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arXiv:1812.10780 · Physical Review A

Magic polarization for cancellation of light shifts in two-photon optical clocks

Shira Jackson, Amar C. Vutha

Published Jun 21, 2019• 12 citations
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Abstract

We find a simple solution to the problem of probe laser light shifts in two-photon optical atomic clocks. We show that there exists a magic polarization at which the light shifts of the two atomic states involved in the clock transition are identical. We calculate the differential polarizability as a function of laser polarization for two-photon optical clocks based on neutral calcium and strontium, estimate the magic polarization angle for these clocks, and determine the extent to which probe laser light shifts can be suppressed. We show that the light shift and the two-photon excitation rate can be independently controlled using the probe laser polarization.

DOI
10.1103/physreva.99.063422

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We find a simple solution to the problem of probe laser light shifts in two-photon optical atomic clocks. We show that there exists a magic polarization at which the light shifts of the two atomic states involved in the clock transition are identical. We calculate the differential polarizability as a function of laser polarization for two-photon optical clocks based on neutral calcium and strontium, estimate the magic polarization angle for these clocks, and determine the extent to which probe laser light shifts can be suppressed. We show that the light shift and the two-photon excitation rate can be independently controlled using the probe laser polarization.
This thesis presents details on the design, construction, and characterization of a novel compact optical clock based on a two-photon transition in calcium. Optical atomic clocks have reached unprecedented accuracy and precision and have the potential to revolutionize metrology. However, many of the applications of optical clocks, such as the detection of dark matter and gravitational waves, deep space navigation, measurements of variations in fundamental constants, and precision geodetic measurements, require compact portable clocks. Building optical atomic clocks on a scale suitable for most field applications is an ongoing challenge in the precision metrology community. This work describes a clock that can be made smaller and simpler than most existing optical clocks, while still operating with state-of-the-art precision. The basis for these improvements is using a two-photon transition, which eliminates the need for sub-Doppler cooling and tight confinement of the atoms. The design for the calcium two-photon clock is given, and the construction of the clock components is described. Experimental results are presented for the search for the clock transition frequency, which has never before been precisely determined. A detailed uncertainty budget is given, showing that this clock should be able to achieve a fractional frequency uncertainty of ∼10−17\sim 10^{-17}∼10−17. In addition, a novel technique of ``magic polarization'' is presented which can be implemented to mitigate probe laser light shifts, long thought to be a serious impediment to precision two-photon clocks. An experiment in which a two-photon clock based on rubidium was launched and operated on a stratospheric balloon and subsequently recovered is also described. This work represents an advancement in the development of compact portable optical clocks which will further push the boundaries of precision measurement and our understanding of the universe.
In the presence of a magnetic field, hyperfine clock qubits can acquire a vector differential light shift that can be tuned via polarization to suppress the total differential light shift of high-power, off-resonant laser light. We experimentally measure this "magic" polarization condition, suppressing differential light shifts in both the 2S1/2{}^2\mathrm{S}_{1/2}2S1/2​ ground and 2F7/2o{}^2\mathrm{F}_{7/2}^o2F7/2o​ metastable clock qubits of 171Yb+^{171}\mathrm{Yb}^+171Yb+. We present calculations of the minimum bias magnetic fields required to suppress differential light shifts in the ground state clock qubits of commonly trapped ion species, finding that they are below the strengths of fields already typically present in experiments. We further present methods for metastable clock-qubit control in 171Yb+^{171}\mathrm{Yb}^+171Yb+, demonstrating a state preparation and measurement infidelity of 2.9−1.5+3.0×10−42.9^{+3.0}_{-1.5}\times10^{-4}2.9−1.5+3.0​×10−4 (−35±4 dB-35 \pm 4 \, \mathrm{dB}−35±4dB).
The light-induced frequency shift due to hyperpolarizability (i.e., terms of second-order in intensity) is studied for a forbidden optical transition, J = 0 --> J = 0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular, or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.
An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the 5s(2) 1S0-->5s5p 3P0 transition of 87Sr atoms as a "clock transition." Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10(-17).
Progress in atomic optical clocks with total uncertainty of ${10}^{\ensuremath{-}18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of 5.33(2)ER5.33(2){E}_{R}5.33(2)ER​ (ER{E}_{R}ER​ is the lattice photon recoil energy) that reduces the total light shift below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ over 1414%14 of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.