Quantum Magnetism with 7LiIvana Dimitrova, Jesse Amato-Grill, Niklas Jepsen, William Lunden, Wolfgang Ketterle

Magnetic Ordering via Superexchange

Two-component Bose-Hubbard Hamiltonian

H = −∑

〈ij〉,σ=↑,↓

(tσa†iσajσ + h.c.

)+ 1

2∑i,σ=↑,↓

Uσniσ(niσ−1)+U↑↓∑i

ni↑ni↓

Why use 7Li?• Fast superexchange timescales

t ≈ ER4π

(V0

ER

)3/4e−√V0/ER U ≈ (kLas)

√8π

(V0

ER

)3/4ER

For fixed V0ER

:t2

U=(t

U

)2U ∝ ask

3L

m∼ 150 Hz in 1D

(up to a logarithmic dependence on (kLas))

• Tunable interactions through Feshbach resonances

��������

200 400 600 800 1000 1200 1400B (Gauss)

-200

-100

100

200aS

aa

ab

bb

bc

cc

calculation by Lawrence Cheuk, MIT

Simulation of the Heisenberg Hamiltonian

1 Mott Insulator with n = 1 atoms/siteThe Hubbard model maps to S = 1

2 Heisenberg model

2 Mott Insulator with n = 2 atoms/siteThe Hubbard models maps to S = 1 Heisenberg model at certain values ofU↑↑, U↑↓, U↓↓

3 For N atoms/site, the Hubbard model maps to a Heisenberg model forU↑↑ = U↓↓ Atlman, E. et al. New Journal of Physics 5, 113.1-113.19, (2003)

Adiabatic State Preparation

How to get to the ground state of these model Hamiltonians?• SN � kBln(2) for 1 atom/site

• Cooling in the lattice• Entropy redistribution to other parts of the system or to other degrees of

freedom• Start from a low entropy state and adiabatically sweep a parameter to

connect to the desired state

Phase Diagram S=1/2

H =∑〈i,j〉

(Jzs

ziszj − Jxy(sxi sxj + syis

yj))− hz

∑i

szi Jz = t2

U↑↓− t2

U↑↑− t2

U↓↓, Jxy = t2

2U↑↓

Duan, L et al. Phys. Rev. Lett. 91, 090402 (2003).

Machine Overview

~ 2mK

~ 1.5mK

~ 60µK ~ 90µK

~ 3µK

~ 10s nK

 

Davis, K. et al. Phys. Rev. Lett. 75, 3969-3973 (1995).

Optical Lattice: observed the superfluid-Mott Insulator transition

B (Gauss)0 500 1000

E (M

Hz)

-2000

-1500

-1000

-500

0

500

1000

1500

2000

dcba

Optical Lattice Stability

• Spin-Flip Spectroscopy

• Light Intensity Noise: Add-Noise Measurement and Nufern Modifications

S(f0) (dB/Hz)

-120 -115 -110 -105 -100 -95

Gam

ma=

1/ta

u (1

/s)

0

10

20

30

40

50

60

mephisto 1-arm, 10ERnufern 1-arm, 10ER

0 100 200 300 400 500 600 700 800 900 1000−160

−150

−140

−130

−120

−110

−100

−90

Frequency (kHz)

Pow

er S

pect

ral D

ensi

ty (d

B/H

z)

NuAmp RIN

Seed (Innolight Mephisto)NoisefloorModified NuAmp (38A)NuAmp (33A)NuAmp (39A)

• AOM Frequency Scans

1/13/2016 OneNote Online

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At detuning of 4MHz, tau =       84.76  (76.03, 93.49) of the 3D lattice at 15ER 

  

ramanspecta

Now plotting all the transitions from k=0 to k=bandedge at 15 ER. In 2D, the states are |1x>|1y>, |1x>|2y>, etc where y and x energies are degenerate Now for all depths (0 ER to 33 ER) 

 It looks like a good place to be is 2.5MHz away  10/19/2015  New AOM frequencies: 1st aom in chain: 87 MHz 2nd aom in chain: 85MHz 

 New lattice 1 frequency: 78.5 MHz driven by Tektronix  Trying a new cf measurement technique: ramp UP the ODT (to 1 V each) while the lattice turns on, and leave it on. This actually seems to work rather well‐‐ atoms don't escape during rampdown, and the thermal fractio n is hot enough to be easily distinguished from the condensate at 5ms TOF. Sweet!  Realigned intro. Tried retro alignment by KD‐‐ didn't work, yielded sloshing. Same for kicking with retro. WTF? Realigned retro by backcoupling. Ahh, nice. Lifetime at 20Er: 1.75+/‐0.25 s 

Now on to lattice 2, still driven by a crystek 80MHz VCO. For this measurement we leave lattice 1 on but block it before the chamber. 

• Lifetimes for decreasing atom numbers

1/12/2016 OneNote Online

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L2 again 

 

 

 

 

11/13/2015  L3 calibration, nominally 25Er 

The fits below 200kHz are bs. The dip at 360kHz corresponds to 22Er. 

After re‐doing the back‐coupling, it's at 380. This is 25Er, as requested :) Moving on… 

 

Found that the switch was not powered. 

Ahh, this is what it's supposed to look like. 

 

Number Dependent Lifetimes 

 

lifetimes_vs_atomnumber

 

We find  a dual exponential captures the decay quite well (why?). The time constants are plotted here: