Post on 28-Jun-2020
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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