Aside: the BKT phase transiton Spontaneous symmetry breaking Mermin-Wagner: – no continuous symmetry breaking in models with short ranged interactions.

Slides:



Advertisements
Similar presentations
Higgs physics theory aspects experimental approaches Monika Jurcovicova Department of Nuclear Physics, Comenius University Bratislava H f ~ m f.
Advertisements

Exploring Topological Phases With Quantum Walks $$ NSF, AFOSR MURI, DARPA, ARO Harvard-MIT Takuya Kitagawa, Erez Berg, Mark Rudner Eugene Demler Harvard.
Dynamics of bosonic cold atoms in optical lattices. K. Sengupta Indian Association for the Cultivation of Science, Kolkata Collaborators: Anirban Dutta,
1 Eniko Madarassy Reconnections and Turbulence in atomic BEC with C. F. Barenghi Durham University, 2006.
Cold Atoms in rotating optical lattice Sankalpa Ghosh, IIT Delhi Ref: Rashi Sachdev, Sonika Johri, SG arXiv: Acknowledgement: G.V Pi, K. Sheshadri,
High T c Superconductors & QED 3 theory of the cuprates Tami Pereg-Barnea
Quantum critical states and phase transitions in the presence of non equilibrium noise Emanuele G. Dalla Torre – Weizmann Institute of Science, Israel.
Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,
Nonequilibrium dynamics of ultracold fermions Theoretical work: Mehrtash Babadi, David Pekker, Rajdeep Sensarma, Ehud Altman, Eugene Demler $$ NSF, MURI,
SUPERSOLIDS? minnesota, july 2007 acknowledgments to: Moses Chan &Tony Clark David Huse & Bill Brinkman Phuan Ong& Yayu Wang Hari Kojima& many other exptlists.
Lattice modulation experiments with fermions in optical lattice Dynamics of Hubbard model Ehud Altman Weizmann Institute David Pekker Harvard University.
Breakdown of the adiabatic approximation in low-dimensional gapless systems Anatoli Polkovnikov, Boston University Vladimir Gritsev Harvard University.
Anderson localization in BECs
Phase Diagram of One-Dimensional Bosons in Disordered Potential Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman-Weizmann Yariv Kafri.
Strongly Correlated Systems of Ultracold Atoms Theory work at CUA.
Fractional Quantum Hall states in optical lattices Anders Sorensen Ehud Altman Mikhail Lukin Eugene Demler Physics Department, Harvard University.
Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.
QCD – from the vacuum to high temperature an analytical approach an analytical approach.
Probing interacting systems of cold atoms using interference experiments Harvard-MIT CUA Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov.
Probing many-body systems of ultracold atoms E. Altman (Weizmann), A. Aspect (CNRS, Paris), M. Greiner (Harvard), V. Gritsev (Freiburg), S. Hofferberth.
Non-equilibrium dynamics of cold atoms in optical lattices Vladimir Gritsev Harvard Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann.
Nonequilibrium dynamics of bosons in optical lattices $$ NSF, AFOSR MURI, DARPA, RFBR Harvard-MIT Eugene Demler Harvard University.
Interference of fluctuating condensates Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir Gritsev Harvard Mikhail Lukin.
Superfluid insulator transition in a moving condensate Anatoli Polkovnikov (BU and Harvard) (Harvard) Ehud Altman, (Weizmann and Harvard) Eugene Demler,
Slow dynamics in gapless low-dimensional systems Anatoli Polkovnikov, Boston University AFOSR Vladimir Gritsev – Harvard Ehud Altman -Weizmann Eugene Demler.
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.
Subir Sachdev Yale University Phases and phase transitions of quantum materials Talk online: or Search for Sachdev on.
SO(5) Theory of High Tc Superconductivity Shou-cheng Zhang Stanford University.
System and definitions In harmonic trap (ideal): er.
Michiel Snoek September 21, 2011 FINESS 2011 Heidelberg Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator Quenches from.
Ultracold Fermi gases University of Trento BEC Meeting, Trento, 2-3 May 2006 INFM-CNR Sandro Stringari.
Quantum Monte Carlo methods applied to ultracold gases Stefano Giorgini Istituto Nazionale per la Fisica della Materia Research and Development Center.
Finite Temperature Field Theory Joe Schindler 2015.
Superfluid dynamics of BEC in a periodic potential Augusto Smerzi INFM-BEC & Department of Physics, Trento LANL, Theoretical Division, Los Alamos.
Correlated States in Optical Lattices Fei Zhou (PITP,UBC) Feb. 1, 2004 At Asian Center, UBC.
Phase Separation and Dynamics of a Two Component Bose-Einstein Condensate.
Strong correlations and quantum vortices for ultracold atoms in rotating lattices Murray Holland JILA (NIST and Dept. of Physics, Univ. of Colorado-Boulder)
Phase transitions in Hubbard Model. Anti-ferromagnetic and superconducting order in the Hubbard model A functional renormalization group study T.Baier,
Nonlinear Optics in Plasmas. What is relativistic self-guiding? Ponderomotive self-channeling resulting from expulsion of electrons on axis Relativistic.
Eiji Nakano, Dept. of Physics, National Taiwan University Outline: 1)Experimental and theoretical background 2)Epsilon expansion method at finite scattering.
Non-Fermi Liquid Behavior in Weak Itinerant Ferromagnet MnSi Nirmal Ghimire April 20, 2010 In Class Presentation Solid State Physics II Instructor: Elbio.
Raman Scattering As a Probe of Unconventional Electron Dynamics in the Cuprates Raman Scattering As a Probe of Unconventional Electron Dynamics in the.
QUANTUM MANY-BODY SYSTEMS OF ULTRACOLD ATOMS Eugene Demler Harvard University Grad students: A. Imambekov (->Rice), Takuya Kitagawa Postdocs: E. Altman.
Higgs boson in a 2D superfluid To be, or not to be in d=2 What’s the drama? N. Prokof’ev ICTP, Trieste, July 18, 2012.
Hidden topological order in one-dimensional Bose Insulators Ehud Altman Department of Condensed Matter Physics The Weizmann Institute of Science With:
Wednesday, Mar. 26, 2003PHYS 5326, Spring 2003 Jae Yu 1 PHYS 5326 – Lecture #18 Monday, Mar. 26, 2003 Dr. Jae Yu Mass Terms in Lagrangians Spontaneous.
Tao Peng and Robert J. Le Roy
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
Higgs Bosons in Condensed Matter Muir Morrison Ph 199 5/23/14.
A New Potential Energy Surface for N 2 O-He, and PIMC Simulations Probing Infrared Spectra and Superfluidity How precise need the PES and simulations be?
1 Vortex configuration of bosons in an optical lattice Boulder Summer School, July, 2004 Congjun Wu Kavli Institute for Theoretical Physics, UCSB Ref:
NTNU 2011 Dimer-superfluid phase in the attractive Extended Bose-Hubbard model with three-body constraint Kwai-Kong Ng Department of Physics Tunghai University,
Arnau Riera, Grup QIC, Dept. ECM, UB 16 de maig de 2009 Intoduction to topological order and topologial quantum computation.
Tunable excitons in gated graphene systems
Spontaneous Symmetry Breaking and the
Spin-Orbit Coupling Effects in Bilayer and Optical Lattice Systems
ultracold atomic gases
Superfluid-Insulator Transition of
Ehud Altman Anatoli Polkovnikov Bertrand Halperin Mikhail Lukin
Atomic BEC in microtraps: Squeezing & visibility in interferometry
Spectroscopy of ultracold bosons by periodic lattice modulations
Nonlinear response of gated graphene in a strong radiation field
Arrangement of Electrons in Atoms
SOC Fermi Gas in 1D Optical Lattice —Exotic pairing states and Topological properties 中科院物理研究所 胡海平 Collaborators : Chen Cheng, Yucheng Wang, Hong-Gang.
a = 0 Density profile Relative phase Momentum distribution
周黎红 中国科学院物理研究所 凝聚态理论与材料计算实验室 指导老师: 崔晓玲 arXiv:1507,01341(2015)
Tony Leggett Department of Physics
Presentation transcript:

Aside: the BKT phase transiton Spontaneous symmetry breaking Mermin-Wagner: – no continuous symmetry breaking in models with short ranged interactions in dimension less than two Homotopy group Vortex free energy: – origin of Berezinskii-Kosterlitz-Thouless transition

Spontaneous symmetry breaking Effective action (d+1 dimensions) potential energy part kinetic energy part distance to transition 0

Mermin-Wagner theorem Phase fluctuations in different dimensions Energetics of long wavelength fluctuations phase fluctuations vs. amplitude fluctuation driven transitions 2D – no long range order, but can have algebraically decaying correlations no LRDO yes LRDO ??

Ingredients of the BKT transition Important for transition: – phase fluctuations – topological defects (destruction of correlations) What is a topological defect? – a loop in the physical space that maps to a non-trivial element of the fundamental group – XY vs. Heisenberg physical space XY model order parameter space

Sketch of transition: free energy of vortex pairs Interaction between a vortex and anti-vortex free energy: bound free transition free vortices bound vortex anti-vortex pairs

The Anderson-Higgs mode in a trapped 2D superfluid on a lattice (close to zero temperature) David Pekker, Manuel Endres, Takeshi Fukuhara, Marc Cheneau, Peter Schauss, Christian Gross, Eugene Demler, Immanuel Bloch, Stefan Kuhr (Caltech, Munich, Harvard)

Bose Hubbard Model ji Mott Insulator Superfluid part of ground state (2 nd order perturbation theory)

What is the Anderson-Higgs mode Motion in a Mexican Hat potential – Superfluid symmetry breaking – Goldstone (easy) mode – Anderson-Higgs (hard) mode Where do these come from – Mott insulator – particle & hole modes – Anti-symmetric combination => phase mode – Symmetric combination => Higgs mode What do these look like – order parameter phase – order parameter amplitude phase mode Higgs mode

A note on field-theory MI-SF transition described by Gross-Pitaevskii actionrelativistic Gross-Pitaevskii action phase (Im  ) Higgs (Re  )

Anderson-Higgs mode, the Higgs Boson, and the Higgs Mechanism Sherson et. al. Nature 2010 Cold Atoms (Munich)Elementary Particles LHC) Massless gauge fields (W and Z) acquire mass

Anderson-Higgs mode in 2D ? Danger from scattering on phase modes In 2D: infrared divergence (branch cut in susceptibility) Different susceptibility has no divergence Higgs   Podolsky, Auerbach, Arovas, arXiv: Higgs

Why it is difficult to observe the amplitude mode Stoferle et al., PRL(2004) Peak at U dominates and does not change as the system goes through the SF/Mott transition Bissbort et al., PRL(2010)

Outline Experimental data – Setup – Lattice modulation spectra Theoretical modeling – Gutzwiller – CMF Conclusions

Experimental sequence Important features: (1)close to unit filling in center (2)gentle modulation drive (3)number oscillations fixed (4)high resolution imaging density Mott Critical Superfluid (theory)

Mode Softening QCP Superfluid Zero Mass Large Mass frequency absorption frequency absorption frequency absorption

What about the Trap? a b c a b c

Mode Softening in Trap QCP Superfluid Zero Mass Large Mass frequency absorption frequency absorption frequency absorption

Higgs mass across the transition Important features: (1)softening at QCP (2)matches mass for uniform system (3)error bars – uncertainty in position of onset (4)dashed bars – width of onset

Gutzwiller Theory (in a trap) Bose Hubbard Hamiltonian Gutzwiller wave function Gutzwiller evolution lattice modulation spectroscopytrap U J What is bad? – quantitative issues – qp interactions What is good? – captures both Higgs and phase modes – effects of trap – non-linearities 2D phase diagram

How to get the eigenmodes? step 1: find the ground state. Use the variation wave function to minimize step 2: expand in small fluctuations density

How to get eigenmodes ? step 3: apply minimum action principle: step 4: linearize step 5: normalize

Higgs Drum – lattice modulation spectroscopy in trap Gutzwiller in a trap Gentle drive – sharp peaks – 20 modulations of lattice depth, measure energy – Discrete mode spectrum – Consistent with eigenmodes from linerized theory – Corresponding “drum” modes – Why no sharp peaks in exp. data? plots, four lowest Higgs modes in trap (after ~100 modulations) Higgs Modes Breathing Modes 0.1% drive

Character of the eigenmodes Phase modes & out of phase Amplitude modes & in phase Introduce “amplitudeness”

Stronger drive Stronger Drive – 0.1%, 1%, 3% lattice depth – Peaks shift to lower freq. & broaden – Spectrum becomes more continuous Features – No fit parameters – OK onset frequency – Breathing mode – Jagged spectrum – Missing weight at high frequencies Averaging over atom # – Spectrum smoothed – Weight still missing

CMF – “Better Gutzwiller” Variational wave functions better captures local physics – better describes interactions between quasi-particles Equivalent to MFT on plaquettes

8Er 9Er 9.5Er 10Er Comparison of CMF & Experiment Theory: average over particle #, uncertainty in V 0 – good: on set, width, absorption amount (no fitting parameters) – bad: fine structure (due to variational wave function?)

Summary Experiment2x2 Clusters1x1 Clusters (Gutzwiller) – “gap” disappears at QCP – wide band – band spreads out deep in SF – captures gap – does not capture width – {0,1,2,3,4} – captures “gap” – captures most of the width – {0,1,2} Existence & visibility of Higgs mode in a superfluid – softening at transition – consistent with calculations in trap Questions – How do we arrive at GP description deep in SF? where does Higgs mode go? – is it ever possible to see discrete “drum” mode (fine structure of absorption spectrum)

Related field-theory consider the GL theory of MI-SF transition Linearize: Gross-Pitaevskii actionrelativistic Gross-Pitaevskii action phase (Im  ) Higgs (Re  )