arXiv:2107.03360 · Physical Review Letters

Prospects of a Pb2+ Ion Clock

K. Beloy

Published Jun 29, 2021• 19 citations

Abstract

We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have I=J=F=0, where I, J, and F are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation, second order Zeeman, Doppler), accommodates "magic" rf trapping, and is robust against decoherence mechanisms that can otherwise limit clock stability. By driving the transition as a two-photon E1+M1 process, the accompanying probe Stark shift is appreciable yet manageable for practical Rabi frequencies.

DOI: 10.1103/physrevlett.127.013201

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arXiv:2107.03360 · Physical Review Letters

Prospects of a Pb2+ Ion Clock

K. Beloy

Published Jun 29, 2021• 19 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.127.013201

Related papers

Zr3+ ion as a prospective terahertz atomic clock

Jyoti, A. Chakraborty, Yanmei Yu +3 more

We demonstrate that the transition between the fine-structure splitting of the ground state of triply ionized zirconium (Zr iv) is suitable for a terahertz (THz) atomic clock. Its transition frequency is about 37.52 THz and is mainly guided by the magnetic dipole (M1) transition, and it is accessible by a readily available laser. We suggest considering stable even isotopes of Zr and ${M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2$ sublevels (i.e., $|4{D}_{3/2},{M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2\ensuremath{\rangle}\ensuremath{\rightarrow}|4{D}_{5/2},{M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2\ensuremath{\rangle}$ clock transition) for experimental advantage. By performing necessary calculations, we estimate possible systematics due to blackbody radiation and ac Stark, electric quadrupole, and second-order Zeeman shifts along with shifts due to the second-order Doppler effects. The proposed THz atomic clock could be very useful in quantum thermometry and frequency metrology.We demonstrate that the transition between the fine-structure splitting of the ground state of triply ionized zirconium (Zr iv) is suitable for a terahertz (THz) atomic clock. Its transition frequency is about 37.52 THz and is mainly guided by the magnetic dipole (M1) transition, and it is accessible by a readily available laser. We suggest considering stable even isotopes of Zr and ${M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2$ sublevels (i.e., $|4{D}_{3/2},{M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2\ensuremath{\rangle}\ensuremath{\rightarrow}|4{D}_{5/2},{M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2\ensuremath{\rangle}$ clock transition) for experimental advantage. By performing necessary calculations, we estimate possible systematics due to blackbody radiation and ac Stark, electric quadrupole, and second-order Zeeman shifts along with shifts due to the second-order Doppler effects. The proposed THz atomic clock could be very useful in quantum thermometry and frequency metrology.

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Prospective of Zr $^{3+}$ ion as a THz atomic clockProspective of Zr$^{3+}$ ion as a THz atomic clock

Jyoti, A. Chakraborty, Yanmei Yu +3 more

We demonstrate transition between the fine structure splitting of the ground state of triply ionized zirconium (Zr IV) is suitable for a terahertz (THz) atomic clock. Its transition frequency is about 37.52 THz and is mainly guided by the magnetic dipole (M1) transition and can be accessible by a readily available laser. We suggest to consider stable even isotopes of Zr and $M_J= \pm 1/2$ sublevels (i.e. $|4D_{3/2},M_J=\pm 1/2\rangle \rightarrow |4D_{5/2},M_J=\pm 1/2\rangle$ clock transition) for the experimental advantage. By performing necessary calculations, we have estimated possible systematics due to blackbody radiation, ac Stark, electric quadrupole and second-order Zeeman shifts along with shifts due to the second-order Doppler effects. The proposed THz atomic clock can be very useful in quantum thermometry and frequency metrology.We demonstrate transition between the fine structure splitting of the ground state of triply ionized zirconium (Zr IV) is suitable for a terahertz (THz) atomic clock. Its transition frequency is about 37.52 THz and is mainly guided by the magnetic dipole (M1) transition and can be accessible by a readily available laser. We suggest to consider stable even isotopes of Zr and $M_J= \pm 1/2$ sublevels (i.e. $|4D_{3/2},M_J=\pm 1/2\rangle \rightarrow |4D_{5/2},M_J=\pm 1/2\rangle$ clock transition) for the experimental advantage. By performing necessary calculations, we have estimated possible systematics due to blackbody radiation, ac Stark, electric quadrupole and second-order Zeeman shifts along with shifts due to the second-order Doppler effects. The proposed THz atomic clock can be very useful in quantum thermometry and frequency metrology.

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We explore the potential of the electric quadrupole transitions $7s\,^2S_{1/2}$ - $6d\,^2D_{3/2}$ , $6d\,^2D_{5/2}$ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive $^A$ Ra $^+$ candidates with $A=$ 223 - 229 are identified. In particular, we show that the transition $7s\,^2S_{1/2}\,(F=2,m_F=0)$ - $6d\,^2D_{3/2}\,(F=0,m_F=0)$ at 828 nm in $^{223}$ Ra $^+$ , with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of $10^{-17}$ . With more experimental effort, the $^{223,225,226}$ Ra $^+$ clocks could be pushed to a projected performance reaching the $10^{-18}$ level.We explore the potential of the electric quadrupole transitions $7s\,^2S_{1/2}$ - $6d\,^2D_{3/2}$, $6d\,^2D_{5/2}$ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive $^A$Ra$^+$ candidates with $A=$ 223 - 229 are identified. In particular, we show that the transition $7s\,^2S_{1/2}\,(F=2,m_F=0)$ - $6d\,^2D_{3/2}\,(F=0,m_F=0)$ at 828 nm in $^{223}$Ra$^+$, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of $10^{-17}$. With more experimental effort, the $^{223,225,226}$Ra$^+$ clocks could be pushed to a projected performance reaching the $10^{-18}$ level.

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Abstract Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.Abstract Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔ 3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.

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Radium Ion Optical Clock

C. A. Holliman, Mingyu Fan, A. Contractor +2 more

We report the first operation of a ${\mathrm{Ra}}^{+}$ optical clock, a promising high-performance clock candidate. The clock uses a single trapped $^{226}{\mathrm{Ra}}^{+}$ ion and operates on the $7s\text{ }^{2}{S}_{1/2}\ensuremath{\rightarrow}6d\text{ }^{2}{D}_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$, where $\ensuremath{\tau}$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}/\ensuremath{\nu}=9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. Using the clock, we realize the first measurement of the ratio of the ${D}_{5/2}$ state to the ${S}_{1/2}$ state Land\'e $g$ -factors: ${g}_{D}/{g}_{S}=0.598\text{ }805\text{ }3(11)$ . A ${\mathrm{Ra}}^{+}$ optical clock could improve limits on the time variation of the fine structure constant, $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.We report the first operation of a ${\mathrm{Ra}}^{+}$ optical clock, a promising high-performance clock candidate. The clock uses a single trapped $^{226}{\mathrm{Ra}}^{+}$ ion and operates on the $7s\text{ }^{2}{S}_{1/2}\ensuremath{\rightarrow}6d\text{ }^{2}{D}_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$, where $\ensuremath{\tau}$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}/\ensuremath{\nu}=9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. Using the clock, we realize the first measurement of the ratio of the ${D}_{5/2}$ state to the ${S}_{1/2}$ state Land\'e $g$-factors: ${g}_{D}/{g}_{S}=0.598\text{ }805\text{ }3(11)$. A ${\mathrm{Ra}}^{+}$ optical clock could improve limits on the time variation of the fine structure constant, $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.

arXiv:2201.07330Physical Review LettersJan 20, 202229 citations

Prospective of Zr

^{3+}

ion as a THz atomic clock

M_J= \pm 1/2

sublevels (i.e.

|4D_{3/2},M_J=\pm 1/2\rangle \rightarrow |4D_{5/2},M_J=\pm 1/2\rangle

clock transition) for the experimental advantage. By performing necessary calculations, we have estimated possible systematics due to blackbody radiation, ac Stark, electric quadrupole and second-order Zeeman shifts along with shifts due to the second-order Doppler effects. The proposed THz atomic clock can be very useful in quantum thermometry and frequency metrology.

In this work, the $4{D}_{3/2}|3,\ifmmode\pm\else\textpm\fi{}2\ensuremath{\rangle}\ensuremath{\rightarrow}4{D}_{5/2}|3,\ifmmode\pm\else\textpm\fi{}2\ensuremath{\rangle}$ transition in the

{\mathrm{Nb}}^{4+}

ion is identified as a promising candidate for a terahertz (THz) atomic clock, with the transition frequency occurring at 56.022 4 THz. This transition is primarily driven by the magnetic dipole decay channel, which can easily be accessed by a laser. We focus on the stable

^{93}\mathrm{Nb}

isotope, which has 100% natural abundance and a nuclear spin of

I=9/2

for experimental advantage. Our data analysis allows us to estimate potential systematic shifts in the proposed clock system, including those due to blackbody radiation, electric quadrupole, second-order Zeeman, and second-order Doppler shifts. The scheme presented in this study can help suppress the ac Stark and electric quadrupole shifts in the clock-frequency measurement. All these analyses suggest that the proposed THz atomic clock using

{\mathrm{Nb}}^{4+}

could be valuable in both quantum thermometry and frequency metrology.

We explore the potential of the electric quadrupole transitions

7s\,^2S_{1/2}

6d\,^2D_{3/2}

6d\,^2D_{5/2}

in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive

^A

^+

candidates with

A=

223 - 229 are identified. In particular, we show that the transition

7s\,^2S_{1/2}\,(F=2,m_F=0)

6d\,^2D_{3/2}\,(F=0,m_F=0)

at 828 nm in

^{223}

^+

, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of

10^{-17}

. With more experimental effort, the

^{223,225,226}

^+

clocks could be pushed to a projected performance reaching the

10^{-18}

level.

We report the first operation of a

{\mathrm{Ra}}^{+}

optical clock, a promising high-performance clock candidate. The clock uses a single trapped

^{226}{\mathrm{Ra}}^{+}

ion and operates on the $7s\text{ }^{2}{S}_{1/2}\ensuremath{\rightarrow}6d\text{ }^{2}{D}_{5/2}$ electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$, where $\ensuremath{\tau}$ is the averaging time in seconds. The total systematic uncertainty is evaluated to be $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}/\ensuremath{\nu}=9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. Using the clock, we realize the first measurement of the ratio of the

{D}_{5/2}

state to the

{S}_{1/2}

state Land\'e

g

-factors:

{g}_{D}/{g}_{S}=0.598\text{ }805\text{ }3(11)

. A

{\mathrm{Ra}}^{+}

optical clock could improve limits on the time variation of the fine structure constant, $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.