Leticia Tarruell ICFO

UPC – 11/11/2013

Engineering synthetic quantum materials with ultracold fermions in a tunable-geometry optical lattice

- Interfering laser beams (optical lattice)

Simulating materials with atoms and light

- Crystalline structure (periodic potential) - Electrons (quantum degenerate fermions)

- Ultracold fermionics atoms (40K)

Fermions in optical lattices as condensed matter model systems

Also fermions in 3D optical lattices: Munich, Boston, Hamburg, Kyoto, Houston...

x

y

z

Energy scales: eV vs. nK

Simulating materials with atoms and light

Free tunability: filling, t, U, T, band structure

U t Fermi-Hubbard model

Relation to solid state systems

Local contact interactions

Spin degree of freedom: atomic hyperfine states

0.5 µm

Condensed matter model systems

Strongly correlated materials (Mott insulators,

high-Tc superconductors)

Novel materials (graphene,

topological insulators)

Ultracold atoms in optical lattices

Our approach: tunable-geometry optical lattice

Spin systems (quantum phase transitions,

frustration, spin-liquids)

An optical lattice of tunable geometry Engineering Dirac points in a honeycomb lattice Short-range quantum magnetism

Outline

An optical lattice of tunable geometry Engineering Dirac points in a honeycomb lattice Short-range quantum magnetism

Outline

The tunable-geometry optical lattice

X and Y X and Y

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

Setup Optical potential

λ = 1064nm

X and Y

X and Y

+

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

The tunable-geometry optical lattice

V [E ] X R

Chequerboard

Triangular

Dimer 1D chains

Square

V =0 X

Honeycomb

Dimer

An optical lattice of tunable geometry Engineering Dirac points in a honeycomb lattice Short-range quantum magnetism

Outline

Deforming the band structure Honeycomb

q x

E q y

x

y

Square

?

Probing the Dirac points Challenges: vanishing density of states

small energy scales

Probe energy splitting of the bands dynamically

T. Salger et al., Phys. Rev. Lett. 99, 190405 (2007)

Bloch oscillations + interband transitions

+ Pot. Gradient ≙ Force

Passing through Dirac point: transfer to 2nd band

Passing away from Dirac point: stay in lowest band

Observable: quasi-momentum distribution

Transfer to 2nd band at the position of the Dirac points

Interband transitions

After a Bloch cycle: t=TB

qx

qy

Spin-polarized 40K gas

Force

E

qx

Quantitative measurements Higher band fraction

Ν( ) Ν( ) ξ =

+ Ν( )

Cone shape

Engineering Dirac points Tunability

Position

A B

Tools Inversion symmetry Tunneling imbalance

vs.

Gap Merging

Breaking inversion symmetry

sub-lattice offset sub-lattice offset

A B

Merging Dirac points

qx

qy

Topological Transition Lifshitz transition, Sov. Phys. JETP 11, 1130 (1960)

Dirac points No Dirac points

qy

E

Laser power

The topological transition V =1.8 E Y R

Engineering Dirac points

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Nature 483, 302 (2012) T. Uehlinger, D. Greif, G. Jotzu, L. Tarruell, T. Esslinger, L. Wang and M. Troyer, EPJ ST 217, 121 (2013)

Outlook

Artificial gauge fields to engineer topologically protected states

Combination of honeycomb lattice and interactions (Mott insulator) T. Uehlinger, G. Jotzu, M. Messer, D. Greif, U. Bissbort, W. Hoffstetter and T. Esslinger, Phys. Rev. Lett. 111, 185307 (2013).

An optical lattice of tunable geometry Engineering Dirac points in a honeycomb lattice Short-range quantum magnetism

Outline

Magnetism: a temperature challenge U > 0 t

Fermi-Hubbard model

U>>t

J=4t2/U

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)

Magnetism: a temperature challenge U > 0 t

Fermi-Hubbard model

S. Trotzky et al., Science 319, 295-299 (2008) S. Nascimbène et al., Phys. Rev. Lett. 108, 205301 (2012) J. Simon et al., Nature 472, 307-312 (2011) J. Struck et al., Science 333, 996-999 (2011)

State of the art Isolated double-wells or plaquettes (Munich)

Mappings Ising spin chain (Harvard) Classical magnets (Hamburg)

Dipolar interactions (JILA, Paris)

U>>t

J=4t2/U

ener

gy

T

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

t ➡ J td ➡ Jd > J

J < kBT < Jd

T J

Dimerized lattice

ener

gy

Reaching magnetism: an energy trick

ts ➡ Js > J

Anisotropic lattice

Jd,s

singlet

triplet Jd,s

Probing: neighboring sites

kBT < Jd,s : NS > NT

Reaching magnetic correlations:

Jd

Detecting magnetic correlations

singlet

or

triplet t0

singlet triplet t0

Dimerized lattice

Singlet-Triplet Imbalance

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

Measuring singlets and triplets

𝑝𝑆

𝑝𝑡𝑡

Sin

glet

s Tr

iple

ts

Merging neighboring sites Singlet-triplet oscillations

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

Dimerization dependence

s=1.7 kB

isotropic strongly dimerized

Anisotropic cubic lattice

transverse spin correlator ⟺ population difference

AFM correlations along x

Dependence on geometry

isotropic strongly anisotropic

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

Dependence on entropy

tS /t=7.3

Comparison with theory

Theory (DCA+LDA): J. Imriška, M. Iazzi, L. Wang, E. Gull, and M. Troyer

Quantum magnetism

Outlook

Explore short range correlations in other geometries (2D, triangular...)

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




Nearest-neighbor magnetic correlations in thermalized ensembles

Quantitative comparison with more advanced theory J. Imriška, M. Iazzi, L. Wang, E. Gull, D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, T. Esslinger, and M. Troyer, arXiv:1309.7362

The ETH lattice team (2011-2012)

Gregor Jotzu Daniel Greif L. T. Thomas Uehlinger Tilman Esslinger

Towards optical lattices at ICFO

Pierrick Cheiney Manel Bosch César Cabrera

Thank you for your attention!

Engineering synthetic quantum materials with ultracold �fermions in a tunable-geometry optical latticeSlide Number 2Slide Number 3Slide Number 4Slide Number 5OutlineOutlineThe tunable-geometry optical latticeThe tunable-geometry optical latticeOutlineSlide Number 11Probing the Dirac pointsInterband transitionsEngineering Dirac pointsBreaking inversion symmetryMerging Dirac pointsThe topological transitionEngineering Dirac pointsOutlineMagnetism: a temperature challengeMagnetism: a temperature challengeReaching magnetism: an energy trickDetecting magnetic correlationsDimerized latticeMeasuring singlets and tripletsDimerization dependenceAnisotropic cubic latticeDependence on geometryDependence on entropyComparison with theoryQuantum magnetismThe ETH lattice team (2011-2012)Towards optical lattices at ICFOSlide Number 34