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
