Simulating Quantum Many-Body Systems in Optical Lattices

Simulating Quantum

Many-Body Systems

in Optical Lattices

Tomasz Sowinski

- 1 -

artificial

crystals

artificial crystals of light

standing(wave(of(light

second(order(shi2(of(the(electronic(energy(

(AC7Stark(effect)

close(to(the(resonant(frequency

ultra-cold bosons in optical lattice

- 2 -

Hubbard

models

single-particle Hamiltonian

Wannier functions

Bose-Hubbard model

Hamiltonian(of(the(system

two7body(interacAons

• contact interactions (short range)

• dipolar interactions (long range)

lowest(band(approximaAon

Bose-Hubbard model

field(operator(decomposiAon

single7parAcle(Hamiltonian

lowest(band(approximaAon

Bose-Hubbard model

single7parAcle(Hamiltonian

interacAon(Hamiltonian

Bose-Hubbard model

Bose-Hubbard model

MI 1

MI 2

MI 3

SF

MI 0

Greiner&et.$al,&Nature&(London)&415,&39&(2002)

groundbreaking experiment

- 3 -

model

extensions

interacAon(Hamiltonian

long-range interactions

interacAons(between(polar(molecules

MI 1

MI 2

SF

MI 0

MI 3/2

MI 1/2

long-range interactions

C.&Bruder&et$al.,&Phys.&Rev.&B&47,&342&(1993)

interacAon(Hamiltonian

long-range interactions

interacAons(between(polar(molecules

(STRONG)

STRONG long-range interactions

T.&Sowiński&et$al.,&Phys.&Rev.&LeF.&108,&115301&(2012)

S.&Fölling&et$al.,&Nature&(London)&448,&1029&(2007)

optical SuperLattices

V _ext (r) = V ₀ cos ² (k · r) + V ¹ cos ² (2k · r)

G.&Wirth&et$al.,&Nature&Phys.&7,&147&(2011)

higher bands physics

field(operator(decomposiAon

T.&Sowiński,&Phys.&Rev.&LeF.&108,&165301&(2012)

…(or(…(shake(the(laMce

resonant(superlaMce

1D chain with orbital degeneracy

V (x, y) = V _x sin ² (k _x x) + V _y sin ² (k _y y)

1D chain with orbital degeneracy

T.&Sowiński&et$al.,&Phys.&Rev.&LeF.&111,&215302&(2013)

possibility f

or

time -rev ersa l

sym metry br

eak ing

and

…many…many…

other scenarios

optical lattices are truly

becoming dedicated

quantum simulators

for the study of different

many-body

configurations

conclusion