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Physical Review A

Zr3+ ion as a prospective terahertz atomic clock

Jyoti, A. Chakraborty, Yanmei Yu, Jingbiao Chen, Bindiya Arora, B. K. Sahoo

Published Aug 10, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.108.023115

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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 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 MJ=\ifmmode±\else\textpm\fi1/2{M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2MJ​=\ifmmode±\else\textpm\fi1/2 sublevels (i.e., ∣4D3/2,MJ=\ifmmode±\else\textpm\fi1/2\ensuremath⟩\ensuremath→∣4D5/2,MJ=\ifmmode±\else\textpm\fi1/2\ensuremath⟩|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}∣4D3/2​,MJ​=\ifmmode±\else\textpm\fi1/2\ensuremath⟩\ensuremath→∣4D5/2​,MJ​=\ifmmode±\else\textpm\fi1/2\ensuremath⟩ 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.
Prospective of Zr3+^{3+}3+ ion as a THz atomic clock
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 MJ=±1/2M_J= \pm 1/2MJ​=±1/2 sublevels (i.e. ∣4D3/2,MJ=±1/2⟩→∣4D5/2,MJ=±1/2⟩|4D_{3/2},M_J=\pm 1/2\rangle \rightarrow |4D_{5/2},M_J=\pm 1/2\rangle∣4D3/2​,MJ​=±1/2⟩→∣4D5/2​,MJ​=±1/2⟩ 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 Nb4+{\mathrm{Nb}}^{4+}Nb4+ 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 93Nb^{93}\mathrm{Nb}93Nb isotope, which has 100% natural abundance and a nuclear spin of I=9/2I=9/2I=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 Nb4+{\mathrm{Nb}}^{4+}Nb4+ could be valuable in both quantum thermometry and frequency metrology.
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.
We explore the potential of the electric quadrupole transitions 7s 2S1/27s\,^2S_{1/2}7s2S1/2​ - 6d 2D3/26d\,^2D_{3/2}6d2D3/2​, 6d 2D5/26d\,^2D_{5/2}6d2D5/2​ 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^AARa+^++ candidates with A=A=A= 223 - 229 are identified. In particular, we show that the transition 7s 2S1/2 (F=2,mF=0)7s\,^2S_{1/2}\,(F=2,m_F=0)7s2S1/2​(F=2,mF​=0) - 6d 2D3/2 (F=0,mF=0)6d\,^2D_{3/2}\,(F=0,m_F=0)6d2D3/2​(F=0,mF​=0) at 828 nm in 223^{223}223Ra+^++, 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 10−1710^{-17}10−17. With more experimental effort, the 223,225,226^{223,225,226}223,225,226Ra+^++ clocks could be pushed to a projected performance reaching the 10−1810^{-18}10−18 level.
We explore the potential of the electric quadrupole transitions 7s2S1/27s {}^{2}{S}_{1/2}7s2S1/2​-6d2D3/26d {}^{2}{D}_{3/2}6d2D3/2​, 6d2D5/26d {}^{2}{D}_{5/2}6d2D5/2​ 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{}^{A}ARa+{}^{+}+ candidates, with A=A=A= 223--229, are identified. In particular, we show that the transition 7s2S1/2(F=2,mF=0)7s {}^{2}{S}_{1/2} (F=2,{m}_{F}=0)7s2S1/2​(F=2,mF​=0)-6d2D3/2(F=0,mF=0)6d {}^{2}{D}_{3/2} (F=0,{m}_{F}=0)6d2D3/2​(F=0,mF​=0) at 828 nm in 223Ra^{223}\mathrm{Ra}223Ra+{}^{+}+, 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 ${10}^{\ensuremath{-}17}$. With more experimental effort, the 223,225,226Ra^{223,225,226}\mathrm{Ra}223,225,226Ra+{}^{+}+ clocks could be pushed to a projected performance reaching the ${10}^{\ensuremath{-}18}$ level.
We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.