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

Short-range quantum magnetism of ultracold fermions in an optical lattice Leticia Tarruell Experiments in Tilman Esslinger’s 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 tunneling interaction

Quantum simulation ? t U Strongly correlated Fermi-Hubbard material model « with a suitable class of quantum machines you could imitate any quantum system » R. P. Feynman, 1981 Quantum simulator

The Fermi-Hubbard model 2005: First experimental realization with cold atoms (non interacting fermions) Metal – band insulator transition Metal Band insulator filling M. Köhl, H. Moritz, T. Stöferle, K. Günter and T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005)

The Fermi-Hubbard model 2008: Strongly correlated regime Metal – Mott insulator transition Delocalization vs. interactions kinetic energy interaction energy

The Fermi-Hubbard model 2008: Strongly correlated regime Metal – Mott insulator transition R. Jördens et al. , Nature 455 , 204 (2008) U. Schneider et al ., Science 322 , 1520 (2008) U/6t=0 Non interacting Mott insulator U/6t=4.8

The Fermi-Hubbard model Next challenge: Quantum magnetism Metal Mott insulator

Temperature scales T > U : metallic behavior T T < U : Mott insulator U>>t energy T J=4t 2 /U T < J : spin ordering R. Jördens et al. , Phys. Rev. Lett. 104 , 180401 (2010) P. Duarte et al. , Phys. Rev. Lett. 114 , 070403 (2015) Superexchange J

Approaches to magnetism Isolated double-wells or plaquettes (Munich, Heidelberg) 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)

Approaches to magnetism Mappings Ising spin chains (Harvard) Classical magnetism, Ising XY (Hamburg) J. Simon et al., Nature 472 , 307 (2011) J. Struck et al., Science 333 , 996 (2011) J. Struck et al., Nature Phys. 9 , 738 (2013)

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)

Approaches to magnetism Short-range quantum magnetism in the Fermi-Hubbard model (ETH, Rice) D. Greif et al. , Science 340 , 1307 (2013) R. A. Hart et al. , Nature 519 , 211 (2015)

The energy trick J d > J Magnetic correlations T < J Dimerized lattice J d J d,s energy J s > J T J J < T < J d,s Anisotropic cubic lattice

Magnetic correlations in dimerized lattice Spin correlations on neighboring sites triplet J d singlet T < J d : N S > N T

Local spin correlations in cubic lattice Nearest-neighbor spin correlations vs. temperature DCA simulation 3D Fermi-Hubbard model antiferromagnetic transition S. Fuchs, E. Gull, L. Pollet, E. Burovski, E. Kozik, T. Pruschke, and M. Troyer, Phys. Rev. Lett. 106 , 030401 (2011)

Merging lattice sites Dimer Chequerboard Square Tool: tunable geometry optical lattice L. Tarruell et al. , Nature 483 , 302 (2012)

Detecting magnetic correlations singlet triplet t 0 or singlet triplet t 0

Dimerized lattice

Measuring singlets and triplets Merging neighboring sites Singlet-triplet oscillations 𝑞 𝑇 Singlets 𝑞 𝑢𝑢 Triplets Singlet-Triplet Imbalance Singlet-triplet oscillations: S. Trotzky et al ., Phys. Rev. Lett. 105 , 265303 (2010)

Dependence on dimerization J d T J isotropic strongly dimerized Theory: second order high-temperature series expansion of coupled dimers s=1.7 k B D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340 , 1307 (2013) 


Dependence on entropy J d T J U/t = 11.0(8) Theory: second order high-temperature series expansion t d /t = 22(2) of coupled dimers t/h = 67(3) Hz D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340 , 1307 (2013) 


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

Dependence on anisotropy normalized spin correlator isotropic strongly anisotropic V Y,Z = 11.0(3) E R D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340 , 1307 (2013) s = 1.8 k B 


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)

Dependence on entropy t S /t=7.3 D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340 , 1307 (2013) 


Comparison with theory T<t Correlations over 2 sites 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) Analogous results with DMRG: B. Sciolla et al. , Phys. Rev. A 88 , 063629 (2013)

Short range magnetic correlations Nearest-neighbor magnetic correlations in thermalized ensembles D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340 , 1307 (2013) Comparison with numerics: effective 1D systems with T<J 
 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)

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

Ultracold Quantum Gases group @ 41 K BEC June 2015 ICFO-The Institute of Photonic Sciences February 2014 October 2013 Barcelona, Spain 40 K MOT September 2014 June 2015

Ultracold Quantum Gases group @ Pierrick Cheiney L. T. Jordi César Sastre Cabrera Luca Tanzi 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) www.qge.icfo.es

Measuring double occupancy 4. Expansion and Stern-Gerlach separation 2. Feshbach-induced energy shift 1. Suppress tunneling 3. RF transfer Doubly occupied sites

Measuring double occupancy Doubly occupied sites m F =-9/2 m F =-7/2 m F =-5/2 Measure D for values as low as 1% !

Exchange energy

With a bit more cooling… T/J Dimers AFM J/J d QCP Geometry-induced quantum phase transitions High-T phase diagram of cuprates Frustration