Physical Review Research

Experimental determination of the E2−M1 polarizability of the strontium clock transition

Sören Dörscher, J. Klose, S. Marathapalli, Christian Lisdat

Published Feb 7, 2023• 9 citations

Abstract

State-of-the-art optical lattice clocks require careful characterization of systematic frequency shifts, which often needs to include contributions to the coupling of atoms to the trapping light field that are beyond the electric-dipole approximation. An experimental determination of the light-shift coefficient that accounts for electric-quadrupole and magnetic-dipole transitions for the clock transition in neutral strontium is reported on, addressing the substantial discrepancy between values detailed in previous works from theory and experiment.

DOI: 10.1103/physrevresearch.5.l012013

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Experimental determination of the E2-M1 polarizability of the strontium clock transition

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Physical Review Research

Experimental determination of the E2−M1 polarizability of the strontium clock transition

Sören Dörscher, J. Klose, S. Marathapalli, Christian Lisdat

Published Feb 7, 2023• 9 citations

Publisher

Abstract

DOI: 10.1103/physrevresearch.5.l012013

Related papers

Experimental determination of the E2-M1 polarizability of the strontium clock transition

Sören Dörscher, J. Klose, S. Marathapalli +1 more

To operate an optical lattice clock at a fractional uncertainty below $10^{-17}$ , one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states $(5s5p)\,{}^{3}\mathrm{P}_{0}$ and $(5s^2)\,{}^{1}\mathrm{S}_{0}$ of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks with uncertainties of few $10^{-18}$ , as the resulting lattice light shift corrections deviate by up to $1 \times 10^{-17}$ from each other at typical trap depths. We have measured the E2-M1 polarizability difference using our ${}^{87}\mathrm{Sr}$ lattice clock and find a value of $Δα_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{μHz}$ . This result is in very good agreement with the value reported by Ushijima et al.To operate an optical lattice clock at a fractional uncertainty below $10^{-17}$, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states $(5s5p)\,{}^{3}\mathrm{P}_{0}$ and $(5s^2)\,{}^{1}\mathrm{S}_{0}$ of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks with uncertainties of few $10^{-18}$, as the resulting lattice light shift corrections deviate by up to $1 \times 10^{-17}$ from each other at typical trap depths. We have measured the E2-M1 polarizability difference using our ${}^{87}\mathrm{Sr}$ lattice clock and find a value of $Δα_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{μHz}$. This result is in very good agreement with the value reported by Ushijima et al.

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The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the $5{S}_{1/2}$ -- $5{D}_{5/2}$ transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the $5{P}_{3/2}$ -- $5{D}_{5/2}$ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the $5{P}_{3/2}$ -- $5{D}_{5/2}$ resonance, and the corresponding reduced E1 matrix element $1.80(6)e{a}_{0}$ (experimental) and $1.96(15)e{a}_{0}$ (theoretical). These values resolve a previous discrepancy between theory and experiment.The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the $5{S}_{1/2}$--$5{D}_{5/2}$ transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the $5{P}_{3/2}$--$5{D}_{5/2}$ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the $5{P}_{3/2}$--$5{D}_{5/2}$ resonance, and the corresponding reduced E1 matrix element $1.80(6)e{a}_{0}$ (experimental) and $1.96(15)e{a}_{0}$ (theoretical). These values resolve a previous discrepancy between theory and experiment.

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In neutral atom optical clocks, the higher-order atomic polarizability terms lead to the clock transition frequency shift which is motion-state dependent and nonlinear with the optical lattice depth. We propose to use an auxiliary optical lattice to compensate the influence of the E2-M1 differential polarizability or tune the associated coefficient to a favorable value. We show that by applying this method to Sr and Hg optical lattice clocks, the low or even sub-10-19 clock transition frequency uncertainty from the optical lattice becomes feasible. Finally, the proposed scheme is simple for experimental realization and can be implemented and tested in the existing setups.In neutral atom optical clocks, the higher-order atomic polarizability terms lead to the clock transition frequency shift which is motion-state dependent and nonlinear with the optical lattice depth. We propose to use an auxiliary optical lattice to compensate the influence of the E2-M1 differential polarizability or tune the associated coefficient to a favorable value. We show that by applying this method to Sr and Hg optical lattice clocks, the low or even sub-10-19 clock transition frequency uncertainty from the optical lattice becomes feasible. Finally, the proposed scheme is simple for experimental realization and can be implemented and tested in the existing setups.

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S01−P23 magnetic quadrupole transition in neutral strontium

Jan Trautmann, Dimitry Yankelev, V. Klüsener +3 more

We present a detailed investigation of the ultranarrow magnetic-quadrupole $^{1}\mathrm{S}_{0}\text{\ensuremath{-}}^{3}\mathrm{P}_{2}$ transition in neutral strontium and show how it can be made accessible for quantum simulation and quantum computation. By engineering the light shift in a one-dimensional optical lattice, we perform high-resolution spectroscopy and observe the characteristic absorption patterns for a magnetic quadrupole transition. We measure an absolute transition frequency of $446,647,242,704(2)$ kHz in $^{88}\mathrm{Sr}$ and an $^{88}\mathrm{Sr}\text{\ensuremath{-}}^{87}\mathrm{Sr}$ isotope shift of $+62.91(4)$ MHz. In a proof-of-principle experiment, we use this transition to demonstrate local addressing in an optical lattice with 532 nm spacing with a Rayleigh-criterion resolution of $494(45)$ nm. Our results pave the way for applications of the magnetic quadrupole transition as an optical qubit and for single-site addressing in optical lattices.We present a detailed investigation of the ultranarrow magnetic-quadrupole $^{1}\mathrm{S}_{0}\text{\ensuremath{-}}^{3}\mathrm{P}_{2}$ transition in neutral strontium and show how it can be made accessible for quantum simulation and quantum computation. By engineering the light shift in a one-dimensional optical lattice, we perform high-resolution spectroscopy and observe the characteristic absorption patterns for a magnetic quadrupole transition. We measure an absolute transition frequency of $446,647,242,704(2)$ kHz in $^{88}\mathrm{Sr}$ and an $^{88}\mathrm{Sr}\text{\ensuremath{-}}^{87}\mathrm{Sr}$ isotope shift of $+62.91(4)$ MHz. In a proof-of-principle experiment, we use this transition to demonstrate local addressing in an optical lattice with 532 nm spacing with a Rayleigh-criterion resolution of $494(45)$ nm. Our results pave the way for applications of the magnetic quadrupole transition as an optical qubit and for single-site addressing in optical lattices.

arXiv:2211.02470Physical Review ResearchMar 30, 202319 citations

To operate an optical lattice clock at a fractional uncertainty below

10^{-17}

, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states

(5s5p)\,{}^{3}\mathrm{P}_{0}

and

(5s^2)\,{}^{1}\mathrm{S}_{0}

of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks with uncertainties of few

10^{-18}

, as the resulting lattice light shift corrections deviate by up to

1 \times 10^{-17}

from each other at typical trap depths. We have measured the E2-M1 polarizability difference using our

{}^{87}\mathrm{Sr}

lattice clock and find a value of

Δα_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{μHz}

. This result is in very good agreement with the value reported by Ushijima et al.

5{S}_{1/2}

5{D}_{5/2}

transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the

5{P}_{3/2}

5{D}_{5/2}

transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the

5{P}_{3/2}

5{D}_{5/2}

resonance, and the corresponding reduced E1 matrix element

1.80(6)e{a}_{0}

(experimental) and

1.96(15)e{a}_{0}

(theoretical). These values resolve a previous discrepancy between theory and experiment.

446,647,242,704(2)

kHz in

^{88}\mathrm{Sr}

and an $^{88}\mathrm{Sr}\text{\ensuremath{-}}^{87}\mathrm{Sr}$ isotope shift of

+62.91(4)

MHz. In a proof-of-principle experiment, we use this transition to demonstrate local addressing in an optical lattice with 532 nm spacing with a Rayleigh-criterion resolution of

494(45)

nm. Our results pave the way for applications of the magnetic quadrupole transition as an optical qubit and for single-site addressing in optical lattices.