on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information...
Transcript of on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information...
![Page 1: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/1.jpg)
Quantum Control and Quantum Simulation
with Ultracold Atoms
with Spin
8/2 (2011) Matsue
6th International School
on Spintronics and Quantum Information Technology
(SPINTECH6)
Kyoto University, JST Y. Takahashi
![Page 2: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/2.jpg)
Outline of Lecture
I) State-of-the-art of ultracold atom technology
II) Quantum simulation of Hubbard model with ultracold atoms
in optical lattice
II-1) quantum magnetism and superfluidity
metal-Mott insulator transition, anti-ferromagnetic order
II-2) adiabatic cooling of atoms with spins
Pomeranchuk cooling
III) Quantum control of atomic spin ensemble
III-1) quantum description of collective atomic spin
coherent spin state, squeezed spin state
III-2) quantum description of polarization of light
quantum Stokes operators
III-3) quantum interface and control
QND measurement of spin, quantum feedback control
![Page 3: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/3.jpg)
Outline of Lecture
I) State-of-the-art of ultracold atom technology
![Page 4: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/4.jpg)
typical experimental setup
![Page 5: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/5.jpg)
Laser Cooling and Trapping
CCD
anti-Helmholtz coils
10mm
“Magneto-optical Trap”
• Number: 107
• Density: 1011/cm3
• Temperature: 10µK
Six laser beams
for laser cooling
mm 500
“optical trap”
“magnetic trap”
EpV int2
)()(
2rErU pot
BV mint
![Page 6: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/6.jpg)
Evaporative Cooling
“remove (=evaporate) energetic atoms in a trap”
“atoms remained in a trap have lower average energy
(=lower temperature)“
1nK 以下の温度まで冷却可!
T~100 nK
![Page 7: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/7.jpg)
Atomic Gases Reach the Quantum Regime !
Momentum Distribution [E. Cornell et al, (1995)]
87Rb
“Bose-Einsten Condensation”
“Boson versus Fermion”
Spatial Distribution [R. Hulet et al, (2000)]
6Li and 7Li
Spatial Distribution [R. Hulet et al, (2000)]
“Fermi Degeneracy”
![Page 8: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/8.jpg)
Feshbach Resonance: ability to tune an inter-atomic interaction
[C. Regal and D. Jin, PRL90, 230404(2003)]
Coupling between “Open Channel” and “Closed Channel”
Control of Interaction(as)
Pote
nti
al
-C6/R3
Two Atoms
Molecular State
F1+F1
F2+F2
)1()(0BB
BaBa bgs
ka ls /22
00 44 saf
Collision is in Quantum Regime !
It is described by s-wave scattering length as
![Page 9: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/9.jpg)
Realization of Atomic BCS
)2
exp(3.0sF
FBCSak
TT
ω3N
2
)(E
31
2
F
m
kTk F
FB
D. Jin Group
T~TBCS T > TBCS T < TBCS
B ~ Bres B ~ Bres B >> Bres >
![Page 10: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/10.jpg)
Optical Lattice
λ/2
)(sin)( 2 xkVxV Loo
Hubbard Model:
i
ii
ji
i nncc UtHj
,
i-th j-th
jit ,
U
Atoms in optical lattice electrons in crystalline lattice
![Page 11: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/11.jpg)
New Technique: Single Site Observation [WS. Bakr, I. Gillen, A. Peng, S. Folling, and M. Greiner, Nature 462(426), 74-77(2009)]
Fluorescence Imaging
87Rb
![Page 12: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/12.jpg)
New Technique: Single Site Manipulation
[C. Ewitenberg et al, Nature 471, 319(2011)]
![Page 13: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/13.jpg)
Outline of Lecture
II) Quantum simulation of Hubbard model with ultracold atoms
in optical lattice
II-1) quantum magnetism and superfluidity
metal-Mott insulator transition, anti-ferromagnetic order
II-2) adiabatic cooling of atoms with spins
Pomeranchuk cooling
![Page 14: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/14.jpg)
Fermions in a 3D optical lattice
i
i
iii
iji
i nnncc UJHj
,,
,
λlattice λlattice
λlattice
λlattice/2
“Fermi-Hubbard Model”
Tunability of
parameters
luck of defects
luck of impurities
![Page 15: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/15.jpg)
Phase Diagram of
Repulsive Fermi-Hubbard Model
U/J
[T. Esslinger, Annu. Rev. Condens. Matter Phys. 2010. 1:129-152,
R. Micnas, J. Ranninger, S. Roaszkiewicw, Rev. Mod. Phys. 62, 113(1990)]
Anti-Ferro
Magnetism
Mott Insulator
Metal
Spin UP Spin DOWN
![Page 16: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/16.jpg)
One of the Goals:
quantum simulation of high-Tc super-conductivity
[in T. Moriya and K. Ueda, Rep. Prog.Phys.66(2003)1299]
(carrier doping) (carrier doping)
SC
SC
AF
hole electron hole electron x
experiment theory
![Page 17: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/17.jpg)
Current Status of
Quantum Simulation of Fermi Hubbard Model: “Formation of (paramagnetic) Mott insulator”
“Suppression of Doubly Occupied Sites
by Strong Repulsion”
[R. Jördens et al., Nature 455, 204 (2008)] [U. Schneider, et al., Science 322,1520(2008)]
![Page 18: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/18.jpg)
Current Status of
Quantum Simulation of Fermi Hubbard Model: “Formation of (paramagnetic) Mott insulator”
[R. Jördens et al., PRL 104, 180401 (2010)]
Quantum Monte-Carlo
Mean-Field
Theory experiment
![Page 19: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/19.jpg)
You Need Cooling for Quantum Magnetism
Anti-Ferro Magnetic Order (paramagnetic)
Mott Insulator
Cooling
)2ln(Bks
![Page 20: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/20.jpg)
Spin Degree of Freedom is Cool
Pomeranchuk Cooling [Pomeranchuk, (1950)]
Discovery of Superfluid 3He by Osheroff, Lee, Richardson
Initial state: Spin-depolarized
and also with degeneracy:
s ~ kB𝜋2T/TF
liquid 3He
Adiabatic change
Final state: Spin depolarized:
s ~kBln(N)
solid 3He atoms in trap atoms in Mott Insulator
“entropy flows from motional degrees of freedom to spin,
which results in the cooling of the system”
![Page 21: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/21.jpg)
Outline of Lecture
III) Quantum control of atomic spin ensemble
III-1) quantum description of collective atomic spin
coherent spin state, squeezed spin state
III-2) quantum description of polarization of light
quantum Stokes operators
III-3) quantum interface and control
QND measurement of spin, quantum feedback control
![Page 22: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/22.jpg)
collective atomic spin
[Jx , Jy]=i Jz
2
Z
YX
JJJ
x
y
AN
J
AN
x
y
z
J
Coherent Spin State
2/JJJ YX
x
y
AN
x
y
z
J
Squeezed Spin State
2/,2/ JJJJ YX
i
i
zZ
i
i
yY
i
i
xX jJjJjJ )()()( ,,
![Page 23: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/23.jpg)
Quantum Interface
Interface Hint= SxJx
QND-interaction:
i
i
zZ
i
i
yY
i
i
xX jJjJjJ )()()( ,,
Atomic Spins:
mm JiJJ ],[zyx ,,,, m
Collective Spin Operators
j(1) j(2) j(3) j(N)
“Memory”
Light Polarization:
Sx =(a+ † a+ - a-
† a- )/2,
Sy =(a+ † a- - a-
† a+ )/2i,
Sz = (a+ †
a- + a- † a+ )/2,
zyx ,,,, m
Quantum Stokes Operators
mm SiSS ],[
Sz z
y
Sy Sx
“Communication”
![Page 24: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/24.jpg)
“Faraday Rotation” as QND interaction
JX
linear polarized off-resonant probe laser light
polarimeter
polarimeter
detector
det
ecto
r
+
probe laser
“Sy” “Hint= α SxJx”
YT et al., PRA 60, 4974, (1999);
A. Kuzmich et al., Europhys. Lett. 42, 481(1998)
![Page 25: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/25.jpg)
“Quantum State Preparation”
Projection of the Result of QND Measurement
x
y
x
y
x
y
x
y
QND pulse
polarization
detection
Jx(0) Jx(t)= Jx(0)
Sy(0) Sy(t) :Measurement Hint= α SxJx
Now, 5 groups in the world have successfully created Squeezed Spin States
![Page 26: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/26.jpg)
Typical Spin-QND Measurement:
Scheme and Result
Joint probability distribution
Optical
Pump. 12.5 µs
“Verifying” “QND” “The squeezed spin state is
created CONDITIONALLY”
![Page 27: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/27.jpg)
Implementing Quantum Feedback Control
Optical
Pump.
“Verifying” “QND”
Joint probability distribution
![Page 28: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/28.jpg)
Experimental Setup for
Quantum Feedback Control
![Page 29: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/29.jpg)
Implementing Quantum Feedback Control
Joint probability distribution
Optical
Pump.
“Verifying” “QND” -1.4dB
Reduction
![Page 30: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/30.jpg)
Maxwell Demon
Reduction of (Thermodynamic) Entropy without Work
“Classical”
“Quantum”
Reduction of Shannon Entropy without Work
![Page 31: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/31.jpg)
Outline of Lecture
I) State-of-the-art of ultracold atom technology
II) Quantum simulation of Hubbard model with ultracold atoms
in optical lattice
II-1) quantum magnetism and superfluidity
metal-Mott insulator transition, anti-ferromagnetic order
II-2) adiabatic cooling of atoms with spins
demagnetization cooling, Pomeranchuk cooling
III) Quantum control of atomic spin ensemble
III-1) quantum description of collective atomic spin
coherent spin state, squeezed spin state
III-2) quantum description of polarization of light
quantum Stokes operators
III-3) quantum interface and control
QND measurement of spin, quantum feedback control
![Page 32: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/32.jpg)
Quantum Magnetism via Quantum Feedback ?
Anti-Ferro Magnetic Order (paramagnetic)
Mott Insulator
Cooling
Measurement & Feedback Control
With Single Atom Level
)2ln(Bks
![Page 33: on Spintronics and Quantum Information Technology...on Spintronics and Quantum Information Technology (SPINTECH6) Kyoto University, JST Y. Takahashi Outline of Lecture I) State-of-the-art](https://reader030.fdocuments.net/reader030/viewer/2022040308/5ed6e466df0eda5e752ae98d/html5/thumbnails/33.jpg)
Thank you very much for attention
16 August Mount Daimonji at Kyoto