プレーナーイオントラップの開発

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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大阪大学

大学院基礎工学研究科

占部研究室


田中

歌子

Aug. 9
th
, 2010

Utako

Tanaka


1. Introduction


2. Ion trap (Conventional trap, Planar trap)


3. Precision spectroscopy



4. Trap layout


5. Characterization using Ca
+

ions


6. Micromotion compensation



7. New design


8

Summary



Ion trap



Confine charged particles by using electromagnetic field


60’s

Proposed by
Dehmelt


80’s

Spectroscopy by
Wineland
,
Werth
, and Walther

90’s

Paul
trap

(
rf

electric field


Penning Trap


static
electric
field
and
static magnetic
field



Linear Paul trap

x

y

z

Since these two types were
established,
structures
of
ion trap
electrodes
had
been basically same.


Planar trap





+

+

-

-

J. Chiaverini et al., Quantum Inf.Comput.
5
, 419
-
439 (2005)

C. E. Pearson et al., Phys. Rev. A
73
, 032307 (2006)

S. Seidelin et al., Phys. Rev. Lett.
96
, 253003 (2006)

Kenneth R. Brown et al., Phys. Rev. A
75
, 015401 (2007)



Complicated layout



Optical access



Coupling ion
traps with other physical systems

Linear Paul trap



Shallow potential

Planar trap


Conventional linear trap

d

x

y

)
(
)
(
ln
)
(
2
2
2
2
d
z
d
z
K
z
W



Positive line charge

Negative line charge

d

d

d

Complex plane

)]
(
Re[
,
1
z
W
d

1
0.5
0
0.5
1
1
0.5
0
0.5
1
Electrostatic potential at a moment

2
)
(
,
1
dz
z
dW
S
d


1
0.5
0
0.5
1
1
0.5
0
0.5
1
Pseudopotential

(
K
:const)

iy
x
z
z
z
K
z
w





),
ln(
)
(
0
Line charge at
z
0

2 dimention, analytic


Planar trap

d

x

y

)
)(
(
))
'
(
))(
'
(
(
ln
)
(
d
z
d
z
d
d
z
d
d
z
z
K
z
W







d’

d

Complex plane

d’

)]
(
Re[
,
4
'
,
1
z
W
d
d


1
0.5
0
0.5
1
0.5
1
1.5
2
Electrostatic potential at a moment

2
)
(
,
4
'
,
1
dz
z
dW
d
d


1
0.5
0
0.5
1
0.5
1
1.5
2
Pseudopotential

Large solid angle

Optical access

Precision spectroscopy

Quantum Optics

Complicated

layout

Electromagnetic field

probe

Quantum information processing


Shuttling ions


Junctions

Coupling ion traps with
other physical systems

Quantum simulation


2D trap

Superconductivity

material

Stability






T
N
S
)
/
(
1
)
(


Allan deviation

T.
Rosenband

et al., Science 319, 1808 (2008)

Frequency Ratio of Al
+

and Hg
+

Single
-
Ion Optical
Clocks; Metrology at the 17th Decimal Place




(S/N)

T


Transition frequency

Linewidth

Signal to noise ratio

Averaging time

Cycle time to make a

Single determination
of the line center

Stability






T
N
S
)
/
(
1
)
(


Lens (insulator) cannot be close to the trapping region
because it affects on the trapping potential.

Detection efficiency

Solid angle



0.01

Optics loss

0.7

Quantum efficiency

0.5

Lens

Filter

Photomultiplier

Trap

Viewport


4



4


0.5 !


Allan deviation

Accuracy

dc potential gradient

Zeeman shifts

Quadrupole

moment shift

Doppler
shift

88
Sr
+

40
Ca

+

171
Yb

+

199
Hg

+

2
S
1/2
-
2
D
5/2


115
In

+

27
Al

+




1
S
0
-
3
P
0


no
quadrupole

moment

D
-
state

order of several hertz or more

137
Ba

+

S
1/2
-
2
D
3/2

(F=2
-
F=0)

Second order

no

first order Zeeman shift

(m
F
=0
-
m
F’
=0)


Compensation

Compensation

Stark shifts

First order

2
S
1/2
-
2
D
5/2


Residual thermal motion and
micromotion


Second order

Motional

induced

Blackbody radiation


(300K 10
-
16
)

Varing

magnetic field due to
currents at
rf

electrode

Doppler cooling limit



10
-
18

7.4

9.3

0.38

-
5.4

-
0.08


10
-
18

Residual thermal motion and
micromotion


10
-
18

Compensation


Simulation



Solver :
Ansoft

Maxwell3D




dc
rf
Q
m
Q







2
2
2
sec
4
Q
:
ion charge
,
m
:
ion mass


rf

:
RF potential

:
DC potential


:
RF frequency

RF

DC

dc

End

L

End

L

End

R

End

R

RF

RF

Center

Middle

Top

Bottom

y

z

x

w
m

w
r

w
c

g


Functions of electrodes




End

L

End

L

End

R

End

R

RF

RF

Center

Middle
Top

Bottom

y

z

x

w
m

w
r

w
c

g

RF



confinement
x
-
y

plane

End



confinement
z axis ,
y
-
direction

Center



y
-
direction

Top/Bottom

compensation of
micromotion

in the
x

direction(ideally 0V)

x
-
y
plane

y
-
z

plane

y = 0.4 mm

0.5 mm

0.5 mm


Design of planar trap


Position of trapped ion
---

several hundred micrometers above the surface

q
-
parameter in Mathieu equation (trapping condition)

---

0.1

0.3

Potential depth
---



1
eV

(conventional trap
---



10
eV
)

Secular frequencies
---
A few MHz for radial direction


Several hundred kHz for axial direction

Overlapping of
rf

potential null and dc potential minimum


---

to minimize
micromotion


Spacing between electrodes




Wire bonding





Potential depth








m iddle width 1.5m m
0
2
4
6
8
0
10
20
30
40
Vend[V]
Potential depth[eV]
A
B
m iddle width 0.5m m
0
1
2
3
4
5
6
7
0
10
20
30
Vend[V]
Potential depth[eV]
A
B
m in{A,B}
0
0.5
1
1.5
2
2.5
3
3.5
0
5
10
15
20
25
30
35
V
end
[V]
Potential depth[eV]
m iddle0.5m m
m iddle0.8m m
m iddle1.0m m
m iddle1.5m m
V
rf
=800V
p
-
p
,Ω/2π
=20
[MHz]
,

w
r
=0.82mm
,

w
c
=0.26mm
,

g=0.05mm
,

r
0
=0.414mm


x direction [mm]

z direction [mm]

4. Trap layout


Ion motion




Secular motion

(Reduced by laser cooling)

micromotion






i
i
i
i
q
a


2
1
2
2
1
2
1
0
,
r
V
2
2
0
2





z
rf
y
x
q
m
Q
q
q
 




0
4
cos
2
2





i
i
i
i
u
t
q
a
u


,
4
2
1
2
0
2
z
m
U
Q
a
a
a
dc
z
y
x







Q
: charge

m
: mass

κ: geometric factor

i = x, y, z

1
,
1


i
i
q
a
Si


phase

)
(


i

Trap condition

















t
q
t
u
t
u
i
Si
i
i
i
cos
2
1
cos
1



Secular frequency

z
u
y
u
x
u
z
y
x
ˆ
ˆ
ˆ



u
ion position


Mathieu equation

Ion motion

i

r
0

V
rf

cosΩt

U
0

z

2
z
0

z

x

y

4. Trap layout

conventional trap




2
0
ˆ
i
i
dc
i
m
u
Q
u



E
2
u
k
u
k
0
y
0
x
y
y
x
x
q
q



0
1
2
3
PMT counts [10
2
counts/50msec]




m
u
Q
u
t
q
a
u
i
dc
i
i
i
i






E
4
cos
2
2


k
x
,
k
y

:
wavevector

component

D. J. Berkeland et al., J. Appl. Phys. 83, 5025 (1998)

Excess
micromotion

Ion motion

Stray electric field
E
dc


















t
q
t
u
u
t
u
i
Si
i
i
i
i
cos
2
1
)
cos
(
1
0


Excess
micromotion


This motion cannot be reduced by laser cooling.

Compensation voltages are applied to reduce the micromotion.

Conventional trap Ideally

( no stray field) (rf null)=(dc potential minimum)

Excitation spectra in the presence of micromotion

Planar
trap It is necessary to design so that the condition is satisfied.

Laser detuning [MHz]

100 MHz

4. Trap layout

Substrate


Alumina

635
μ
m thickness

99.5
%)

Electrode


Gold plating Ti/Pb/Au




thickness 6
±
1

2
μ
m


Mount ceramic pin grid array (CPGA)


Wire bonding Al wire

11.5
mm

4. Trap layout


SEM images of trap electrode





Acknowledgement:
Dr.
Shimakage

at NICT

Previous trap

Current trap

50μm

50μm

4. Trap layout

106 mm

Vacuum level

10
-
11

Torr

4. Trap layout


Loading Laser cooling


photoionization

2
S
1/2

2
P
1/2

2
P
3/2

2
D
3
/2

2
D
5
/2

τ

1


Continuum

423 nm

390 nm

4
s
2 1
S
0

4
s
4
p
1
P
1

Energy level diagram of
40
Ca

Energy level diagram of
40
Ca
+




397 nm

Oven

Trap

Vacuum chamber

~2
×
10
-
11

Torr

Ca beam

To pump

RF
20MHz


800
V
pp
(typ.)

Amp

Lens

Trap

Interference

filter

Image
intensifier

x

z

y

Beam

splitter

Photomultiplier


Experimental setup

y

z

x

397 nm

423 nm

375 nm

866 nm





Trapping ions

Ions are trapped 405
μm

above from the surface.

(Design 400
μm

above)

Photoionization

Fluorescence from trapped ions









Quantum jumps

2
S
1/2

2
P
1/2

2
P
3/2

2
D
3
/2

2
D
5
/2

τ

1


Energy level diagram of
40
Ca
+

τ

1


15μm

0
50
100
150
200
250
300
350
400
450
500
0
5
10
15
20
25
30
35
40
Vend[V]
ω
z
[kHz]
Experim ent
Sim ulation

Measurement of secular frequency

ω
z

V
rf
=256V
p
-
p

V
center
=9.8V


V
end
=14V

V
top
=V
bottom
=0V


An
ac
voltage of 0.4 V
amp

is
applied
to the
middle top. When it resonates

to the
secular frequency, ions are heated and
fluorescence drops.

End

L

End

L

End

R

End

R

RF

RF

Center

Middle

Top

Bottom

y

z

x

Detection with side beam


electrode

Before

compensation[V]

After
compensation
[V]

End left

8.8

8.8

End right

8.8

8.8

Center

6.2

6.2

Top middle

0

0

Bottom middle

0

3.0

Vrf

90

90

6. Micromotion compensation

x

z

y

397 nm

Side beam

ω
z

End

L

End

L

End

R

End

R

RF

RF

Center

Bottom

y

x

Middle

Top

z

Problems

397 nm

Oven

Trap

Ca beam

To pump

x

z

y

397 nm

423 nm

375 nm

866 nm

When loading, calcium beam
contaminates the surface of the trap,
which changes the trap condition such as
compensation voltages.

Loading

region

Ca beam

hole

Moving

ions

Detection

region

Trap electrode

Laser

beams

z

x

y

Oven

Summary

Planar trap for precision spectroscopy

Stability
---

will be improved

Accuracy Choose the species of ion example:
Ba
+

and In
+

?


Currents at the
rf

electrode would be problem




Second order Zeeman shift

Ca beam

Trap electrode

Laser

beams

z

x

y

Trapping Ca
+

ions

405
μm

above the surface (almost same as the designed value)

Near future

Measurement of secular frequencies (Difference from simulation)

Method of
micromotion

compensation in the y
-
direction