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Exploring many-body physics with synthetic matter

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Presentation on theme: "Exploring many-body physics with synthetic matter"— Presentation transcript:

1 Exploring many-body physics with synthetic matter
Theory: David Pekker (CalTech) Andrey Maltsev (Landau Institute), Aleksander Prokofiev (Landau Institute), Eugene Demler (Harvard University) Experiment: Immanuel Bloch’s group at MPQ/LMU Supported by NSF, DARPA, AFOSR MURI, ARO MURI

2 How cold are ultracold atoms?
Density of atoms cm-1 Distance between atoms 300 nm BEC temperature mK feV peV neV µeV meV eV keV MeV GeV TeV pK nK µK mK K He N room temperature LHC current experiments with optical lattices K

3 Single atom resolution in optical lattices
Bakr et al., Science 2010 density y x

4 Many-body physics with ultracold atoms
Decoupling from external environment - Long coherence times Long intrinsic time scales - Interaction energy and bandwidth ~ 1kHz - System parameters can be changed over this time scale Can achieve highly non equilibrium quantum many-body states New detection methods - Single atom resolution New frontier in many-body physics: quantum many-body dynamics

5 Outline Observation of the amplitude Higgs mode
in the superfluid state of bosons in optical lattices M. Endres, D. Pekker et al., arXiv: , Nature in press Universal nonlinear semiclassical hydrodynamics of lattice spin models and strongly correlated bosons in optical lattices A. Maltsev, E.D., Annals of Physics 326:1775 (2011) A. Maltsev, A. Prokofiev, E.D., arXiv:

6 Intoroduction: Ultracold atoms in optical lattice. Bose Hubbard model

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

8 Single atom resolved imaging of a Mott insulator
Bose Hubbard Model. Phase diagram Weak lattice t<<U superfluid phase n=3 Mott 2 Superfluid n=2 Mott Strong lattice t>>U Mott state 1 n=1 Mott Single atom resolved imaging of a Mott insulator Sherson et al., Nature 2010

9 Observation of the amplitude Higgs mode
in the superfluid state of bosons in optical lattices Experiment: Manuel Endres, Immanuel Bloch and MPQ team Theory: David Pekker (Caltech), Eugene Demler M. Endres, D. Pekker et al., arXiv: , Nature in press D. Pekker et al., arXiv: Philosophy similar to Grigory Volovik’s “Universe in a helium droplet”: Find condensed matter analogues of high energy particles and phenomena

10 Collective modes of strongly interacting superfluid bosons
Order parameter Breaks U(1) symmetry Phase (Goldstone) mode = gapless Bogoliubov mode Gapped amplitude mode (Higgs mode)

11 Excitations of the Bose Hubbard model
2 Mott Superfluid n=3 Mott 2 Superfluid n=2 Mott 1 n=1 Mott Softening of the amplitude mode is the defining characteristic of the second order Quantum Phase Transition

12 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

13 Is there a Higgs resonance 2d?
D. Podolsky et al., arXiv: Earlier work: S. Sachdev (1999), W. Zwerger (2004)

14 Exciting the amplitude mode
Absorbed energy

15 Exciting the amplitude mode
M. Endres et al., arXiv: , Nature in press Mott n=1 Mott n=1 Mott n=1

16 Experiments: full spectrum
Manuel Endres, Immanuel Bloch and MPQ team

17 Gutzwiller model for the amplitude mode
Bogoliubov mode comes from the phase and charge degrees of freedom: and Amplitude/Higgs mode comes from and Time dependent mean-field: project dynamics to factorizable Gutzwiller wavefunctions. It is equivalent to Landau-Lifshitz eqs. It gives collective modes but not coupling between them. Threshold for absorption is captured very well

18 Time dependent cluster mean-field
Lattice height 9.5 Er: (1x1 vs 2x2) single amplitude mode excited single amplitude mode excited multiple modes excited? breathing mode breathing mode 2x2 captures width of spectral feature

19 Absorption spectra. Theory (1x1 calculations)
disappearing amplitude mode Breathing mode details at the QCP spectrum remains gapped due to trap

20 Higgs Drum Modes 1x1 calculation, 20 oscillations
Eabs rescaled so peak heights coincide Similar to Higgs mode in compactified dimensions

21 Universal nonlinear hydrodynamics of
Beyond linear analysis of collective modes Universal nonlinear hydrodynamics of lattice spin models and strongly correlated bosons in optical lattices A. Maltsev, E.D., Annals of Physics 326:1775 (2011) A. Maltsev, A. Prokofiev, E.D., arXiv:

22 Bogoliubov mode in weakly interacting gas
Probing Bogoliubov mode with light scattering: D. Stamper-Kurn et al., PRL 83:2876 (1999) Detailed study of dispersion Ozeri et al., RMP 77:187 (2005) Dark soliton in BEC, C. Becker et al., Nature (2008) Our goal: study solitons in strongly correlated states of bosons in optical lattices

23 Equilibration of density inhomogeneity
Vbefore(x) Suddenly change the potential. Observe density redistribution Vafter(x) Strongly correlated atoms in an optical lattice: appearance of oscillation zone on one of the edges Semiclassical dynamics of bosons in optical lattice: Kortweg- de Vries equation Instabilities to transverse modulation

24 Bose Hubbard model in the hard core limit
Spin representation of the hard core limit of the Hubbard Hamiltonian

25 Quantum magnetism of bosons in optical lattices
Theory: Duan et al., PRL (2003) Kuklov, Svistunov, PRL (2003) Expt: S. Trotzky et al., Science (2008)

26 Semiclassical soliton dynamics: stable regime
Character of solitons: KdV type (Gutzwiller wavfunctions) density superfluid velocity t=0 t=10 t=50

27 Semiclassical soliton dynamics: unstable regime
Formation of lump solutions

28 Universal phase diagram of dynamics
in 2d and 3d anisotropic Heisenberg model Particle solitons. Unstable to 2d modulation 2d lamp solutons Hole solitons. Stable to 2d modulation Both particle and hole solitons allowed Particle solitons. Stable to 2d modulation Decay of inhomogeneities to short wavelength oscillations Hole solitons. Unstable to 2d modulation 2d lamp solutions

29 Semiclassical dynamics of anisotropic Heisenberg Hamiltonian
Semiclassical dynamics of anisotropic Heisenberg Hamiltonian. Density step decay.

30 Effect of parabolic potential
Solitons break apart when crossing boundaries of distinct “universality” regions

31 Summary Observation of the amplitude Higgs mode
in the superfluid state of bosons in optical lattices Universal nonlinear semiclassical hydrodynamics of lattice spin models and strongly correlated bosons in optical lattices

32 How cold are ultracold atoms?
Density cm-1 Distance between atoms nm BEC temperature mK feV peV neV µeV meV eV keV MeV GeV TeV pK nK µK mK K He N room temperature LHC first BEC of alkali atoms

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