ana maria rey · ana maria rey $ funding $ nsf, afosr, aro, aro-darpa-ole, the 11th us-japan joint...
TRANSCRIPT
![Page 1: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/1.jpg)
Ana Maria Rey
$ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE,
The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”
![Page 2: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/2.jpg)
Theory team: B. Yan, S. Moses, J. Covey, B. Neyenhuis and B. Gadway
D. Jin Jun Ye
KRb team:
A. Gorshkov,M. Foss-Feig, K. Hazzard, B. Zhu, S. Manmana, M. Lukin
The Sr team:
M. Swallows, M. Martin, M. Bishof, S. Blatt, X. Zhang, C. Benko
![Page 3: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/3.jpg)
Fully controllable quantum systems
The most precise measurements, e.g. clocks Quantum sensors A tool for understanding quantum complexity
Richard Feynman
Quantum simulation
Atoms ↔ Electrons
Optical lattice ↔ Ionic Crystal
![Page 4: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/4.jpg)
Possible but challenging
Optical lattice spacing much larger than ionic lattice spacing
Atoms heavier than electrons
Extra low temperatures
10-11 K in atomic systems ~ K in solid state systems
• Develop sophisticated cooling methods
• Explore new type of systems • Take advantage of
ultra-precise tools
Solutions
Trapped Ions
Magnetic Atoms
Polar molecules
Rydberg Atoms
Alkaline earth atoms
(~ KHz) (~ Hz)
![Page 5: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/5.jpg)
Understanding quantum systems from few- to many-body
with “clock” precision and control
![Page 6: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/6.jpg)
No Doppler, No Recoil No Stark shift
Metastable state
1S0 (g)
3P0(e)
698 nm (~ 150 s)
Sr and Yb
Ye, Kimble, & Katori, Science 320, 1734 (2008). Magic wave length
JILA Ultra-coherent spectroscopy: Nicholson et al., Phys. Rev. Lett. 109 (2012) 230801
Q~1015, seconds coherence time Ye’s talk this afternoon
![Page 7: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/7.jpg)
ν0 g
e
τ
νL
exp [iδτ]
Measure # of e atoms
2π/τ
e-a
tom
s
N. Ramsey. Nobel prize 1989
What happens in the real experiment with N particles?
B=2π(νL− ν0 )=δ
e
g
δ: Detuning
z
x y
Contrast
Non-interacting: Collective-spin S ∑=n
zyxSS ,,nzy,x, Interactions?
![Page 8: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/8.jpg)
Effective spin 1/2 system during clock interrogation
Array of pancakes reactive
Mode occupation is conserved. No laser/interaction induced mode changing collisions.
1S0 (g)
3P0 (e)
Dominant p-wave collisions
Both elastic and inelastic
n ν~500 Hz,V~ 1 Hz n1
n2 n3 n4 ∑−=
n
znSH δ ∑Ω−
n
xnnS
zn
zn'
znn'n
n'nSBSSSSJ nnnnnn ',',
,',[ ++⋅+ ∑ ⊥ χ
( ) ( ) )(2 ',',',',',',',',',',ggnn
eennnn
ggnn
eenn
egnnnn
egnn
egnnnn VVBVVVUVJ −=−−=−=⊥ χ
δ: Detuning
Ωn: Rabi Frequency
Interaction parameters
Decoupled motional/spin
ν~500 Hz
![Page 9: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/9.jpg)
Long range!!
∑∆++⋅+Ω−−−−= ⊥
'.',))1((
nnnnHSSSJSSBNH 2
zxz χδ
constant n n’
',', , nnnnJ χ⊥
',
',
',',',', ,,,
nn
nn
nnnnnnnn
BB
JJBJ
χχ
χ
∆+
∆+
∆+→ ⊥⊥⊥
J=N/2
⊥JN
H∆ Same Hamiltonian that two component Bose Einstein Condensate: Sorensen, Moller, Cirac, Zoller, Lewenstein, …
∑=n
zyxSS ,,nzy,x,
S S A. M. Rey, L. Jiang, M. Fleischhauer, E. Demler, and M. D. Lukin, PRA 77, 052305 (2008) .
![Page 10: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/10.jpg)
Treat other surrounding atoms as an average
H=- (Sz )2→2 Sz Sz= B Sz
x
z
Sz
Spin precesses with a modified rate with depends on atom number
θ
θ controlled by first pulse
B=-2Sz=-Ncos θ
Excitation fraction: 1/2+Sz/N
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
M. Martin et al arXiv:1212.6291
![Page 11: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/11.jpg)
Quantum correlations should manifest on the amplitude of the oscillations
• At the mean field level interactions only affect the precession rate. • Amplitude remains constant
But….. in the experiments there are many pancakes with different atom number. Due to interactions the pancakes with more atoms precess faster.
1D
• Atom number decay aslo leads to decay of the amplitude
Signal adds → amplitude of the oscillations decay due to dephasing or destructive interference between pancakes
M. Martin et al arXiv:1212.6291
![Page 12: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/12.jpg)
Ramsey fringe decay vs. the spin tipping angle
Shif
t
Excitation fraction
To eliminate the effect of decay we normalize the amplitude with atom number
N
orm
alize
d Am
plitu
de
time
Mean filed fails to reproduce the amplitude decay at tipping angles where the density shift vanishes
M. Martin et al arXiv:1212.6291
![Page 13: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/13.jpg)
Interplay between interactions and decoherence: complicated
few many
We were able to solve the full master Eq for the collective model.
Nor
mal
ized
Cont
rast
Quantum correlations induce faster decay of the amplitude
![Page 14: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/14.jpg)
![Page 15: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/15.jpg)
dipole moment
“spin” N
Rotation
Select two dressed levels : Effective spin ½ system
Rigid Rotor
N=0
EdBNH iirot
i
⋅−= 2
~GHz
N=1
E=0 |
|
Increasing E
Related previous work Other schemes: Micheli et al, Nat. Phys. 2 341 (2006); Brennen et al, NJP 9 138 (2007); Buechler et al, Nat. Phys. 3 726 (2007); Perez-Rios, et al NJP 12, 103007; Wall-Carr Phys. Rev. A 82, 013611 (2010)…
Gorshkov et al: PRL.107.115301(2011), PRA 84,033619 (2011)
|1,-1
|1,0
|1,1
|0,0
N
![Page 16: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/16.jpg)
( )[ ]∑ ++= ⊥ji
yj
yi
xj
xi
zj
ziz
ijdddd SSSSdJSSdJVH
,'' )()( σσσσ
3
2
||)cos31(
ji
ij
rrV
dd −−
=θ
• Project di on the two selected rotational levels '
', ',ˆ iii dzd σσσσ σσ∑=
Ising Flip-flop
'|' σσσσ dd =
ijddjidd VddH =
0,0 ===↓ MN
0,1 ===↑ MN
𝐽𝑧 = (𝑑↑↑ − 𝑑↓↓)2
𝐽⊥ = 2(𝑑↑↓)2
![Page 17: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/17.jpg)
Use direct dipole-dipole interaction to generate direct strong (~KHz) spin exchange interaction: 10-100 larger than super-exchange or magnetic dipoles Fully tunable coefficients by E field (microwaves) Gorshkov et al: PRL.107.115301(2011), PRA 84,033619 (2011) Long-range (1/r3) and anisotropic interactions: S. R. Manmana et al PRB 87, 081106(R) (2013), A. V. Gorshkov et al arXiv:1301.5636
dipole moment
N
Spin temperature, not motional temperature matters: Relevant ratio is interaction time (~ms) to cloud lifetime (25 sec!): K. R.A. Hazzard et al PRL 110, 075301 (2013)
![Page 18: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/18.jpg)
• Empty sites act as defects • Need to perform disorder average
Dipolar interactions will be visible in the Ramsey fringe contrast even in dilute samples
θ=π/2, π/10
K. R.A. Hazzard et al PRL 110, 075301 (2013)
θ=π/2, π/10
![Page 19: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/19.jpg)
Current experiments are carried out in a 3D lattice with a B field B: determines quantization axis |= |N=1,M=-1
|= |N=0,M=0
Magic wavelength for their lattice
B. Neyenhuis et al Phys. Rev. Lett. 109, 230403 (2012)
B
ε φ Polarization
trapping light
• Non-trivial dependence on the geometry due to the anisotropic dipolar interactions.
B 3
2
||)cos31(
ji
ij
rrV
dd −−
=θ
![Page 20: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/20.jpg)
𝐻 = 𝐽⊥ 𝑉𝑖𝑖 𝑆𝑥𝑖𝑆𝑥𝑖 + 𝑆𝑦𝑖𝑆𝑦𝑖<𝑖,𝑖>
𝐽⊥ = −(𝑑↑↓)2
Cluster Expansion
• Spins grouped in cluster of max size g.
• Intra-cluster interactions kept • Inter-cluster interactions
neglected or treated as a perturbation.
g=4
![Page 21: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/21.jpg)
Solid lines: Cluster expansion g=10 Gaussian distribution:
π/2 pulse Filling factor: 7 % 14% 21%
![Page 22: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/22.jpg)
𝜏/8 𝜏/4 𝜏/8 𝜏/8 𝜏/4 𝜏/8
𝜋2 𝑦
𝜋2 𝜙
𝜋2 −𝑥
𝜋2 𝑥
𝜋2 −𝑥
𝜋2 𝑥
𝜋 𝑥
𝜏/2 𝜏/2
𝜋2 𝑦
𝜋2 𝜙
𝜋 𝑥
𝜏
𝜋2 𝑦
𝜋2 𝜙
Wahuha + echo
echo
Learn from NMR: By applying the proper pulse sequence it is possible to eliminate dipolar interactions.
Preliminary pulse scheme for KRb
![Page 23: Ana Maria Rey · Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”](https://reader033.vdocuments.us/reader033/viewer/2022042422/5f5adc38b659370be86655fe/html5/thumbnails/23.jpg)
• Ultra-cold polar matter offers a unique controllable laboratory for the exploration of many-body physics
Strongly interacting open driven quantum systems
• Manifestation of quantum magnetism observable even in a non-quantum degenerate gas
• Rich physics a lot to be understood
Thanks