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Leonardo Leonardo FallaniFallani
Dipartimento di Fisica e Astronomia &Dipartimento di Fisica e Astronomia & LENS LENS –– Università di FirenzeUniversità di Firenze
[email protected]@lens.unifi.it
Napoli, September 20Napoli, September 20thth 20122012
CongressoCongresso SocietàSocietà ItalianaItaliana didi FisicaFisica
Quantum Quantum PhysicsPhysics withwith UltracoldUltracold AtomsAtoms in in OpticalOptical LatticesLattices
Introduction
Quantum simulation with strongly-interacting atoms
Ytterbium quantum gases
Introduction
Quantum simulation with strongly-interacting atoms
Ytterbium quantum gases
Reaching the quantum limits of motion
Lase
r +
evap
ora
ive
co
olin
g
BOSONS FERMIONS
T T 100 100 nKnK
Ultracold atoms in optical lattices
Ultracold atoms in optical lattices
Precision measurements
Quantum information
qubit
Quantum simulation
Low-dim systems
1D 2D
Quantum simulation with atoms in optical lattices
atoms in optical lattices electrons in a solid
Introduction
Quantum simulation with strongly-interacting atoms
Ytterbium quantum gases
Bose-Hubbard model
Bose-Hubbard model for interacting bosons in a lattice:
SUPERFLUID
Long-range phase coherence Poissonian number fluctuations Gapless excitation spectrum Compressible
MOTT INSULATOR
No phase coherence No number fluctuations (Fock states) Gap in the excitation spectrum Not compressible
Superfluid-Mott transition
first experimental demonstration in M. Greiner et al., Nature 415, 39 (2002)
quantum phase transition induced by repulsive interactions
superfluid
Mott insulator
Scattering provides information on the structure of matter:
excitations
Probing excitations D. Clément et al., PRL 102, 155301 (2009)
Bragg scattering as stimulated inelastic scattering of light
absorption
1st beam
stimulated emission
2nd beam
ultracold atoms
Bragg scattering D. Clément et al., PRL 102, 155301 (2009)
3rd band
3rd band
N. Fabbri et al., PRL 109, 055301 (2012)
U<<J Superfluid
U>>J Mott Insulator
Bragg scattering
Spectroscopy of the entire dispersion curve with one momentum transfer only
momentum distribution
Mott Insulator
momentum distribution
Superfluid
3rd band SF
3rd band MI / SF
3rd band
quasimomentum [kL]
energ
y [
kH
z]
Band mapping: measurement of excited atoms momentum
N. Fabbri et al., PRL 109, 055301 (2012) Bragg scattering
From the asymmetry of the peaks we extract information on:
• density of states
• coherence of excitations in the Mott phase
sx=8 sx=9 sx=10
N. Fabbri et al., PRL 109, 055301 (2012) Bragg scattering
Introduction
Quantum simulation with strongly-interacting atoms
Ytterbium quantum gases
Periodic table
Yb
Rb
Yb two-electron structure
578 nm mHz
Optical clocks
Optical clocks based on 1S0 – 3P0 transition in alkaline-earth atoms (and ions)
microwave atomic clocks
(f 109 Hz)
optical atomic clocks (f 1014 Hz)
Many isotopes
168Yb 0.13% I=0 boson
170Yb 3.04% I=0 boson
171Yb 14.28% I=1/2 fermion
172Yb 21.83% I=0 boson
173Yb 16.13% I=5/2 fermion
174Yb 31.83% I=0 boson
176Yb 12.76% I=0 boson
Natural Ytterbium comes in seven stable isotopes:
http://periodictable.com
399nm 399nm slowerslower
556nm MOT556nm MOT
BEC BEC 174174YbYb
400k 400k atomsatoms opticaloptical latticelattice
174Yb BEC
T ≈ 100 nK lower temperature
173Yb Fermi gas
ManipulationManipulation ofof nuclearnuclear spinspin statestate
T < 0.5 TF
OnsetOnset ofof Fermi Fermi degeneracydegeneracy
NuclearNuclear spinspin I=5/2I=5/2
--5/25/2 --3/23/2
--1/21/2
+1/2+1/2
+3/2+3/2 +5/2+5/2
Quantum information with long-lived qubits
low coupling to magnetic fields long coherence times
no hyperfine interaction ultra-narrow clock transition
nuclear qubits electronic qubits
Two-electron atoms offer possibilities of encoding quantum information
with long coherence times Review paper: A. Daley, arXiv:1106.5712
Artificial magnetic fields
Synthetic gauge potentials
AharonovAharonov--Bohm Bohm geometricgeometric phasephase forfor thethe closedclosed looploop ofof an an electronelectron in a in a magneticmagnetic fieldfield
Artificial magnetic field Quantum Hall effect Topological insulators (non-abelian) …
f
Artificial magnetic fields
LaserLaser--assistedassisted tunnellingtunnelling in in statestate--dependentdependent potentialspotentials
D. Jaksch and P. Zoller, NJP 5, 56 (2003) F. Gerbier and J. Dalibard, NJP 12, 033007 (2010)
Optical Optical fluxflux latticeslattices
N. Cooper, PRL 106, 175301 (2011)
SeveralSeveral proposalsproposals usingusing statestate--selectiveselective latticeslattices forfor twotwo--electronelectron atomsatoms
SU(N) physics
Neel state Valence Bond Solids Chiral Spin Liquids
Some references to SU(N): M. A Cazalilla et al., New J. Phys. 11, 103033 (2009). M. Hermele et a., Phys. Rev. Lett. 103, 135301 (2009). A. V. Gorshko et al., Nature Physics 6, 289 (2010).
No hyperfine interaction in the ground state
Interaction strength between different nuclear spin states are the same!
SU(6) for 173Yb I=5/2
Quantum simulation with strongly-interacting atoms
Ytterbium quantum gases
• Superfluid-Mott transition in Bose-Hubbard gas • Probe of excitations with inelastic scattering of light
• Two-electron structure • Experimental realization of BEC (174Yb) and Fermi gases (173Yb) • Quantum information and novel quantum simulations
N. Fabbri et al., PRL 109, 055301 (2012)
D. Clément et al., PRL 102, 155301 (2009)
