Leonardo Leonardo FallaniFallani

Dipartimento di Fisica e Astronomia &Dipartimento di Fisica e Astronomia & LENS LENS –– Università di FirenzeUniversità di Firenze

fallani@lens.unifi.itfallani@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)