1. The 4th Yamada Symposium Advanced Photons and Science Evolution
14 June JICA, Osaka
Quantum Simulator Using Ultracold Two-Electron Atoms In an Optical Lattice
Thank you chairman.
First I thank the organizers for kind invitation to this nice seminar, and giving me a chance to talk about our recent work on Ytterbium. 
Title of my talk is quantum degenerate gases of Ytterbium atoms.
% I am Takahashi from Kyoto University.
Kyoto University, JST
Y. Takahashi

2. Quantum Optics Group Members
Let me first introduce our group members.
These people have been working very hard for the experiments described in this talk.
Before going to the discussion of the Yb experiments, let me briefly show you the results for Rb BEC,
% which is related to Okano`s poster.
%Our lab is located in the North campus, and is quite close from here, so please visit our lab. at any time.
%Mr. Okano and Mr. Fukuhara will present posters tomorrow, so please also visit their posters.
NTT:
K. Inaba
M.Yamashita
R. Yamazaki, YT, R. Inoue, K. Shibata, J. Doyle, S. Kato
Y. Yoshkawa, S. Uetake, S. Sugawa, S. Taie, H. Hara, H. Shimizu, R. Yamamoto, I. Takahashi
R. Namiki , H. Yamada, Y. Takasu, R. Murakami, S. Imai, (S. Tanaka. N. Hamaguchi)

3. Quantum Simulation “Interesting” “HARD” “Controllable” Many-body
Quantum System
“Interesting”
Many-body
Classical System
“HARD”
Many-body
Quantum System
“Controllable”

4. Quantum Simulation Hubbard Model: Magnetism, Superconductivity
i-th
j-th
Magnetism, Superconductivity
λ/2
Cold Atoms in Optical Lattice

5. Quantum Simulation of Hubbard Model using “Cold Atoms in Optical Lattice”
λ/2
, as : scattering length
Controllable Parameters
hopping between lattice sites : t
lattice potential :V0
On-site interaction :U
Feshbach Resonance :as
filling factor (e- or h-doping) :n
atom density :n
No impurity, No lattice defects, Various geometry

6. Phase Diagram of High-Tc Cuprate Superconductor
experiment
theory AF SC SC x
hole
electron
hole
electron
(carrier doping)
(carrier doping)
[in T. Moriya and K. Ueda, Rep. Prog.Phys.66(2003)1299]
There is controversy in the under-dope region

7. Quantum Simulators using Alkali Atoms
Bose-Hubbard Model:
Yb Atoms
Our Approach
two-electron atom
87Rb
“Superfluid - Mott-insulator Transition”
[M. Greiner, et al., Nature 415,39 (2002)] …
Fermi-Hubbard Model:
“Formation of Mott-insulator state”
[R. Jördens et al., Nature 455, 204 (2008)]
40K
[U. Schneider, et al., Science 322,1520(2008)]
[K. Günter, et al, PRL96, (2006)]
[S. Ospelkaus, et al, PRL96, (2006)]
Bose-Fermi-Hubbard Model:
[Th. Best, et al, PRL102, (2008)]
87Rb +
40K
Bose-Bose-Hubbard Model:
[J. Catani, et al, PRA77, (R) (2008)]
87Rb +
41K

8. Unique Features of Ytterbium Atoms
Rich Variety of Isotopes
168Yb
(0.13%)
170Yb
(3.05%)
171Yb
(14.3%)
172Yb
(21.9%)
173Yb
(16.2%)
174Yb
(31.8%)
176Yb
(12.7%)
This is the result of the calculation of the scattering lengths based on this formula given in this paper.
As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy.
We do not know the exact value of this parameter.
However, from our previous photoassociation measurement and BEC experiment,
We can exclude the very large and very small and negative scattering length for 174Yb.
So this is the allowed window.
You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation.
Boson
Boson
Fermion
Boson
Fermion
Boson
Boson

9. Isotopic Tuning of Interatomic Interaction25 20 15 10 5 -5
-10
-15
-20
-25
168
170
171
172
173
174
176 13
6.2
4.7
3.4
2.0
0.1
-19
1.9
-0.1
-4.3
-27 11
-0.2
-4.5
-31 23
7.5
-32 22
5.6
7.3
4.2
2.9
-1.3
(nm)
Mass
number
Scattering Length
[M. Kitagawa, et al, PRA77, (2008)]
This is the result of the calculation of the scattering lengths based on this formula given in this paper.
As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy.
We do not know the exact value of this parameter.
However, from our previous photoassociation measurement and BEC experiment,
We can exclude the very large and very small and negative scattering length for 174Yb.
So this is the allowed window.
You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation.
Collaboration with R. Ciurylo, P. Naidon, P. Julienne

10. Unique Features of Ytterbium Atoms
Ultra-narrow Optical Transitions
~15 s (10~40 mHz)
~23 s (15 mHz)
507 nm
578 nm
1S0
3P0
3P2
High-resolution laser spectroscopy
as a Local Probe
This is the result of the calculation of the scattering lengths based on this formula given in this paper.
As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy.
We do not know the exact value of this parameter.
However, from our previous photoassociation measurement and BEC experiment,
We can exclude the very large and very small and negative scattering length for 174Yb.
So this is the allowed window.
You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation.
High-spatial resolution Optical
Magnetic Resonance Imaging

11. Outline of Talk Preparation of Quantum Degenerate Gases
BEC, Fermi Degeneracy, Mixture
Experiments of Atoms in an Optical Lattice
Let me Now switch to the main topic of Yb experiments.
First I show you unique properties of Yb atoms.
Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes.
Finally, I summarize my talk and I will mention the unique future possibility, if I have a time.
Boson, Fermion, Mixtures
Prospects

12. Outline of Talk Preparation of Quantum Degenerate Gases
BEC, Fermi Degeneracy, Mixture
Experiments of Atoms in an Optical Lattice
Let me Now switch to the main topic of Yb experiments.
First I show you unique properties of Yb atoms.
Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes.
Finally, I summarize my talk and I will mention the unique future possibility, if I have a time.
Boson, Fermion, Mixtures
Prospects

13. Optical Imaging Cold Atoms CCD Time-of-Flight Image: Iincident(x,y)
resonant probe light
Iincident(x,y)
lens
CCD
Itransmission(x,y)
“The atom distribution after certain time from the sudden release of the atoms
corresponds to the momentum distribution”
Time-of-Flight Image:

14. Preparation of Quantum Degenerate Gases
Optical Trap
(FORT)
Cold
Hot
Bose-Einstein Condensation
N~105
T~100nK
174Yb
[Y. Takasu et al., PRL 91, (2003)]
gravity
This is the result of the calculation of the scattering lengths based on this formula given in this paper.
As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy.
We do not know the exact value of this parameter.
However, from our previous photoassociation measurement and BEC experiment,
We can exclude the very large and very small and negative scattering length for 174Yb.
So this is the allowed window.
You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation.

15. Quantum Degenerate Yb Gases
Boson
[Y. Takasu et al., PRL 91, (2003)]
[T. Fukuhara et al., PRA 76, (R)(2007)]
174Yb
160µm
TOF:
10ms
120 µm
TOF: 8 ms
176Yb
168Yb(0.13%)
30 µm
170Yb
This is the result of the calculation of the scattering lengths based on this formula given in this paper.
As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy.
We do not know the exact value of this parameter.
However, from our previous photoassociation measurement and BEC experiment,
We can exclude the very large and very small and negative scattering length for 174Yb.
So this is the allowed window.
You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation.
Fermion
[T. Fukuhara et al., PRL. 98, (2007)] [S. Taie et al ., arxiv: ]
171Yb(I=1/2)
T/TF =0.3
(2-component)
173Yb(I=5/2)
T/TF =0.14
(6-component)

16. Ultracold 173Yb: Fermi Gas with 6-spin components
[S. Taie et al ., arxiv: ]
SU(6) system
novel magnetism
[M. A. Cazalilla, et al., N. J. Phys11, (2009); M. Hermele et al.,PRL 103, (2009),
A. V. Gorshkov, et al., Nat. Phys. 6, 289(2010)]
mF=
-3/2
-1/2
-5/2
+3/2
+1/2
+5/2
“Optical Stern-Gerlach Effect” σ+ σ–
-5/2, -3/2, -1/2
+5/2, +3/2, +1/2 g
TOF 7ms
1S0–3P1 Δ~2π×4GHz,
10mW, 3.4ms, 90µm

17. Quantum Degenerate Mixtures of Yb
[T. Fukuhara et al., Phys. Rev. A 79, (R) (2008); in preparation ]
173Yb(Fermion) +174Yb(Boson)
NB~3×104, BEC
173Yb(Fermion) +170Yb(Boson)
NB~8×103, BEC
170Yb(10ms)
173Yb(4ms)
174Yb(Boson)+ 176Yb(Boson)
NB~6×104, BEC
NB~2×104
171Yb(Fermion) + 173Yb(Fermion)
171Yb(m=+1/2)
173Yb(m=+5/2)
T/TF = 0.3
T/TF = 0.33

18. SU(2)×SU(6) Symmetry 171Yb: N = 8.0×103 T = 95 nK
[S. Taie et al ., arxiv: ]
171Yb:
N = 8.0×103
T = 95 nK
T/TF = (2-component)
173Yb:
N = 1.1×104
T = 87 nK
T/TF = 0.54 (6-component)
[Theory: D. B. M. Dickerscheid et al ., Phys. Rev. A 77, (2008)]
“Spinor Superfluidity”

19. Outline of Talk Preparation of Quantum Degenerate Gases
BEC, Fermi Degeneracy, Mixture
Experiments of Atoms in an Optical Lattice
Let me Now switch to the main topic of Yb experiments.
First I show you unique properties of Yb atoms.
Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes.
Finally, I summarize my talk and I will mention the unique future possibility, if I have a time.
Boson, Fermion, Mixtures
Prospects

20. Bose-Fermi Mixture in a 3D optical lattice
Repulsive Interaction: aBF = +7.3 nm
174Yb(Boson) +173Yb(Fermion):
aBB = +5.6 nm aFF = nm
Attractive Interaction: aBF = -4.3 nm
170Yb(Boson) +173Yb(Fermion):
aBB = +3.4 nm aFF = nm
λlattice= 532 nm
VB ~ VF
ωB ~ ωF
tB ~ tF
ΔzB ~ ΔzF
λlattice= 532 nm
λlattice= 532 nm

21. Photoassociation(PA) Study of Atoms in an Optical Lattice
[T. Rom, et al., PRL93, (2004)]

22. Outline of Talk Preparation of Quantum Degenerate Gases
BEC, Fermi Degeneracy, Mixture
Experiments in an Optical Lattice
Let me Now switch to the main topic of Yb experiments.
First I show you unique properties of Yb atoms.
Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes.
Finally, I summarize my talk and I will mention the unique future possibility, if I have a time.
Boson, Fermion, Mixtures
Prospects

23. Prospects f Optical Feshbach Resonance
Using Intercombination Transition
Modulation Index
λ/2=278 nm
174Yb BEC
[K. Enomoto et al.,PRL. 101, (2008)]
[R. Yamazaki et al.,arXiv: ]
Single Site Addressing
in an Optical Lattice f
[K. Shibata et al.,
App. Phys. B 97, 753(2009)]
171Yb Nuclear Spin Squeezing
[T. Takano et al., PRL. 102, (2009), T. Takano et al., PRL. 104, (2010)]
YbLi polar molecule
[M. Okano et al., App. Phys. B 98, 2(2009)]
Simultaneous Optical Trapping

24. Single Site Addressing: Optical Magnetic Resonance Imaging (MRI)
[K. Shibata et al., App. Phys. B 97, 753(2009)]
3P2
Spatial resolution: 250 nm
Magnetic field gradient
Spectral Resolution
Optical absorption line of linewidth 15 mHz
~15 s
1S0-3P2:
507 nm
In addition, it is also interesting to perform the optical MRI using this transition.
With the modest conditions of 1kHz resolution and 10 G/cm field gradient,
Spatial resolution becomes less than 1 micron.
The field gradient like this is created by such saddle coils.
Esspecially interesting is To apply this technique to atoms in an optical lattice.
By 1D field gradient, we can select one particular layer.
And by 2D field gradient, we can select one particular line.
And by 3D field gradient, we can ultimately select one lattice site.
1S0 f
“Optical Spectrum
of 1S0-3P2 transition”
Nagaoka-ferro
Quantum
Computation

25. Cold Atoms in a Thin Glass Cell
1D lattice
Transfered
Optical Tweezer
BEC Formation
MOT
14 mm

26. Summary Preparation of Quantum Degenerate Gases:
BEC: 174Yb, 170Yb, 176Yb, 168Yb
FDG: 173Yb, 171Yb,
Mixture: 174Yb+ 173Yb(BF), 170Yb+ 173Yb(BF),
176Yb+ 174Yb(BB), 171Yb+ 173Yb(FF)
Experiments of Atoms in an Optical Lattice:
Bose-Fermi Mixtures in a 3D Optical Lattice
Prospects:
Optical Feshbach Resonance
Single Site Addressing Using 3P2 State in an Optical Lattice
171Yb Nuclear Spin Squeezing
YbLi polar molecule

27. Thank you very much for attention
16 August Mount Daimonji at Kyoto