高精度分光を目指したCaH+の
生成とトラップ
富山大学・理 森脇喜紀
Motivation
Spectroscopy of 40CaH+
the pure vibrational transition (v=0, J=0, F=1/2,
M=±1/2) → (v=1, J=0, F=1/2, M=±1/2) can potentially
be measured with an uncertainty of 10-16
by use of
simultaneous trapping with Ca+ ions
sympathetic cooling
P.O.Schmidt et al.
quantum logic measurement Science 309, 749(2005)
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Application to the test of the time invariance of
fundamental constants e.g. electron-proton mass ratio
Shelkovnikov et al. PRL100, 150801 (2008)
Vibrational transition of SF6 Dn/n～10-14
Proposal: High precision measurements of
the pure vibrational transition of 40CaH+
Kajita and Moriwaki J. Phys. B 42, 154022(2009)
• Simultaneous trapping of a 40CaH+ and a 40Ca+
in a linear trap
Long interaction time reduces the homogeneous
linewidth
Ions in a crystal state inside a linear trap are free from
Stark shift
Some transition frequencies of molecular ions are free
from Zeeman shift
Estimated frequency uncertainty (order of 10-16)
CaH+ （v = 0, J = 0, F = 1/2, M = ±1/2）
→ （v = 1, J = 0, F = 1/2, M = ±1/2） transition
f = 42.24 THz (7.1 mm)
(1) Natural linewidth 2.5 Hz
(2) Zeeman shift (magnetic field < 1 G) < 1.3 x 10-17
(3) Stark shift induced by the trapping electric field < 10-17
(4) Electric quadrupole shift is zero because of F = 1/2
(5) Stark shift induced by probe laser light is most dominant
~ 1.2 x 10-16 with saturation power (32 mW/cm2)
Production of CaH+
(1) Laser ablation of Ca containing solids
(2) Ca++H2 → CaH+ +H
Georgiadis et al. J. Chem. Phys. 92, 7060
(1988)
endothermic reaction
2.5 eV
Ca+ (4p 2P 1/2) + H2 CaH+ + H
?
Laser system
To Trap
Pump laser
(397 nm)
Repump laser
(866 nm)
RF Trap
Vdc+Vac cos Ωt
Hyperboloid electrodes
r0=7.5 mm
Vdc=0 V
Vac=350 V
Ω/2π=1.65 MHz
Dz=25 eV
LIF dependence on He pressure and qz
4eVac
qz
mr02 2
Temperature and size of ion cloud
Doppler width
~2 GHz
T~600 K
Δr~0.45 mm
Δz~0.23 mm
LIF decay with H2 buffer gas
Photon Counts (cps)
20000
LIF signal is proportional to
the number of Ca+ ions.
t~11000 s
He 4.5*10-6 Torr
10000
Ca+
(4p2P1/2)+H2→CaH++H ?
H2 4.4*10-6 Torr
t~3600 s
5000
0
500
1000
Time (s)
With H2 buffer gas, LIF
decay significantly.
1500
mass signal (m=41)
Q-Mass spectrum
Buffer gas : H2 (99.99995%)
0.5
The mass signal (m=41u) is
normalized by that of m=40 u
Laser on
0.4
0.3
M=41u signals appear with the
laser irradiation.
0.2
0.1
Laser off
0
50
100
150
Time (s)
200
250
With D2 buffer gas, m=42 u
signals are observed.
Production of CaH+, CaD+ has been confirmed !
Indication of some loss mechanisms of Ca+
Without 397nm and 866nm laser, LIF decays slowly.
Without 866 nm laser, LIF decays fast although the 2D3/2 state is
optically pumped.
20000
Photon Counts (cps)
H2 4.4*10-6 Torr
397&866 laser chopped
10000
/
Ca+ (3d 2D 3/2) + H2 CaH+ + H
866nm laser chopped
5000
0
500
Time (s)
1000
Photoassociated ion loss?
spectroscopy of
+
CaH
There have been no experimental data on CaH+.
Needs for reliable theoretical data
ab initio calculations of Ca+-H potential curves
electric energy levels, vibrational levels, Rotational
constants, transition dipole moments
by M. Abe (collaborator)
Potential energy curves
Ca+ 2P [(4p)1] + H 2S [(1s)1]
Ca+ 2D [(3d)1] + H 2S [(1s)1]
Ca+ 2S [(4s)1] + H 2S [(1s)1]
Spectroscopic constants
of the ground state of CaH+ (11S)
Correlation method
SA-CASSCF/
MS-CASPT2
State specific
CASSCF/
single state CASPT2
Re(Å) we
(cm–1)
Be
(cm–1)
De (cmDe (eV)
1)
1.892
1484.8
4.782
2.1837
17613
1.898
1478.4
4.748
2.1634
17449
CCSD(T)
1.896
1502.7
4.805
2.2455
18111
Previous worka
1.936
1511.0
4.609
1.8355
14804
Previous workb
1.864
1468.0
---
2.1077
17000
a 4th
order MBPT: Canuto et al. Phys. Rev. A. 1993.
b Two-elec. valence CI and core polarization: Boutalib et al. Chem. Phys. 1992.
Vibrational TDM in atomic unit (21S)
Excited state 2 1S
Ground state
1 1S
v=0
v=1
v=2
v=3
v=4
v=5
v=6
v=7
v=8
v=9
v=10
v=11
v=12
v=13
v=14
v=15
v=16
v=17
v=0
v=1
v=2
v=3
v=4
v=5
v=6
v=7
v=8
v=9
v=10 v=11
0.206
0.446
0.659
0.762
0.723
0.572
0.374
0.196
0.076
0.018
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.333
0.517
0.431
0.074
0.384
0.717
0.793
0.635
0.373
0.148
0.027
0.006
0.003
0.001
0.000
0.000
0.000
0.000
0.396
0.388
0.021
0.392
0.477
0.127
0.419
0.798
0.809
0.530
0.206
0.019
0.017
0.000
0.003
0.001
0.000
0.000
0.399
0.179
0.263
0.382
0.019
0.428
0.448
0.052
0.663
0.898
0.650
0.229
0.013
0.026
0.009
0.001
0.002
0.002
0.358
0.016
0.340
0.124
0.314
0.338
0.138
0.516
0.252
0.468
0.929
0.725
0.203
0.065
0.018
0.019
0.009
0.003
0.297
0.151
0.268
0.125
0.333
0.020
0.397
0.171
0.395
0.441
0.271
0.928
0.753
0.117
0.116
0.022
0.011
0.013
0.232
0.218
0.137
0.250
0.164
0.259
0.247
0.238
0.364
0.180
0.518
0.101
0.912
0.721
0.027
0.119
0.074
0.032
0.174
0.232
0.015
0.255
0.024
0.288
0.017
0.336
0.016
0.398
0.047
0.505
0.036
0.882
0.615
0.192
0.031
0.064
0.127
0.215
0.069
0.195
0.142
0.193
0.185
0.210
0.224
0.232
0.286
0.231
0.426
0.148
0.821
0.426
0.296
0.115
0.091
0.182
0.111
0.121
0.182
0.077
0.225
0.046
0.266
0.006
0.309
0.085
0.332
0.300
0.241
0.709
0.182
0.241
0.064
0.144
0.117
0.061
0.168
0.003
0.190
0.056
0.202
0.118
0.195
0.209
0.118
0.324
0.137
0.305
0.536
0.032
0.042
0.103
0.098
0.024
0.126
0.035
0.130
0.083
0.122
0.134
0.089
0.190
0.005
0.212
0.202
0.038
0.297
0.313
Candidate transitions in LIF
31S
21S
Absorption
Emission
21S state
around 400nm
more than 600nm
31S state
21P state
240 nm
240 nm
400 nm
380 nm
Conclusion
• We proposed high precision measurements of the
pure vibrational transition of 40CaH+
• production of CaH+ , CaD+ is confirmed
Future
•laser spectroscopy of CaH+
Cryogenic ion trap:
99% of CaH+ ions are localized in
the (v,J)=(0,0) state at T=4 K
H2 vapor pressure ~ 10-7 Torr
共同研究者
• 梶田雅稔 (NICT)
• 阿部穣里 (Tokyo Metropolitan Univ.)
• 松島房和, 小林かおり, 榎本勝成(富山大学)
小山達也, 中口利彦, 日比野誠(学生)
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