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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
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