Exploring manybody physics with synthetic matter Theory David
Exploring many-body physics with synthetic matter Theory: David Pekker (Cal. Tech) 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
How cold are ultracold atoms? Density of atoms 1013 cm-1 Distance between atoms 300 nm BEC temperature fe. V p. K pe. V n. K ne. V µK current experiments with optical lattices 10 -11 - 10 -10 K µe. V m. K me. V ke. V Me. V 1 m. K Ge. V Te. V K He N room temperature LHC
Single atom resolution in optical lattices density Bakr et al. , Science 2010 y x
Many-body physics with ultracold atoms Decoupling from external environment - Long coherence times Long intrinsic time scales - Interaction energy and bandwidth ~ 1 k. Hz - 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
Outline Observation of the amplitude Higgs mode in the superfluid state of bosons in optical lattices M. Endres, D. Pekker et al. , ar. Xiv: 1204. 518, 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. , ar. Xiv: 1201. 6400
Intoroduction: Ultracold atoms in optical lattice. Bose Hubbard model
Bose Hubbard model U t tunneling of atoms between neighboring wells repulsion of atoms sitting in the same well Confining potential
Bose Hubbard Model. Phase diagram n=3 Weak lattice t<<U superfluid phase Mott 2 Superfluid n=2 Mott 1 n=1 Strong lattice t>>U Mott state Mott 0 Single atom resolved imaging of a Mott insulator Sherson et al. , Nature 2010
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. , ar. Xiv: 1204. 518, Nature in press D. Pekker et al. , ar. Xiv: 1206. 1648 Philosophy similar to Grigory Volovik’s “Universe in a helium droplet”: Find condensed matter analogues of high energy particles and phenomena
Collective modes of strongly interacting superfluid bosons Order parameter Breaks U(1) symmetry Phase (Goldstone) mode = gapless Bogoliubov mode Gapped amplitude mode (Higgs mode)
Excitations of the Bose Hubbard model n=3 Mott Superfluid 2 n=2 2 Mott 1 n=1 Mott Superfluid 0 Softening of the amplitude mode is the defining characteristic of the second order Quantum Phase Transition
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
Is there a Higgs resonance 2 d? D. Podolsky et al. , ar. Xiv: 1108. 5207 Earlier work: S. Sachdev (1999), W. Zwerger (2004)
Exciting the amplitude mode Absorbed energy
Exciting the amplitude mode M. Endres et al. , ar. Xiv: 1204. 518, Nature in press n=1 Mott
Experiments: full spectrum Manuel Endres, Immanuel Bloch and MPQ team
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
Time dependent cluster mean-field Lattice height 9. 5 Er: (1 x 1 vs 2 x 2) single amplitude mode excited breathing mode single amplitude breathing mode excited 2 x 2 captures width of spectral feature multiple modes excited?
Absorption spectra. Theory (1 x 1 calculations) disappearing amplitude mode Breathing mode details at the QCP spectrum remains gapped due to trap
Higgs Drum Modes 1 x 1 calculation, 20 oscillations Eabs rescaled so peak heights coincide Similar to Higgs mode in compactified dimensions
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. , ar. Xiv: 1201. 6400
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
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
Bose Hubbard model in the hard core limit t t Spin representation of the hard core limit of the Hubbard Hamiltonian
Quantum magnetism of bosons in optical lattices Theory: Duan et al. , PRL (2003) Kuklov, Svistunov, PRL (2003) Expt: S. Trotzky et al. , Science (2008)
Semiclassical soliton dynamics: stable regime Character of solitons: Kd. V type (Gutzwiller wavfunctions) density superfluid velocity t=0 t=10 t=50
Semiclassical soliton dynamics: unstable regime t=0 t=80 Formation of lump solutions t=40 t=90
Universal phase diagram of dynamics in 2 d and 3 d anisotropic Heisenberg model Particle solitons. Unstable to 2 d modulation 2 d lamp solutons Hole solitons. Stable to 2 d modulation Both particle and hole solitons allowed Particle solitons. Stable to 2 d modulation Decay of inhomogeneities to short wavelength oscillations Hole solitons. Unstable to 2 d modulation 2 d lamp solutions
Semiclassical dynamics of anisotropic Heisenberg Hamiltonian. Density step decay.
Effect of parabolic potential Solitons break apart when crossing boundaries of distinct “universality” regions
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
How cold are ultracold atoms? 1013 cm-1 Density fe. V p. K pe. V n. K ne. V µK µe. V m. K first BEC of alkali atoms me. V Distance between atoms 300 nm BEC temperature 1 m. K ke. V Me. V Ge. V Te. V K He N room temperature LHC
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