Synthetic dimensions workshop, Zurich 20-23/11/17 Synthetic Hofstadter strips as minimal quantum Hall experimental systems Alessio Celi
More informationNotes on Topological Insulators and Quantum Spin Hall Effect. Jouko Nieminen Tampere University of Technology.
Notes on Topological Insulators and Quantum Spin Hall Effect Jouko Nieminen Tampere University of Technology. Not so much discussed concept in this session: topology. In math, topology discards small details
More informationFully symmetric and non-fractionalized Mott insulators at fractional site-filling
Fully symmetric and non-fractionalized Mott insulators at fractional site-filling Itamar Kimchi University of California, Berkeley EQPCM @ ISSP June 19, 2013 PRL 2013 (kagome), 1207.0498...[PNAS] (honeycomb)
More informationRef: Bikash Padhi, and SG, Phys. Rev. Lett, 111, (2013) HRI, Allahabad,Cold Atom Workshop, February, 2014
Cavity Optomechanics with synthetic Landau Levels of ultra cold atoms: Sankalpa Ghosh, Physics Department, IIT Delhi Ref: Bikash Padhi, and SG, Phys. Rev. Lett, 111, 043603 (2013)! HRI, Allahabad,Cold
More information5 Topological insulator with time-reversal symmetry
Phys62.nb 63 5 Topological insulator with time-reversal symmetry It is impossible to have quantum Hall effect without breaking the time-reversal symmetry. xy xy. If we want xy to be invariant under, xy
More information2D Electron Systems: Magneto-Transport Quantum Hall Effects
Hauptseminar: Advanced Physics of Nanosystems 2D Electron Systems: Magneto-Transport Quantum Hall Effects Steffen Sedlak The Hall Effect P.Y. Yu,, M.Cardona, Fundamentals of Semiconductors, Springer Verlag,
More informationTopological Insulators
Topological Insulators A new state of matter with three dimensional topological electronic order L. Andrew Wray Lawrence Berkeley National Lab Princeton University Surface States (Topological Order in
More informationDirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators. Nagoya University Masatoshi Sato
Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators Nagoya University Masatoshi Sato In collaboration with Yukio Tanaka (Nagoya University) Keiji Yada (Nagoya University) Ai Yamakage
More informationSummer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases. 27 August - 7 September, 2007
1859-5 Summer School on Novel Quantum Phases and Non-Equilibrium Phenomena in Cold Atomic Gases 27 August - 7 September, 2007 Dipolar BECs with spin degrees of freedom Yuki Kawaguchi Tokyo Institute of
More informationSynthetic topology and manybody physics in synthetic lattices
Synthetic topology and manybody physics in synthetic lattices Alessio Celi EU STREP EQuaM May 16th, 2017 Atomtronics - Benasque Plan Integer Quantum Hall systems and Edge states Cold atom realizations:
More informationEmergent topological phenomena in antiferromagnets with noncoplanar spins
Emergent topological phenomena in antiferromagnets with noncoplanar spins - Surface quantum Hall effect - Dimensional crossover Bohm-Jung Yang (RIKEN, Center for Emergent Matter Science (CEMS), Japan)
More informationTopological insulator part II: Berry Phase and Topological index
Phys60.nb 11 3 Topological insulator part II: Berry Phase and Topological index 3.1. Last chapter Topological insulator: an insulator in the bulk and a metal near the boundary (surface or edge) Quantum
More informationQuantum simulation with SU(N) fermions: orbital magnetism and synthetic dimensions. Leonardo Fallani
Quantum simulation with SU(N) fermions: orbital magnetism and synthetic dimensions Frontiers in Quantum Simulation with Cold Atoms, Seattle, April 1 st 2015 Leonardo Fallani Department of Physics and Astronomy
More informationBeyond the Quantum Hall Effect
Beyond the Quantum Hall Effect Jim Eisenstein California Institute of Technology School on Low Dimensional Nanoscopic Systems Harish-chandra Research Institute January February 2008 Outline of the Lectures
More informationExperimental realization of spin-orbit coupling in degenerate Fermi gas. Jing Zhang
QC12, Pohang, Korea Experimental realization of spin-orbit coupling in degenerate Fermi gas Jing Zhang State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics,
More informationExperimental realization of spin-orbit coupled degenerate Fermi gas. Jing Zhang
Hangzhou Workshop on Quantum Matter, 2013 Experimental realization of spin-orbit coupled degenerate Fermi gas Jing Zhang State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of
More informationClassification of Symmetry Protected Topological Phases in Interacting Systems
Classification of Symmetry Protected Topological Phases in Interacting Systems Zhengcheng Gu (PI) Collaborators: Prof. Xiao-Gang ang Wen (PI/ PI/MIT) Prof. M. Levin (U. of Chicago) Dr. Xie Chen(UC Berkeley)
More informationElectronic transport in topological insulators
Electronic transport in topological insulators Reinhold Egger Institut für Theoretische Physik, Düsseldorf Alex Zazunov, Alfredo Levy Yeyati Trieste, November 011 To the memory of my dear friend Please
More informationDefects in topologically ordered states. Xiao-Liang Qi Stanford University Mag Lab, Tallahassee, 01/09/2014
Defects in topologically ordered states Xiao-Liang Qi Stanford University Mag Lab, Tallahassee, 01/09/2014 References Maissam Barkeshli & XLQ, PRX, 2, 031013 (2012) Maissam Barkeshli, Chaoming Jian, XLQ,
More informationOn the K-theory classification of topological states of matter
On the K-theory classification of topological states of matter (1,2) (1) Department of Mathematics Mathematical Sciences Institute (2) Department of Theoretical Physics Research School of Physics and Engineering
More informationTopology of electronic bands and Topological Order
Topology of electronic bands and Topological Order R. Shankar The Institute of Mathematical Sciences, Chennai TIFR, 26 th April, 2011 Outline IQHE and the Chern Invariant Topological insulators and the
More informationINT International Conference, Frontiers in Quantum Simulation with Cold Atoms, March 30 April 2, 2015
Ana Maria Rey INT International Conference, Frontiers in Quantum Simulation with Cold Atoms, March 30 April 2, 2015 The JILA Sr team: Jun Ye A. Koller Theory: S. Li X. Zhang M. Bishof S. Bromley M. Martin
More informationSingle particle Green s functions and interacting topological insulators
1 Single particle Green s functions and interacting topological insulators Victor Gurarie Nordita, Jan 2011 Topological insulators are free fermion systems characterized by topological invariants. 2 In
More informationQuantum noise studies of ultracold atoms
Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Mikhail Lukin, Anatoli Polkovnikov Funded by NSF,
More information