Quantum Phase Transitions, Strongly Interacting Systems, and Cold Atoms Eugene Demler Physics Department, Harvard University Collaborators: Ehud Altman,

Slides:



Advertisements
Similar presentations
Dynamics of Spin-1 Bose-Einstein Condensates
Advertisements

High T c Superconductors & QED 3 theory of the cuprates Tami Pereg-Barnea
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA,
Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.
Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,
Subir Sachdev Quantum phase transitions of ultracold atoms Transparencies online at Quantum Phase Transitions Cambridge.
Nonequilibrium dynamics of ultracold fermions Theoretical work: Mehrtash Babadi, David Pekker, Rajdeep Sensarma, Ehud Altman, Eugene Demler $$ NSF, MURI,
Subir Sachdev Science 286, 2479 (1999). Quantum phase transitions in atomic gases and condensed matter Transparencies online at
Lattice modulation experiments with fermions in optical lattice Dynamics of Hubbard model Ehud Altman Weizmann Institute David Pekker Harvard University.
Hubbard model(s) Eugene Demler Harvard University Collaboration with
Interacting Ultra Cold Atoms a brief overview Fei Zhou PITP, University of British Columbia at Quantum Nanoscience conference, Noosa Blue, Australia, Jan.
Fermi surface change across quantum phase transitions Phys. Rev. B 72, (2005) Phys. Rev. B (2006) cond-mat/ Hans-Peter Büchler.
World of ultracold atoms with strong interaction National Tsing-Hua University Daw-Wei Wang.
World of zero temperature --- introduction to systems of ultracold atoms National Tsing-Hua University Daw-Wei Wang.
Eugene Demler Harvard University Strongly correlated many-body systems: from electronic materials to ultracold atoms.
Strongly correlated many-body systems: from electronic materials to ultracold atoms to photons Eugene Demler Harvard University Thanks to: E. Altman, I.
Modeling strongly correlated electron systems using cold atoms Eugene Demler Physics Department Harvard University.
Phase Diagram of One-Dimensional Bosons in Disordered Potential Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman-Weizmann Yariv Kafri.
Multicomponent systems of ultracold atoms Eugene Demler Harvard University Dynamical instability of spiral states In collaboration with Robert Cherng,
Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Boston University Ehud Altman Weizmann Vladimir Gritsev Harvard.
Spinor condensates beyond mean-field
Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA, MURI Collaborators: Ehud Altman,
Strongly Correlated Systems of Ultracold Atoms Theory work at CUA.
Eugene Demler Harvard University
Eugene Demler Harvard University Collaborators:
Fractional Quantum Hall states in optical lattices Anders Sorensen Ehud Altman Mikhail Lukin Eugene Demler Physics Department, Harvard University.
Quantum Simulation MURI Review Theoretical work by groups lead by Luming Duan (Michigan) Mikhail Lukin (Harvard) Subir Sachdev (Harvard) Peter Zoller (Innsbruck)
Measuring correlation functions in interacting systems of cold atoms
Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.
Eugene Demler Harvard University Robert Cherng, Adilet Imambekov,
Probing interacting systems of cold atoms using interference experiments Harvard-MIT CUA Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov.
Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir.
Probing many-body systems of ultracold atoms E. Altman (Weizmann), A. Aspect (CNRS, Paris), M. Greiner (Harvard), V. Gritsev (Freiburg), S. Hofferberth.
Strongly correlated systems: from electronic materials to cold atoms Collaborators: E. Altman, R. Barnett, I. Cirac, L. Duan, V. Gritsev, W. Hofstetter,
Non-equilibrium dynamics of cold atoms in optical lattices Vladimir Gritsev Harvard Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann.
Nonequilibrium dynamics of ultracold atoms in optical lattices. Lattice modulation experiments and more Ehud Altman Weizmann Institute Peter Barmettler.
Quick and Dirty Introduction to Mott Insulators
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Takuya Kitagawa, Susanne Pielawa,
Magnetism of spinor BEC in an optical lattice
Probing phases and phase transitions in cold atoms using interference experiments. Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman- The.
Interference of fluctuating condensates Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir Gritsev Harvard Mikhail Lukin.
T. Kitagawa (Harvard), S. Pielawa (Harvard), D. Pekker (Harvard), R. Sensarma (Harvard/JQI), V. Gritsev (Fribourg), M. Lukin (Harvard), Lode Pollet (Harvard)
Dynamics of repulsively bound pairs in fermionic Hubbard model David Pekker, Harvard University Rajdeep Sensarma, Harvard University Ehud Altman, Weizmann.
New physics with polar molecules Eugene Demler Harvard University Outline: Measurements of molecular wavefunctions using noise correlations Quantum critical.
Stringing together the quantum phases of matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.
Subir Sachdev Yale University Phases and phase transitions of quantum materials Talk online: or Search for Sachdev on.
Ana Maria Rey March Meeting Tutorial May 1, 2014.
Eugene Demler Harvard University
Polar molecules in optical lattices Ryan Barnett Harvard University Mikhail Lukin Harvard University Dmitry Petrov Harvard University Charles Wang Tsing-Hua.
Anatoli Polkovnikov Krishnendu Sengupta Subir Sachdev Steve Girvin Dynamics of Mott insulators in strong potential gradients Transparencies online at
Correlated States in Optical Lattices Fei Zhou (PITP,UBC) Feb. 1, 2004 At Asian Center, UBC.
Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir.
Atoms in optical lattices and the Quantum Hall effect Anders S. Sørensen Niels Bohr Institute, Copenhagen.
Optical lattice emulator Strongly correlated systems: from electronic materials to ultracold atoms.
Condensed matter physics in dilute atomic gases S. K. Yip Academia Sinica.
D. Jin JILA, NIST and the University of Colorado $ NIST, NSF Using a Fermi gas to create Bose-Einstein condensates.
Hidden topological order in one-dimensional Bose Insulators Ehud Altman Department of Condensed Matter Physics The Weizmann Institute of Science With:
The Center for Ultracold Atoms at MIT and Harvard Strongly Correlated Many-Body Systems Theoretical work in the CUA Advisory Committee Visit, May 13-14,
Exploring many-body physics with synthetic matter
Functional Integration in many-body systems: application to ultracold gases Klaus Ziegler, Institut für Physik, Universität Augsburg in collaboration with.
1 Vortex configuration of bosons in an optical lattice Boulder Summer School, July, 2004 Congjun Wu Kavli Institute for Theoretical Physics, UCSB Ref:
Phase separation and pair condensation in spin-imbalanced 2D Fermi gases Waseem Bakr, Princeton University International Conference on Quantum Physics.
Analysis of quantum noise
Ehud Altman Anatoli Polkovnikov Bertrand Halperin Mikhail Lukin
Part II New challenges in quantum many-body theory:
Measuring correlation functions in interacting systems of cold atoms
Spectroscopy of ultracold bosons by periodic lattice modulations
Strongly Correlated Systems of Cold Atoms Detection of many-body quantum phases by measuring correlation functions Anatoli Polkovnikov.
Introduction. Systems of ultracold atoms.
Eugene Demler Physics Department, Harvard University Collaborators:
Presentation transcript:

Quantum Phase Transitions, Strongly Interacting Systems, and Cold Atoms Eugene Demler Physics Department, Harvard University Collaborators: Ehud Altman, Ignacio Cirac, Bert Halperin, Walter Hofstetter, Adilet Imambekov, Ludwig Mathey, Mikhail Lukin, Anatoli Polkovnikov, Anders Sorensen, Charles Wang, Fei Zhou, Peter Zoller

Classical phase transitions: Phase diagram for water

Ising model in transverse field LiHoF Bitko et al., PRL 77:940 (1996) H x Ferro Para H(kOe) 0.4

Superconductor to Insulator transition in thin films Marcovic et al., PRL 81:5217 (1998) Bi films Superconducting films of different thickness

High temperature superconductors Maple, JMMM 177:18 (1998)

Quantum phase transitions E g E g Level crossing at T=0 Avoided level crossing. Second order phase transition True level crossing. First order phase transition © Subir Sachdev

Quantum critical region H T quantum-critical Quantum critical point controls a wide quantum critical region Quantum critical region does not have well defined quasiparticles

Quantum critical point in YbRh Si AF – antiferromagnetic LFL – Landau Fermi liquid NFL – non Fermi liquid 22 Gegenwart et al., PRL 89:56402(2002)

Quantum states of matter. Why are they interesting? Understanding fundamental properties of complex quantum systems Technological applications

Applications of quantum materials: Ferroelectric RAM Non-Volatile Memory High Speed Processing FeRAM in Smart Cards V _ _ _ _

Applications of quantum materials: High Tc superconductors

Bose-Einstein condensation Cornell et al., Science 269, 198 (1995) Ultralow density condensed matter system Interactions are weak and can be described theoretically from first principles

New era in cold atoms research Optical lattices Feshbach resonances Rotating condensates One dimensional systems Systems with long range dipolar interactions Focus on systems with strong interactions

Feshbach resonance and fermionic condensates Greiner et al., Nature 426:537 (2003) Zwierlein et al., PRL 91: (2003) See alsoJochim et al., Science 302:2101 (2003)

Atoms in optical lattices Theory: Jaksch et al. PRL 81:3108(1998) Experiment: Kasevich et al., Science (2001); Greiner et al., Nature (2001); Phillips et al., J. Physics B (2002) Esslinger et al., PRL (2004);

Strongly correlated systems Atoms in optical latticesElectrons in Solids Simple metals Perturbation theory in Coulomb interaction applies. Band structure methods wotk Strongly Correlated Electron Systems Band structure methods fail. Novel phenomena in strongly correlated electron systems: Quantum magnetism, phase separation, unconventional superconductivity, high temperature superconductivity, fractionalization of electrons …

Cold atoms with strong interactions Resolve long standing questions in condensed matter physics (e.g. the origin of high Tc superconductivity) Resolve matter of principle questions (e.g. spin liquids in two and three dimensions) Find new exciting physics Goals

Outline Introduction. Cold atoms in optical lattices. Bose Hubbard model Two component Bose mixture Quantum magnetism. Competing orders. Fractionalized phases Spin one bosons Spin exchange interactions. Exotic spin order (nematic) Fermions Pairing in systems with repulsive interactions. Unconventional pairing. High Tc mechanism Boson-Fermion mixtures Polarons. Competing orders BEC on chips Interplay of disorder and interactions. Bose glass phase

Atoms in optical lattice. Bose Hubbard model

Bose Hubbard model tunneling of atoms between neighboring wells repulsion of atoms sitting in the same well U t

4 Bose Hubbard model. Mean-field phase diagram M.P.A. Fisher et al., PRB40:546 (1989) MottN=1 N=2 N=3 Superfluid Superfluid phase Mott insulator phase Weak interactions Strong interactions Mott

Set. Bose Hubbard model Hamiltonian eigenstates are Fock states 24

Bose Hubbard Model. Mean-field phase diagram Particle-hole excitation Mott insulator phase MottN=1 N=2 N=3 Superfluid Mott Tips of the Mott lobes

Gutzwiller variational wavefunction Normalization Interaction energy Kinetic energy z – number of nearest neighbors

Phase diagram of the 1D Bose Hubbard model. Quantum Monte-Carlo study Batrouni and Scaletter, PRB 46:9051 (1992)

Optical lattice and parabolic potential N=1 N=2 N=3 SF MI Jaksch et al., PRL 81:3108 (1998)

Superfluid phase Order parameter Phase (Bogoliubov) mode = gapless Goldstone mode. Breaks U(1) symmetry Gapped amplitude mode.

Mott Insulating phase Ground state Particle excitation (gapped) Hole excitation (gapped)

2 Excitations of the Bose Hubbard model MottSuperfluid

Superfluid to Insulator transition Greiner et al., Nature 415:39 (2002) t/U Superfluid Mott insulator

Excitations of bosons in an optical lattice Schori et al., PRL 93: (2004)

Time of flight experiments Quantum noise interferometry of atoms in an optical lattice Second order coherence

Second order coherence in the insulating state of bosons. Hanburry-Brown-Twiss experiment Theory: Altman et al., PRA 70:13603 (2004) Experiment: Folling et al., Nature 434:481 (2005)

Hanburry-Brown-Twiss stellar interferometer

Hanburry-Brown-Twiss interferometer

Second order coherence in the insulating state of bosons Bosons at quasimomentum expand as plane waves with wavevectors First order coherence : Oscillations in density disappear after summing over Second order coherence : Correlation function acquires oscillations at reciprocal lattice vectors

Second order coherence in the insulating state of bosons. Hanburry-Brown-Twiss experiment Theory: Altman et al., PRA 70:13603 (2004) Experiment: Folling et al., Nature 434:481 (2005)

Interference of an array of independent condensates Hadzibabic et al., PRL 93: (2004) Smooth structure is a result of finite experimental resolution (filtering)

Extended Hubbard Model - on site repulsion - nearest neighbor repulsion Checkerboard phase: Crystal phase of bosons. Breaks translational symmetry

Extended Hubbard model. Mean field phase diagram van Otterlo et al., PRB 52:16176 (1995) Hard core bosons. Supersolid – superfluid phase with broken translational symmetry

Extended Hubbard model. Quantum Monte Carlo study Sengupta et al., PRL 94: (2005)Hebert et al., PRB 65:14513 (2002)

Dipolar bosons in optical lattices Goral et al., PRL88: (2002)

How to detect a checkerboard phase Correlation Function Measurements

Two component Bose mixture in optical lattice Quantum magnetism. Competing orders. Fractionalized phases

t t Two component Bose mixture in optical lattice Example:. Mandel et al., Nature 425:937 (2003) Two component Bose Hubbard model

Two component Bose mixture in optical lattice. Magnetic order in an insulating phase Insulating phases with N=1 atom per site. Average densities Easy plane ferromagnet Easy axis antiferromagnet

Quantum magnetism of bosons in optical lattices Duan et al., PRL (2003) Ferromagnetic Antiferromagnetic Kuklov and Svistunov, PRL (2003)

Exchange Interactions in Solids antibonding bonding Kinetic energy dominates: antiferromagnetic state Coulomb energy dominates: ferromagnetic state

Two component Bose mixture in optical lattice. Mean field theory + Quantum fluctuations 2 nd order line Hysteresis 1 st order Altman et al., NJP 5:113 (2003)

Probing spin order of bosons Correlation Function Measurements

Engineering exotic phases Optical lattice in 2 or 3 dimensions: polarizations & frequencies of standing waves can be different for different directions ZZ YY Example: exactly solvable model Kitaev (2002), honeycomb lattice with Can be created with 3 sets of standing wave light beams ! Non-trivial topological order, “spin liquid” + non-abelian anyons …those has not been seen in controlled experiments

Spin F=1 bosons in optical lattices Spin exchange interactions. Exotic spin order (nematic )

Spinor condensates in optical traps Spin symmetric interaction of F=1 atoms Antiferromagnetic Interactions for Ferromagnetic Interactions for

Antiferromagnetic F=1 condensates Mean field Three species of atoms Ho, PRL 81:742 (1998)Ohmi, Machida, JPSJ 67:1822 (1998) Beyond mean field. Spin singlet ground state Law et al., PRL 81:5257 (1998); Ho, Yip, PRL 84:4031 (2000) Experiments: Review in Ketterle’s Les Houches notes

Antiferromagnetic spin F=1 atoms in optical lattices Hubbard Hamiltonian Symmetry constraints Demler, Zhou, PRL (2003) Nematic Mott Insulator Spin Singlet Mott Insulator

Nematic insulating phase for N=1 Effective S=1 spin model Imambekov et al., PRA 68:63602 (2003) When the ground state is nematic in d=2,3. One dimensional systems are dimerized: Rizzi et al., cond-mat/

Nematic insulating phase for N=1. Two site problem Singlet state is favored when One can not have singlets on neighboring bonds. Nematic state is a compromise. It corresponds to a superposition of and on each bond

Coherent spin dynamics in optical lattices Widera et al., cond-mat/ atoms in the F=2 state

Fermionic atoms in optical lattices Pairing in systems with repulsive interactions. Unconventional pairing. High Tc mechanism

Fermionic atoms in a three dimensional optical lattice Kohl et al., PRL 94:80403 (2005)

Fermions with attractive interaction U t t Hofstetter et al., PRL 89: (2002) Highest transition temperature for Compare to the exponential suppresion of Tc w/o a lattice

Reaching BCS superfluidity in a lattice 6 Li 40 K Li in CO 2 lattice K in NdYAG lattice Turning on the lattice reduces the effective atomic temperature Superfluidity can be achived even with a modest scattering length

Fermions with repulsive interactions t U t Possible d-wave pairing of fermions

Picture courtesy of UBC Superconductivity group High temperature superconductors Superconducting Tc 93 K Hubbard model – minimal model for cuprate superconductors P.W. Anderson, cond-mat/ After many years of work we still do not understand the fermionic Hubbard model

Positive U Hubbard model Possible phase diagram. Scalapino, Phys. Rep. 250:329 (1995) Antiferromagnetic insulator D-wave superconductor

Second order interference from the BCS superfluid n(r) n(r’) n(k) k BCS BEC k F

Momentum correlations in paired fermions Greiner et al., PRL 94: (2005)

Fermion pairing in an optical lattice Second Order Interference In the TOF images Normal State Superfluid State measures the Cooper pair wavefunction One can identify unconventional pairing

Boson Fermion mixtures Fermions interacting with phonons. Polarons. Competing orders

Boson Fermion mixtures BEC Experiments: ENS, Florence, JILA, MIT, Rice, … Bosons provide cooling for fermions and mediate interactions. They create non-local attraction between fermions Charge Density Wave Phase Periodic arrangement of atoms Non-local Fermion Pairing P-wave, D-wave, …

Boson Fermion mixtures “Phonons” : Bogoliubov (phase) mode Effective fermion-”phonon” interaction Fermion-”phonon” vertex Similar to electron-phonon systems

Boson Fermion mixtures in 1d optical lattices Cazalila et al., PRL (2003); Mathey et al., PRL (2004) Spinless fermions Spin ½ fermions Note: Luttinger parameters can be determined using correlation function measurements in the time of flight experiments. Altman et al. (2005)

BF mixtures in 2d optical lattices 40K -- 87Rb 40K -- 23Na =1060 nm (a) =1060nm (b) =765.5nm Poster by Charles Wang, cond-mat/

1D Boson Fermion mixture. NO optical lattice Model is exactly solvable, if Density distribution in the trap “Counterflow” collective modes boson fraction frequency Poster by Adilet Imambekov, cond-mat/

BEC in microtraps Interplay of disorder and interactions. Bose glass phase

Fragmented BEC in magnetic microtraps Theory: Wang et.al., PRL 92: (2004) Thywissen et al., EPJD (1999); Kraft et al., JPB (2002); Leanhardt et al., PRL (2002); Fortagh et al., PRA (2002); …

BEC on atom chips Esteve et al., PRA 70:43629 (2004) Outlook: interplay of interactions and disorder: probing Bose glass phase SEM image of wire

Conclusions: Systems of cold atoms and molecules can be used for engineering and manipulation of strongly correlated quantum states Simulating fundamental models in CM physics (e.g. Hubbard model) Understanding quantum magnetism and unconventional fermion pairing Answering matter of principle questions. For example, can we have two dimensional systems with topological order without T-reversal breaking? Understanding the interplay of disorder and interactions Studying far from equilibrium dynamics of strongly correlated quantum states This opens possibilities for