Short-range quantum magnetism of ultracold …aias.au.dk/fileadmin/ quantum magnetism of ultracold fermions in an optical lattice t U > 0 40 K The repulsive Fermi-Hubbard model Antiferromagnetic

Leticia Tarruell

Aahrus – 26/06/2014

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

U > 0 t

40K

The repulsive Fermi-Hubbard model

Antiferromagnetic spin interaction from super-exchange

J=4t2/U

A temperature challenge

U>>t

J

ener

gy

T > U: metallic behaviour

T < U: Mott insulator

T

T < J: spin ordering

T

R. Jördens et al., Phys. Rev. Lett. 104, 180401 (2010)

Approaches to magnetism

S. Trotzky et al., Science 319, 295 (2008) S. Nascimbène et al., Phys. Rev. Lett. 108, 205301 (2012)

Isolated double-wells or plaquettes (Munich)

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

Mapping: Ising spin chains (Harvard)

J. Struck et al., Science 333, 996 (2011)

Classical magnetism (Hamburg)

Dipolar interactions (JILA, Paris)

B. Yan et al., Nature 501, 521-525 (2013) A. de Paz et al., Phys. Rev. Lett. 111 , 185305 (2013)

J < T < Jd,s

T J

Jd

Jd > J

Dimerized lattice

ener

gy

Our approach: an energy trick

Quantum magnetism T < J

Js > J

Anisotropic cubic lattice

Jd,s

Detecting magnetic correlations

singlet

triplet

Jd

Spin correlations on neighboring sites

T < Jd : NS > NT

Our tool: tunable-geometry optical lattice

)cos()cos(2)(cos)(cos)2/(cos),( 222 kykxVVkyVkxVkxVyxV YXYXX αθ ++++=

λ = 1064nm

X and Y

X and Y

+

Other non-standard lattices: NIST, Munich, Bonn, Hamburg, Berkeley

Our tool: tunable-geometry optical lattice

Chequerboard

Triangular

Dimer 1D chains

Square Honeycomb

L. Tarruell et al., Nature 483, 302 (2012)

Merging lattice sites

Chequerboard

Dimer

Square

Detecting magnetic correlations

singlet

or

triplet t0

singlet triplet t0

Dimerized lattice

Singlet-Triplet Imbalance

Measuring singlets and triplets

𝑝𝑆

𝑝𝑡𝑡 Sin

glet

s Tr

iple

ts

Merging neighboring sites Singlet-triplet oscillations

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

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

Dependence on dimerization

s=1.7 kB

Jd

T J

isotropic strongly dimerized

Dependence on entropy

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

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

Jd T

J

Anisotropic cubic lattice

transverse spin correlator ⟺ population difference

Redistribution of entropy: incoherent spin chains, entropy stored in between

AFM correlations along x

Effective 1D chains

Dependence on anisotropy

isotropic strongly anisotropic

VY,Z = 11.0(3) ER s = 1.8 kB

normalized spin correlator

Dependence on entropy

tS /t=7.3

Comparison with theory

Theory: DCA+LDA for anisotropic simple cubic lattice J. Imriška, M. Iazzi, L. Wang, E. Gull and M. Troyer – ETH Zurich

Correlations over 2 sites

T<t

Short-range quantum magnetism

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

Nearest-neighbor magnetic correlations in thermalized ensembles

Comparison with numerical simulations: T< t in effective 1D systems 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 lattice team’ 2012

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

Funding: EU (ERC SQMS), SNF, NCCR QSIT, NCCR MaNEP

Towards isotopic potassium mixtures 40K-41K with tunable interactions

February 2014 Last Tuesday

The ICFO quantum gases group’ 2014

L. T.

Pierrick Cheiney

Vincent Lienhard

Manel Bosch

César Cabrera

PhD position open in Barcelona

www.qge.icfo.es