Quantum Magnetism with 7LiIvana Dimitrova, Jesse Amato-Grill, Niklas Jepsen, William Lunden, Yichao Yu, Michael Messer, Graciana Puentes, David Weld,

Wolfgang KetterleMIT-Harvard Center for Ultracold Atoms, Research Laboratory of ElectronicsDepartment of Physics, Massachusetts Institute of Technology, Cambridge

The Need For Speed

Two-component Bose-Hubbard Hamiltonian

H = −∑

〈ij〉,σ=↑,↓

(tσa†iσajσ + h.c.

)+

12

∑

i ,σ=↑,↓Uσniσ(niσ−1)+U↑↓

∑

i

ni↑ni↓

Super-exchange dominated spin-interactions J = t2/U

(a) Neighboring atoms

U

T

(b) Virtual Excitation of energy U

T

(c) Particle tunnels back

Advantages of our experimental setup:

(1) Light mass of Li-7

(2) Green optical lattice

(3) Feshbach resonance

ER =�2k2

2m

U ≈ a ·�

8

πk(V0/ER)3/4ER

t ≈ ER · 4√π

(V0/ER)3/4e−√

V0/ER

⇒ Higher critical temperature for magnetic ordering (kBTc ∼ t2/U)⇒ Faster spin dynamics within experimentally relevant timescales

Implementation

Design Realization

Cooling 7Li to Degeneracy

IMOT ∼ 2mK∼ 1× 1010

atomsICMOT

IGray Molasses∼ 60µK

IDark StatePumping∼ 90µK

IEvaporation ina QuadrupoleMagnetic trapfor 2.5sec∼ 4µK∼ 7×107atoms

ITransfer toOptical Dipoletrap ∼ 100µm∼ 15W /arm

ISpin Flip(F ,mF) =(2,2)→ (1,1)

IFeshbachResonance in(1,1)

IEvaporation inOptical DipoleTrap

IBEC∼ 5× 105

atoms

Quantum Simulation

IAnisotropic Heisenberg Model (XXZ model)H =

∑

<i ,j>

[Jzszi sz

j − Jxy(sxi sx

j + syi sy

j )]− hz

∑

i

szi

Jz =t2↑ + t2

↓2U↑↓

−t2↑

U↑↑−

t2↓

U↓↓Jxy =

t↑t↓2U↑↓

IMagnetic phase diagram

0

1

2

3

-1

-20 1 2 3

hz/ZJxyLongitudinal magnetic field

Long

itudi

nal i

nter

actio

nJ

z/J

xy Z-Antiferromagnet

XY-Ferromagnet

Z-Ferromagnet

Spin Dynamics

ISpin transport by super-exchange interactions

(n) Prepare a 50-50spin mixture

(o) Separate spins bymagnetic field gradient

(p)Apply optical lattice (q)Allow spins to mix (bydecreasing magneticfield gradient)

Funding Acknowledgements