arXiv:physics/0611134 · Physical Review A

Measurement of the hyperfine structure of the S1∕2−D5∕2 transition in Ca+43

Jan Benhelm, Gerhard Kirchmair, Umakant D. Rapol, T. Körber, Christian F. Roos, R. Blatt

Published Mar 15, 2007• 39 citations

Abstract

The hyperfine structure of the $4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{\ensuremath{-}}3d\phantom{\rule{0.2em}{0ex}}^{2}S_{5∕2}$ quadrupole transition at $729\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ in $^{43}\mathrm{Ca}^{+}$ has been investigated by laser spectroscopy using a single trapped $^{43}\mathrm{Ca}^{+}$ ion. We determine the hyperfine structure constants of the metastable level as ${A}_{{D}_{5∕2}}=3.8931(2)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$ and ${B}_{{D}_{5∕2}}=4.241(4)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. The isotope shift of the transition with respect to $^{40}\mathrm{Ca}^{+}$ was measured to be ${\ensuremath{\Delta}}_{\mathrm{iso}}^{43,40}=4134.713(5)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at nonzero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known ``clock transitions'' between $m=0$ levels at zero magnetic field.

DOI: 10.1103/physreva.75.032506

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Measurement of the 2 S 1 / 2 − 2 D 5 / 2 clock transition in a single 171 Yb + ion

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Measurement of infrared magic wavelength for an all-optical trapping of $^{40}$Ca$^{+}$ ion clock

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arXiv:physics/0611134 · Physical Review A

Measurement of the hyperfine structure of the S1∕2−D5∕2 transition in Ca+43

Jan Benhelm, Gerhard Kirchmair, Umakant D. Rapol, T. Körber, Christian F. Roos, R. Blatt

Published Mar 15, 2007• 39 citations

arXiv HTML PDF

Abstract

The hyperfine structure of the

4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{\ensuremath{-}}3d\phantom{\rule{0.2em}{0ex}}^{2}S_{5∕2}

quadrupole transition at

729\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

^{43}\mathrm{Ca}^{+}

has been investigated by laser spectroscopy using a single trapped

^{43}\mathrm{Ca}^{+}

ion. We determine the hyperfine structure constants of the metastable level as

{A}_{{D}_{5∕2}}=3.8931(2)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

and

{B}_{{D}_{5∕2}}=4.241(4)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

. The isotope shift of the transition with respect to

^{40}\mathrm{Ca}^{+}

was measured to be

{\ensuremath{\Delta}}_{\mathrm{iso}}^{43,40}=4134.713(5)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at nonzero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known ``clock transitions'' between

m=0

levels at zero magnetic field.

DOI: 10.1103/physreva.75.032506

Related papers

Observation of the hyperfine structure of the 2S1/2−2D5/2 transition in 87Sr+

G. P. Barwood, K. Gao, Patrick Robert Gill +2 more

The hyperfine structure of the ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{D}_{5/2}$ quadrupole transition at 674 nm in ${}^{87}{\mathrm{Sr}}^{+}$ has been observed. The ion was confined in a Paul trap and cooled using laser radiation at 422 and 1092 nm. The quadrupole transition was observed by monitoring quantum jumps in the 422-nm fluorescence. The odd isotope of strontium has ``clock'' transitions independent of the first-order Zeeman shift and the ${}^{2}{D}_{5/2}$ state hyperfine structure constants have been determined as ${A}_{{D}_{5/2}}=2.1743(14)\mathrm{MHz}$ and ${B}_{{D}_{5/2}}=49.11(6)\mathrm{MHz}.$ Standard uncertainties have been added in parentheses. These values allow the second-order Zeeman shifts to be calculated. The ${}^{88}{\mathrm{Sr}}^{+}{\ensuremath{-}}^{87}{\mathrm{Sr}}^{+}$ isotope shift for the 674-nm quadrupole transition has been measured to be 247.99(4) MHz.The hyperfine structure of the ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{D}_{5/2}$ quadrupole transition at 674 nm in ${}^{87}{\mathrm{Sr}}^{+}$ has been observed. The ion was confined in a Paul trap and cooled using laser radiation at 422 and 1092 nm. The quadrupole transition was observed by monitoring quantum jumps in the 422-nm fluorescence. The odd isotope of strontium has ``clock'' transitions independent of the first-order Zeeman shift and the ${}^{2}{D}_{5/2}$ state hyperfine structure constants have been determined as ${A}_{{D}_{5/2}}=2.1743(14)\mathrm{MHz}$ and ${B}_{{D}_{5/2}}=49.11(6)\mathrm{MHz}.$ Standard uncertainties have been added in parentheses. These values allow the second-order Zeeman shifts to be calculated. The ${}^{88}{\mathrm{Sr}}^{+}{\ensuremath{-}}^{87}{\mathrm{Sr}}^{+}$ isotope shift for the 674-nm quadrupole transition has been measured to be 247.99(4) MHz.

Physical Review AJan 8, 200344 citations

High-Resolution Spectroscopy of $^{173}$ Yb $^{+}$ IonsHigh-Resolution Spectroscopy of $^{173}$Yb$^{+}$ Ions

J. Jiang, A. V. Viatkina, Saaswath JK +7 more

Compared to other stable isotopes of $\rm{Yb}^+$ , $^{173}\rm{Yb}^+$ has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped $^{173}\rm{Yb}^+$ ion. The previously unobserved $^2\!S_{1/2} \rightarrow {}^2\!D_{3/2}$ electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between $^{171}\rm{Yb}^+$ and $^{173}\rm{Yb}^+$ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the ${}^2\!D_{3/2}$ state with a relative uncertainty below $10^{-8}$ . From the HFS measurement data, we infer for ${}^{173}$ Yb a nuclear magnetic octupole moment $Ω= -0.062(8)\,({\rm b} \times μ_N)$ with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the ${}^2\!S_{1/2}$ and ${}^2\!D_{3/2}$ states.Compared to other stable isotopes of $\rm{Yb}^+$, $^{173}\rm{Yb}^+$ has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped $^{173}\rm{Yb}^+$ ion. The previously unobserved $^2\!S_{1/2} \rightarrow {}^2\!D_{3/2}$ electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between $^{171}\rm{Yb}^+$ and $^{173}\rm{Yb}^+$ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the ${}^2\!D_{3/2}$ state with a relative uncertainty below $10^{-8}$. From the HFS measurement data, we infer for ${}^{173}$Yb a nuclear magnetic octupole moment $Ω= -0.062(8)\,({\rm b} \times μ_N)$ with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the ${}^2\!S_{1/2}$ and ${}^2\!D_{3/2}$ states.

physics.atom-phCross-listedarXiv:2601.09585Physical Review LettersJan 15, 20261 citation

Measurement of the 2 S 1 / 2 − 2 D 5 / 2 clock transition in a single 171 Yb + ion

M. Roberts, P. Taylor, S. Gateva +3 more

Spectroscopy of the 411-nm transition in ${}^{171}{\mathrm{Yb}}^{+}$ has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The ${}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)$ frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu} ${\mathrm{T})}^{2}$ . In addition, the hyperfine structure of the ${}^{2}{D}_{5/2}$ level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The ${}^{2}{D}_{5/2}$ hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.Spectroscopy of the 411-nm transition in ${}^{171}{\mathrm{Yb}}^{+}$ has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The ${}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)$ frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu}${\mathrm{T})}^{2}$. In addition, the hyperfine structure of the ${}^{2}{D}_{5/2}$ level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The ${}^{2}{D}_{5/2}$ hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.

Physical Review AOct 1, 199959 citations

Absolute frequency measurement of the $^{40}$ Ca $^{+}$ clock transition using a GNSS link to the SI secondAbsolute frequency measurement of the $^{40}$Ca$^{+}$ clock transition using a GNSS link to the SI second

M. Guevara-Bertsch, M. K. Joshi, M. I Hussain +2 more

We report the absolute frequency measurement of the $4s$ $ ^{2}S_{1/2}\leftrightarrow 3d$ $^{2}D_{5/2}$ $^{40}$ Ca $^{+}$ clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5 $\times$ 10 $^{-15}$ . The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the $D_{5/2}$ sublevels and reevaluate the Landé g-factor of the $3d$ $^{2}D_{5/2}$ level to be g $_{5/2}= 1.200329(1)$ .We report the absolute frequency measurement of the $4s$ $ ^{2}S_{1/2}\leftrightarrow 3d$ $^{2}D_{5/2}$ $^{40}$Ca$^{+}$ clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5 $\times$ 10$^{-15}$. The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the $D_{5/2}$ sublevels and reevaluate the Landé g-factor of the $3d$ $^{2}D_{5/2}$ level to be g$_{5/2}= 1.200329(1)$.

physics.atom-phCross-listedarXiv:2609.15844Sep 15, 2026

Precision measurement of the Mg+25 ground-state hyperfine constant

Zhilin Xu, Ke Deng, H. Che +3 more

We report an experimental determination of the ground-state hyperfine constant $A$ of the $^{25}\mathrm{Mg}^{+}$ ions by measuring the $|{S}_{1/2},F=2,m=0\ensuremath{\rangle}$ to $|{S}_{1/2},F=3,m=0\ensuremath{\rangle}$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=\ensuremath{-}596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.We report an experimental determination of the ground-state hyperfine constant $A$ of the $^{25}\mathrm{Mg}^{+}$ ions by measuring the $|{S}_{1/2},F=2,m=0\ensuremath{\rangle}$ to $|{S}_{1/2},F=3,m=0\ensuremath{\rangle}$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=\ensuremath{-}596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.

Physical Review ANov 21, 201715 citations

Measurement of infrared magic wavelength for an all-optical trapping of $^{40}$ Ca $^{+}$ ion clockMeasurement of infrared magic wavelength for an all-optical trapping of $^{40}$Ca$^{+}$ ion clock

Yao Huang, Hua Guan, Chengbin Li +6 more

For the first time, we experimentally determine the infrared magic wavelength for the $^{40}$ Ca $^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$ electric quadrupole transition by observation of the light shift canceling in $^{40}$ Ca $^{+}$ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be $-44.32(32)$ ~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of $^{40}$ Ca $^{+}$ optical clock.For the first time, we experimentally determine the infrared magic wavelength for the $^{40}$Ca$^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$ electric quadrupole transition by observation of the light shift canceling in $^{40}$Ca$^{+}$ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be $-44.32(32)$~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of $^{40}$Ca$^{+}$ optical clock.

arXiv:2202.07828Feb 16, 20221 citation

The hyperfine structure of the

4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{\ensuremath{-}}3d\phantom{\rule{0.2em}{0ex}}^{2}S_{5∕2}

quadrupole transition at

729\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

^{43}\mathrm{Ca}^{+}

has been investigated by laser spectroscopy using a single trapped

^{43}\mathrm{Ca}^{+}

ion. We determine the hyperfine structure constants of the metastable level as

{A}_{{D}_{5∕2}}=3.8931(2)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

and

{B}_{{D}_{5∕2}}=4.241(4)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

. The isotope shift of the transition with respect to

^{40}\mathrm{Ca}^{+}

was measured to be

{\ensuremath{\Delta}}_{\mathrm{iso}}^{43,40}=4134.713(5)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

m=0

levels at zero magnetic field.

The hyperfine structure of the ${}^{2}{S}_{1/2}{\ensuremath{-}}^{2}{D}_{5/2}$ quadrupole transition at 674 nm in

{}^{87}{\mathrm{Sr}}^{+}

has been observed. The ion was confined in a Paul trap and cooled using laser radiation at 422 and 1092 nm. The quadrupole transition was observed by monitoring quantum jumps in the 422-nm fluorescence. The odd isotope of strontium has ``clock'' transitions independent of the first-order Zeeman shift and the

{}^{2}{D}_{5/2}

state hyperfine structure constants have been determined as

{A}_{{D}_{5/2}}=2.1743(14)\mathrm{MHz}

and

{B}_{{D}_{5/2}}=49.11(6)\mathrm{MHz}.

Standard uncertainties have been added in parentheses. These values allow the second-order Zeeman shifts to be calculated. The ${}^{88}{\mathrm{Sr}}^{+}{\ensuremath{-}}^{87}{\mathrm{Sr}}^{+}$ isotope shift for the 674-nm quadrupole transition has been measured to be 247.99(4) MHz.

High-Resolution Spectroscopy of

^{173}

^{+}

Ions

Compared to other stable isotopes of

\rm{Yb}^+

^{173}\rm{Yb}^+

has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped

^{173}\rm{Yb}^+

ion. The previously unobserved

^2\!S_{1/2} \rightarrow {}^2\!D_{3/2}

electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between

^{171}\rm{Yb}^+

and

^{173}\rm{Yb}^+

on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the

{}^2\!D_{3/2}

state with a relative uncertainty below

10^{-8}

. From the HFS measurement data, we infer for

{}^{173}

Yb a nuclear magnetic octupole moment

Ω= -0.062(8)\,({\rm b} \times μ_N)

with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the

{}^2\!S_{1/2}

and

{}^2\!D_{3/2}

states.

Spectroscopy of the 411-nm transition in

{}^{171}{\mathrm{Yb}}^{+}

has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The

{}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)

frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu}

{\mathrm{T})}^{2}

. In addition, the hyperfine structure of the

{}^{2}{D}_{5/2}

level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The

{}^{2}{D}_{5/2}

hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.

Absolute frequency measurement of the

^{40}

^{+}

clock transition using a GNSS link to the SI second

We report the absolute frequency measurement of the

4s

$ ^{2}S_{1/2}\leftrightarrow 3d$

^{2}D_{5/2}

^{40}

^{+}

clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5

\times

^{-15}

. The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the

D_{5/2}

sublevels and reevaluate the Landé g-factor of the

3d

^{2}D_{5/2}

level to be g

_{5/2}= 1.200329(1)

We report an experimental determination of the ground-state hyperfine constant

A

of the

^{25}\mathrm{Mg}^{+}

ions by measuring the $|{S}_{1/2},F=2,m=0\ensuremath{\rangle}$ to $|{S}_{1/2},F=3,m=0\ensuremath{\rangle}$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=\ensuremath{-}596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.

Measurement of infrared magic wavelength for an all-optical trapping of

^{40}

^{+}

ion clock

For the first time, we experimentally determine the infrared magic wavelength for the

^{40}

^{+}

4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}

electric quadrupole transition by observation of the light shift canceling in

^{40}

^{+}

optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be

-44.32(32)

~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of

^{40}

^{+}

optical clock.