1. 大阪大学 大学院基礎工学研究科 占部研究室 田中 歌子
Aug. 9th, 2010
平面型トラップによるイオンの捕獲
Confinement of Ca+ ions in a planar trap
大阪大学　大学院基礎工学研究科
占部研究室
田中　歌子
Utako Tanaka

2. Outline 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

3. 1. Introduction
Ion trap　　
　　Confine charged particles by using electromagnetic field
60’s Proposed by Dehmelt
80’s Spectroscopy by Wineland, Werth, and Walther
Paul trap　(rf electric field）
Penning Trap（ static electric field and static magnetic field）
Since these two types were established, structures of ion trap electrodes had been basically same.
90’s
Linear Paul trap x y z

4. 1. Introduction Planar trap ○ Complicated layout ○ Optical access
J. Chiaverini et al., Quantum Inf.Comput. 5, (2005)
C. E. Pearson et al., Phys. Rev. A 73, (2006)
S. Seidelin et al., Phys. Rev. Lett. 96, (2006)
Kenneth R. Brown et al., Phys. Rev. A 75, (2007)
Linear Paul trap -
Planar trap + + -
○ Complicated layout
○ Optical access
○ Coupling ion traps with other physical systems
▲ Shallow potential

5. 2. Ion trap Conventional linear trap Line charge at z0
2 dimention, analytic
Line charge at z0
(K:const)
Complex plane y d x
Positive line charge d d d
Negative line charge
Pseudopotential
Electrostatic potential at a moment

6. 2. Ion trap Planar trap y x Complex plane d’ d d d’ Pseudopotential
Electrostatic potential at a moment

7. Planar trap Quantum information processing Shuttling ions Junctions
Precision spectroscopy
Quantum simulation
2D trap
Electromagnetic field
probe
Large solid angle
Optical access
Complicated
layout
Quantum Optics
Coupling ion traps with other physical systems
Superconductivity
material

8. 3. Precition spectroscopy
Stability
Transition frequency
Linewidth
Allan deviation
(S/N)
Signal to noise ratio T
Cycle time to make a
Single determination of the line center
T. Rosenband et al., Science 319, (2008)
Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place
Averaging time

9. 3. Precition spectroscopy
Stability
Allan deviation
Detection efficiency
Solid angle　 ～0.01
Optics loss
Quantum efficiency
Trap
Filter
Photomultiplier
Lens
Viewport
～0.5 !
Lens (insulator) cannot be close to the trapping region because it affects on the trapping potential.

10. 3. Precition spectroscopy
Accuracy
88Sr Ca Yb Hg +
137Ba +
115In Al + 　
2S1/2-2D5/2
2S1/2-2D5/2
S1/2-2D3/2
(F=2-F=0)
1S0-3P0
Doppler shift
Doppler cooling limit　　 ～10-18
Second order
Residual thermal motion and micromotion
Quadrupole moment shift
D-state
order of several hertz or more
no quadrupole moment
dc potential gradient
Zeeman shifts
no first order Zeeman shift
(mF=0-mF’=0)
Compensation
Compensation
First order
Second order
Compensation
Varing magnetic field due to currents at rf electrode
Stark shifts
～10-18
Residual thermal motion and micromotion
～10-18
Motional –induced
0.38
-0.08
Blackbody radiation　
(300K 10-16)
7.4
9.3
-5.4

11. 4. Trap layout Simulation Solver : Ansoft Maxwell3D
Middle
Top
End L
End R g RF wc
Center wr RF x
End L
End R RF DC
Bottom y z wm
Q: ion charge, m: ion mass
: RF potential
: DC potential
: RF frequency

12. 4. Trap layout Functions of electrodes g RF wc Center wr RF x y z wm
MiddleTop
End L
End R g RF wc
Center wr RF x
End L
End R
Bottom y z wm
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)

13. 4. Trap layout
x-y plane
y-z plane

14. 4. Trap layout
y = 0.4 mm
0.5 mm
0.5 mm

15. 4. Trap layout Design of planar trap
Position of trapped ion --- several hundred micrometers above the surface
q-parameter in Mathieu equation (trapping condition) ～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

16. 4. Trap layout Potential depth
x direction [mm]
z direction [mm]
Vrf=800Vp-p,Ω/2π=20 [MHz] , wr=0.82mm , wc=0.26mm , g=0.05mm , r0=0.414mm

17. 4. Trap layout Ion motion x y z conventional trap z 2z0 ion position
Vrf　cosΩt
　Mathieu equation
i = x, y, z U0
Q: charge
m: mass
κ: geometric factor
Trap condition
Ion motion
micromotion
Secular motion
(Reduced by laser cooling)
：Secular frequency
：phase

18. 4. Trap layout Excess micromotion Stray electric field Edc Ion motion
This motion cannot be reduced by laser cooling.
D. J. Berkeland et al., J. Appl. Phys. 83, 5025 (1998)
Compensation voltages are applied to reduce the micromotion.
Excitation spectra in the presence of micromotion
100 MHz
kx, ky : wavevector component
Laser detuning [MHz]
Conventional trap Ideally　( no stray field) (rf null)=(dc potential minimum)
Planar trap It is necessary to design so that the condition is satisfied.

19. 4. Trap layout 11.5 mm Substrate Alumina （635μm thickness、99.5％）
Electrode　 Gold plating Ti/Pb/Au
　　　　 thickness 6±1～2μm
Mount ceramic pin grid array (CPGA)　
Wire bonding Al wire

20. 4. Trap layout SEM images of trap electrode Current trap Previous trap
Acknowledgement: Dr. Shimakage at NICT

21. 4. Trap layout
Vacuum level　10-11 Torr
106 mm

22. 5. Characterization using Ca+ ions
Loading Laser cooling
photoionization
Energy level diagram of 40Ca
Energy level diagram of 40Ca+
Continuum
2P3/2
854
2P1/2
390 nm
850
2D5/2
866
4s4p 1P1
2D3/2
397nm
τ～1ｓ
423 nm
729
4s2 1S0
2S1/2

23. 5. Characterization using Ca+ ions
Experimental setup
Photomultiplier y z x
RF 20MHz
800 Vpp(typ.) x z y
Oven
Interference
filter
Amp
Ca beam
Helical
resonator
Image intensifier
866 nm
Beam
splitter
Vacuum chamber
~2×10-11 Torr
397 nm
423 nm
375 nm
Lens
Trap
397 nm
To pump
Trap

24. 5. Characterization using Ca+ ions
Trapping ions
Fluorescence from trapped ions
Photoionization
Ions are trapped 405 μm above from the surface.
(Design 400 μm above)

25. 5. Characterization using Ca+ ions
Quantum jumps
15μm
2P3/2
854
2P1/2
850
τ～1ｓ
2D5/2
866
2D3/2
397nm
τ～1ｓ
2S1/2
Energy level diagram of 40Ca+

26. 5. Characterization using Ca+ ions
Middle
Top
Measurement of secular frequency
End L
End R
An ac voltage of 0.4 Vamp is applied to the middle top. When it resonates to the secular frequency, ions are heated and fluorescence drops. RF
Center ωz RF x
End L
End R y
Bottom z
Vrf=256Vp-p、Vcenter=9.8V、 Vend =14V Vtop=Vbottom=0V

27. After compensation[V]
6. Micromotion compensation x z y
Detection with side beam
397 nm
Side beam
Middle
Top
End L
End R
electrode
Before
compensation[V]
After compensation[V]
End left
8.8
End right
Center
6.2
Top middle
Bottom middle
3.0
Vrf 90 RF
Center ωz RF x
End L
End R y z
Bottom

28. Problems solution x z y x z Oven Moving ions Ca beam Loading Detection
When loading, calcium beam contaminates the surface of the trap, which changes the trap condition such as compensation voltages.
solution
Oven
Moving
ions x z y
Ca beam
Loading
region
Detection
region
Helical
resonator
Laser
beams
866 nm
hole
397 nm
Trap electrode
423 nm z x y
Ca beam
375 nm
Oven
Trap
397 nm
To pump

29. Summary x z 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
Trapping Ca+ ions
405 μm above the surface (almost same as the designed value)
Measurement of secular frequencies (Difference from simulation)
Method of micromotion compensation in the y-direction
Near future
Laser
beams
Trap electrode z x y
Ca beam