Quantum Magnetism with 7LiNiklas Jepsen, Ivana Dimitrova, Jesse Amato-Grill, Michael Messer, Graciana Puentes, David Weld, David Pritchard, Wolfgang Ketterle

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

IntroductionThe Need 4 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

are enabled by

(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

Possible ExperimentsSpin Dynamics

ISpin transport by super-exchange interactions

(d)Prepare a 50-50 spinmixture

(e) Separate spins bymagnetic field gradient

(f)Apply optical lattice (g)Allow spins to mix (bydecreasing magnetic fieldgradient)

Quantum Simulation

IRealization of 2-component Spin HamiltoniansIAnisotropic Heisenberg Model (XXZ model)

H =∑

<i ,j>

[λzszi sz

j − λxy(sxi sx

j + syi sy

j )]− Bz

∑

i

szi

λz =t2↑ + t2

↓2U↑↓

−t2↑

U↑↑−

t2↓

U↓↓λxy =

t↑t↓2U↑↓

IMagnetic phase diagram

L.-M. Duan, E. Demler, and M. Lukin, Phys. Rev. Lett. 91, 090402 (2003)

Anti-Ferromagnet

Z-Ferromagnet

XY-Ferromagnet

hz/6�?Magnetic field gradient

Part

icle

Inte

ract

ions

U"# < U"", U##

U"", U## < U"#

�z/�

?

L.-M. Duan, E. Demler, and M. Lukin, Phys. Rev. Lett. 91, 090402 (2003)

Anti-Ferromagnet

Z-Ferromagnet

XY-Ferromagnet

hz/6�?Magnetic field gradient

Part

icle

Inte

ract

ions

U"# < U"", U##

U"", U## < U"#

�z/�

?

hz/6�xy

�z/�

xy

L.-M. Duan, E. Demler, and M. Lukin, Phys. Rev. Lett. 91, 090402 (2003)

Anti-Ferromagnet

Z-Ferromagnet

XY-Ferromagnet

hz/6�?Magnetic field gradient

Part

icle

Inte

ract

ions

U"# < U"", U##

U"", U## < U"#

�z/�

?

Experimental RealizationExperimental Model

ITwo-component Hamiltonian realized by 7Li atoms in two hyperfine statesplaced in an optical lattice

IFreely tunable experimental parameters:IEnergy ratio t/U by optical lattice depthIOn-site interaction energy U by a Feshbach resonanceISpin separating potential by a magnetic field gradientITemperature by evaporation time

Experimental Sequence

1. Zeeman-slowing and Magneto-optical trapping2. Evaporative cooling in a plug trap3. BEC in a dipole trap supported by a Feshbach resonance4. Green lattice plus dipole trap

Machine Table

Design Realization

Performance of the Magneto-optical Trap

I Atom number: 3 · 1010

I Loading time: 5s

I Decay constants: 13s, 75s

I Temperature: 10mK

I Velocity: 1ms−1

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Time in seconds

Tra

pped fra

ction

Loading

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

Time in seconds

Tra

pped fra

ction

Lifetime

Funding Acknowledgements