Short-range quantum magnetism of ultracold fermions in an optical - - PowerPoint PPT Presentation

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Short-range quantum magnetism of ultracold fermions in an optical - - PowerPoint PPT Presentation

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Short-range quantum magnetism of ultracold fermions in an optical lattice Leticia Tarruell Experiments in Tilman Esslingers group, ETH Zurich Warsaw 26/06/2015 z y 50.000 40 K fermionic atoms T<0.1T F x The Fermi-Hubbard model t U

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Leticia Tarruell

Short-range quantum magnetism of ultracold fermions in an optical lattice

Experiments in Tilman Esslinger’s group, ETH Zurich

Warsaw – 26/06/2015

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x y z

50.000 40K fermionic atoms T<0.1TF

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The Fermi-Hubbard model

tunneling interaction

t U

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Quantum simulation

Strongly correlated material Fermi-Hubbard model

« with a suitable class of quantum machines you could imitate any quantum system »

  • R. P. Feynman, 1981

Quantum simulator

t U

?

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2005: First experimental realization with cold atoms (non interacting fermions)

Metal – band insulator transition

The Fermi-Hubbard model

Metal Band insulator

filling

  • M. Köhl, H. Moritz, T. Stöferle, K. Günter and T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005)
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2008: Strongly correlated regime

The Fermi-Hubbard model

Metal – Mott insulator transition kinetic energy interaction energy

Delocalization vs. interactions

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The Fermi-Hubbard model

2008: Strongly correlated regime

Metal – Mott insulator transition

U/6t=4.8 U/6t=0

Non interacting Mott insulator

  • R. Jördens et al., Nature 455, 204 (2008)
  • U. Schneider et al.,

Science 322, 1520 (2008)

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Metal Mott insulator

The Fermi-Hubbard model

Next challenge:

Quantum magnetism

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Temperature scales

U>>t

energy T > U: metallic behavior T < U: Mott insulator

T

T < J: spin ordering

T

  • R. Jördens et al., Phys. Rev. Lett. 104, 180401 (2010)
  • P. Duarte et al., Phys. Rev. Lett. 114, 070403 (2015)

J=4t2/U

Superexchange J

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Approaches to magnetism

  • S. Trotzky et al., Science 319, 295 (2008)
  • S. Nascimbène et al., Phys. Rev. Lett. 108, 205301 (2012)
  • S. Murmann et al., Phys. Rev. Lett. 114, 080402 (2015)

Isolated double-wells or plaquettes (Munich, Heidelberg)

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Approaches to magnetism

  • J. Simon et al., Nature 472, 307 (2011)

Ising spin chains (Harvard)

  • J. Struck et al., Science 333, 996 (2011)
  • J. Struck et al., Nature Phys. 9, 738 (2013)

Classical magnetism, Ising XY (Hamburg)

Mappings

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Approaches to magnetism

Dipolar interactions (JILA, Paris)

  • B. Yan et al., Nature 501, 521-525 (2013)
  • A. de Paz et al., Phys. Rev. Lett. 111, 185305 (2013)
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  • D. Greif et al., Science 340, 1307 (2013)
  • R. A. Hart et al., Nature 519, 211 (2015)

Approaches to magnetism

Short-range quantum magnetism in the Fermi-Hubbard model (ETH, Rice)

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J < T < Jd,s

T J Jd

Jd > J

Dimerized lattice

energy

The energy trick

Magnetic correlations T < J

Js > J

Anisotropic cubic lattice

Jd,s

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Magnetic correlations in dimerized lattice

singlet triplet

Jd

Spin correlations on neighboring sites T < Jd : NS > NT

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Local spin correlations in cubic lattice

Nearest-neighbor spin correlations vs. temperature

antiferromagnetic transition DCA simulation 3D Fermi-Hubbard model

  • S. Fuchs, E. Gull, L. Pollet, E. Burovski, E. Kozik, T. Pruschke, and M. Troyer,
  • Phys. Rev. Lett. 106, 030401 (2011)
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Merging lattice sites

Chequerboard Dimer Square

Tool: tunable geometry optical lattice

  • L. Tarruell et al., Nature 483, 302 (2012)
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Detecting magnetic correlations

singlet

  • r

triplet t0 singlet triplet t0

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Dimerized lattice

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Singlet-Triplet Imbalance

Measuring singlets and triplets

𝑞𝑇 𝑞𝑢𝑢

Singlets Triplets

Merging neighboring sites Singlet-triplet oscillations

Singlet-triplet oscillations: S. Trotzky et al., Phys. Rev. Lett. 105, 265303 (2010)

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Theory: second order high-temperature series expansion of coupled dimers

Dependence on dimerization

s=1.7 kB

Jd T J

isotropic strongly dimerized

  • D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340, 1307 (2013)




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Dependence on entropy

Theory: second order high-temperature series expansion

  • f coupled dimers

U/t = 11.0(8) td/t = 22(2) t/h = 67(3) Hz

Jd T J

  • D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340, 1307 (2013)




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Anisotropic simple cubic lattice

transverse spin correlator ⟺ population difference Redistribution of entropy: incoherent spin chains, entropy stored in between AFM correlations along x Effective 1D chains

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Dependence on anisotropy

isotropic strongly anisotropic VY,Z = 11.0(3) ER s = 1.8 kB normalized spin correlator

  • D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340, 1307 (2013)




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  • J. Imriška, M. Iazzi, L. Wang, E. Gull, D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell,
  • T. Esslinger, and M. Troyer, Phys. Rev. Lett. 112, 115301 (2014)

Theory: DCA+LDA for anisotropic simple cubic lattice

Comparison with theory

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Dependence on entropy

tS /t=7.3

  • D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340, 1307 (2013)




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Comparison with theory

Theory: DCA+LDA for anisotropic simple cubic lattice

  • J. Imriška, M. Iazzi, L. Wang, E. Gull, D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell,
  • T. Esslinger, and M. Troyer, Phys. Rev. Lett. 112, 115301 (2014)

Correlations over 2 sites

T<t

Analogous results with DMRG: B. Sciolla et al., Phys. Rev. A 88, 063629 (2013)

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Short range magnetic correlations

  • D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340, 1307 (2013)




Nearest-neighbor magnetic correlations in thermalized ensembles

  • J. Imriška, M. Iazzi, L. Wang, E. Gull, D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell,
  • T. Esslinger, and M. Troyer, Phys. Rev. Lett. 112, 115301 (2014)
  • B. Sciolla, A. Tokuno, S. Uchino, P. Bartmettler, T. Giamarchi, and C. Kollath,
  • Phys. Rev. A 88, 063629 (2013)

Comparison with numerics: effective 1D systems with T<J

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The ETH quantum magnetism team

Gregor Jotzu Daniel Greif

  • L. T. Thomas Uehlinger Tilman Esslinger

Theory: J. Imriška, M. Iazzi, L. Wang, E. Gull and M. Troyer Many discussions with C. Kollath and T. Giamarchi’s groups

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October 2013

Ultracold Quantum Gases group @

February 2014 September 2014 ICFO-The Institute of Photonic Sciences Barcelona, Spain June 2015

41K BEC 40K MOT

June 2015

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Ultracold Quantum Gases group @

  • L. T.

Pierrick Cheiney César Cabrera

www.qge.icfo.es

Luca Tanzi Jordi Sastre Julio Sanz Manel Bosch (now at Laboratoire Kastler Brossel, Paris) Vincent Lienhard (now student at ENS Cachan) Lisa Saemisch (now at ICFO’s Molecular Nanophotonics group)

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Measuring double occupancy

  • 2. Feshbach-induced energy shift
  • 4. Expansion and Stern-Gerlach separation
  • 1. Suppress tunneling
  • 3. RF transfer

Doubly occupied sites

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Measuring double occupancy

mF=-9/2 mF=-5/2 mF=-7/2

Doubly occupied sites

Measure D for values as low as 1% !

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Exchange energy

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With a bit more cooling…

High-T phase diagram of cuprates

QCP Dimers AFM T/J J/Jd

Geometry-induced quantum phase transitions Frustration