High voltage radio frequency (RF) supply is a critical part in an ion trapping system. The RF supply should have high Q-factor and relatively high driving frequency. A frequently used RF supply for an ion trap system is a helical resonator. In certain applications, it is advantageous to have a predictable resonant frequency and Q-factor when the helical resonator is connected to a capacitive load. We develop a model to describe the behavior of a helical resonator with capacitive load. With this model, we can correctly predict the loaded resonant frequency and the loaded Q-factor. To test our prediction, we construct a helical resonator, and measure its resonant frequencies and Q-factors under different capacitive loads. The experimental results agree with our prediction.
REFERENCES
1.
D. J.
Douglas
, A. J.
Frank
, and D.
Mao
, “Linear ion traps in mass spectrometry
,” Mass Spectrom. Rev.
24
, 1
(2005
).2.
J. P.
Karr
, “Precision measurements with non-laser-cooled trapped ions
,” J. Phys. B
42
, 154018
(2009
).3.
H.
Häffner
, C. F.
Roos
, and R.
Blatt
, “Quantum computing with trapped ions
,” Phys. Rep.
469
, 155
(2008
).4.
E. A.
Burt
, S.
Taghavi-Larigani
, and R. L.
Tjoelker
, “High-resolution spectroscopy of 201Hg+ hyperfine structure: A sensitive probe of nuclear structure and the hyperfine anomaly
,” Phys. Rev. A
79
, 062506
(2009
).5.
J. W.
Zhang
, Z. B.
Wang
, S. G.
Wang
, K.
Miao
, B.
Wang
, and L. J.
Wang
, “High-resolution laser microwave double-resonance spectroscopy of hyperfine splitting of trapped 113Cd+ and 111Cd+ ions
,” Phys. Rev. A
86
, 022523
(2012
).6.
C. W.
Chou
, D. B.
Hume
, J. C. J.
Koelemeij
, D. J.
Wineland
, and T.
Rosenband
, “Frequency comparison of two high-accuracy Al+ optical clocks
,” Phys. Rev. Lett.
104
, 070802
(2010
).7.
A. A.
Madej
, P.
Dubé
, Z.
Zhou
, J. E.
Bernard
, and M.
Gertsvolf
, “88Sr+ 445-THz single-ion reference at the 10−17 level via control and cancellation of systematic uncertainties and its measurement against the SI second
,” Phys. Rev. Lett.
109
, 203002
(2012
).8.
C.
Schneider
, D.
Porras
, and T.
Schaetz
, “Experimental quantum simulations of many-body physics with trapped ions
,” Rep. Prog. Phys.
75
, 024401
(2012
).9.
D. J.
Wineland
and D.
Leibfried
, “Quantum information processing and metrology with trapped ions
,” Laser Phys. Lett.
8
, 175
(2011
).10.
W.
Paul
, “Electromagnetic traps for charged and neutral particles
,” Rev. Mod. Phys.
62
, 531
(1990
).11.
Q. A.
Turchette
, D.
Kielpinski
, B. E.
King
, D.
Leibfried
, D. M.
Meekhof
, C. J.
Myatt
, M. A.
Rowe
, C. A.
Sackett
, C. S.
Wood
, W. M.
Itano
, C.
Monroe
, and D. J.
Wineland
, “Heating of trapped ions from the quantum ground state
,” Phys. Rev. A
61
, 063418
(2000
).12.
S. R.
Jefferts
, C.
Monroe
, E. W.
Bell
, and D. J.
Wineland
, “Coaxial-resonator-driven rf (Paul) trap for strong confinement
,” Phys. Rev. A
51
, 3112
(1995
).13.
W. W.
Macalpine
and R. O.
Schildknecht
, “Coaxial resonators with helical inner conductor
,” Proc. IRE
47
, 2099
(1959
).14.
J. H.
Yang
, Y.
Zhang
, X. M.
Li
, and L.
Li
, “An improved helical resonator design for rubidium atomic frequency standards
,” IEEE Trans. Instrum. Meas.
59
, 1678
(2010
).15.
P.
Bletzinger
, “Dual mode operation of a helical resonator discharge
,” Rev. Sci. Instrum.
65
, 2975
(1994
).16.
K.
Niazi
, A. J.
Lichtenberg
, and M. A.
Lieberman
, “The dispersion and matching characteristics of the helical resonator plasma source
,” IEEE Trans. Plasma Sci.
23
, 833
(1995
).17.
R. J.
Deri
, “Dielectric measurements with helical resonators
,” Rev. Sci. Instrum.
57
, 82
(1986
).18.
J. W.
Zhu
, T.
Hao
, C. J.
Stevens
, and D. J.
Edwards
, “Optimal design of miniaturized thin-film helical resonators
,” Appl. Phys. Lett.
93
, 234105
(2008
).19.
R. F.
Welton
, E. W.
Thomas
, R. K.
Feeney
, and T. F.
Moran
, “Simple method to calculate the operating frequency of a helical resonator-RF discharge tube configuration
,” Meas. Sci. Technol.
2
, 242
(1991
).20.
P.
Dubé
, A. A.
Madej
, M.
Tibbo
, and J. E.
Bernard
, “High-Accuracy measurement of the differential scalar polarizability of a 88Sr+ clock using the time-dilation effect
,” Phys. Rev. Lett.
112
, 173002
(2014
).21.
J. D.
Siverns
, L. R.
Simkins
, S.
Weidt
, and W. K.
Hensinger
, “On the application of radio frequency voltages to ion traps via helical resonators
,” Appl. Phys. B
107
, 921
(2012
).22.
H. T.
Kohlhaas
and F. J.
Mann
, Reference Data for Radio Engineers
, 2nd ed. (Federal Telephone and Radio Corporation
, New York
, 1946
).23.
R. F.
Eaton
and C. J.
Kmiec
, “Electrical losses in coaxial cable
,” in Proceedings of the 57th International Wire & Cable Symposium
(IWCS, Inc.
, 2008
), p. 515
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