Quantum Magnetism with 7Li - BEC 5 2014.pdf · Quantum Magnetism with 7Li Ivana Dimitrova, Jesse...
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Quantum Magnetism with 7 Li Ivana Dimitrova, Jesse Amato-Grill, Niklas Jepsen, William Lunden, Yichao Yu, Michael Messer, Graciana Puentes, David Weld, Wolfgang Ketterle MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics Department of Physics, Massachusetts Institute of Technology, Cambridge The Need For Speed Two-component Bose-Hubbard Hamiltonian H = - X hij i,σ =↑,↓ t σ a † i σ a j σ + h .c . + 1 2 X i ,σ =↑,↓ U σ n i σ (n i σ - 1)+ U ↑↓ X i n i ↑ n i ↓ Super-exchange dominated spin-interactions J = t 2 /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 E R = 2 k 2 2m U ≈ a · 8 π k (V 0 /E R ) 3/4 E R t ≈ E R · 4 √ π (V 0 /E R ) 3/4 e − √ V 0 /E R ⇒ Higher critical temperature for magnetic ordering (k B T c ∼ t 2 /U ) ⇒ Faster spin dynamics within experimentally relevant timescales Implementation Design Realization Cooling 7 Li to Degeneracy I MOT ∼ 2mK ∼ 1 × 10 10 atoms I CMOT I Gray Molasses ∼ 60μK I Dark State Pumping ∼ 90μK I Evaporation in a Quadrupole Magnetic trap for 2.5sec ∼ 4μK ∼ 7 × 10 7 atoms I Transfer to Optical Dipole trap ∼ 100μm ∼ 15W /arm I Spin Flip (F , m F )= (2, 2) → (1, 1) I Feshbach Resonance in (1, 1) I Evaporation in Optical Dipole Trap I BEC ∼ 5 × 10 5 atoms Quantum Simulation I Anisotropic Heisenberg Model (XXZ model) H = X <i ,j > [J z s z i s z j - J xy (s x i s x j + s y i s y j )] - h z X i s z i J z = t 2 ↑ + t 2 ↓ 2U ↑↓ - t 2 ↑ U ↑↑ - t 2 ↓ U ↓↓ J xy = t ↑ t ↓ 2U ↑↓ I Magnetic phase diagram 0 1 2 3 -1 -2 0 1 2 3 h z /ZJ xy Longitudinal magnetic field Longitudinal interaction J z /J xy Z-Antiferromagnet XY-Ferromagnet Z-Ferromagnet Spin Dynamics I Spin transport by super-exchange interactions (n) Prepare a 50-50 spin mixture (o) Separate spins by magnetic field gradient (p) Apply optical lattice (q) Allow spins to mix (by decreasing magnetic field gradient) Funding Acknowledgements
Transcript of Quantum Magnetism with 7Li - BEC 5 2014.pdf · Quantum Magnetism with 7Li Ivana Dimitrova, Jesse...
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
