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arXiv:2306.00981 · Physical Review Letters

Accurate Determination of Blackbody Radiation Shifts in a Strontium Molecular Lattice Clock

Brandon Iritani, Emily Tiberi, Wojciech Skomorowski, Robert Moszyński, Mateusz Borkowski, Tanya Zelevinsky

Published Dec 26, 2023• 4 citations
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Abstract

Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr_{2} molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the 10^{-16} level. This constitutes an important step toward millihertz-level molecular spectroscopy in Sr_{2} and provides a framework for evaluating BBR shifts in other homonuclear molecules.

DOI
10.1103/physrevlett.131.263201

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Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr_{2} molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the 10^{-16} level. This constitutes an important step toward millihertz-level molecular spectroscopy in Sr_{2} and provides a framework for evaluating BBR shifts in other homonuclear molecules.
We evaluated the static and dynamic polarizabilities of the 5s21S05{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}5s21S0​ and 5s5p3P0o5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}5s5p3P0o​ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1% uncertainty; $\ensuremath{-}0.1492(16)Hz.ThedynamiccorrectiontotheBBRshiftisunusuallylargeinthecaseofSr(70.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (70.1492(16)Hz.ThedynamiccorrectiontotheBBRshiftisunusuallylargeinthecaseofSr(7%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.
Optical clocks have the potential to be 100 times more accurate than current best cesium atomic clocks within a fraction of the averaging time.This corresponds to a fractional uncertainty of the clock frequency on the level of 10 -18 and requires highaccuracy knowledge of systematic frequency shifts, such that they can be avoided or corrected for.In strontium optical lattice clocks an ensemble of ultracold strontium atoms is conned in an optical lattice, to allow for spectroscopy of the reference transition 5s 2 1 S 0 5s5p 3 P 0 in the Lamb-Dicke regime.The by far largest systematic frequency shift of the strontium clock transition is caused by its high sensitivity to blackbody radiation (BBR).The knowledge of the resulting frequency shift limited the achievable clock uncertainty to about 1 × 10 -16 .In this thesis for the rst time an experimental approach was followed, to determine the sensitivity of the strontium clock transition to blackbody radiation.At an environmental temperature of 300 K the resulting frequency shift corresponds to 2.277 8(23) Hz.The achieved uncertainty contributes with 5 × 10 -18 to the fractional systematic uncertainty of the clock frequency.The determination is based on a precision measurement of the dierence of static polarizabilities of the two clock states ∆α dc = α(5s5p 3 P 0 ) -α(5s 2 1 S 0 ) = 4.078 73(11) × 10 -39 Cm 2 /V.For this the dc Stark shift of the clock transition has been measured in the accurately known electric eld of a precision plate capacitor, which has been developed in this work.The attained static polarizability dierence ∆α dc corresponds to the rst term of a power series of the sensitivity to BBR.Higher orders are accumulated as dynamic part of the BBR shift.Which has been modelled using ∆α dc and experimental data for other atomic properties.To interrogate the ultracold atoms in the electric eld a novel transport technique has been developed, which uses the magic wavelength (813 nm) optical lattice to convey the atoms.For this, the interference pattern is translated together with the foci of the far-detuned lattice beams, by simultaneous translation of the lattice optics.In this way ultracold atoms have been transported within 250 ms over 5 cm, or several Rayleigh ranges respectively without signicant atom loss or heating.In the course of this work the rst frequency measurement with the strontium lattice clock of Physikalisch-Technischen Bundesanstalt (PTB) has been performed.The frequency of the 87 Sr clock transition was measured to be 429 228 004 229 872.9(5)Hz.The strontium lattice clock itself contributed with 1.5 × 10 -16 to the overall fractional uncertainty.Furthermore the thermal radiation eld in a cryogenic blackbody environment was modelled and a draft of a corresponding environment of the atoms was designed, which is suitable to be implemented in the strontium lattice clock of PTB.
A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87-Sr: firstly, by a measurement of the dc Stark shift of the clock transition and, secondly, by interrogating the atoms in a cryogenic environment. Both approaches rely on transporting ultracold atoms over several cm within a probe cycle. We evaluate this approach of mechanically moving the optical lattice and conclude that it is feasible to transport the atoms over 50 mm within 300 ms. With this transport a dc Stark shift measurement will allow to reduce the contribution of the blackbody radiation to the fractional uncertainty below 2 * 10^-17 at room temperature by improving the shift coefficient known only from atomic structure calculations up to now. We propose a cryogenic environment at 77 K that will reduce this contribution to few parts in 10^-18.
The strontium ion clock developed at the National Research Council of Canada has reached an uncertainty level of 5 mHz in recent years. This low level of uncertainty was achieved in great part by using methods that harness specific properties of the clock transition that allow either a very high level of cancellation or a strong suppression of frequency shifts that would otherwise dominate the uncertainty budget. The shifts controlled by these methods are the electric quadrupole shift, the tensor Stark shifts, and the micromotion shifts. With these methods in place, the main limitation to the accuracy of the clock transition frequency is the uncertainty in the evaluation of blackbody radiation (BBR) field. In this paper, we review the methods used to control the shifts to the 5 mHz level and present our plans for the evaluation of the BBR field that is expected to reduce the total uncertainty to the mHz level.
Controlling the Stark perturbation from ambient thermal radiation is key to advancing the performance of many atomic frequency standards. This thermal radiation perturbs the atomic energy levels, inducing a Stark shift to the clock frequency conventionally known as the BBR shift. For over four decades, the BBR shift has been a persistent challenge in the pursuit of better atomic clock performance. For room-temperature optical lattice clocks (OLCs) based on Yb and Sr, the BBR shift represents the largest uncanceled systematic frequency shift while typically also constituting the largest source of uncertainty in these state-of-the-art clocks at the ≈ 1 × 10−18 level. In this thesis, I report on the design, assembly and integration of a BBR enclosure, or “shield,” that achieves an unprecedented BBR shift uncertainty of 1.7 × 10−20 by furnishing the interrogated atoms with a near-ideal BBR environment at a cryogenic temperature, while still allowing all the critical quantum control functions required for clock operation. Also, I present a novel lattice loading technique, known as ratchet loading, which enables programmable control over the spatial distribution of ultra-cold atoms confined in an optical lattice. This method allows for the loading of a large number of atoms, effectively reducing quantum projection noise (QPN) while also mitigating frequency shifts caused by atomic interactions. Additionally, ratchet loading facilitates the creation of spatially resolved atomic ensembles along the lattice, making it particularly useful for lattice light shift measurements and potentially advantageous for emerging techniques that probe atomic coherence beyond the local oscillator (LO) coherence time. With the near-elimination of blackbody radiation (BBR) uncertainty and improved clock stability for systematic evaluations, the realization of a mid- to low-10−19 uncertainty Yb optical lattice clock is now more attainable than ever.
Ytterbium lattice frequency standard is an outstanding optical clock with a demonstrated relative frequency accuracy of 3.4·10-16, presently limited by the uncertainty on the blackbody radiation (BBR), lattice polarizabilities and cold collisions shifts. In particular the BBR shift is looming as a major component in the uncertainty budget of many optical frequency standards. In fact the uncertainty on BBR systematic shift in Ytterbium atoms is due both to experimental and theoretical limits in the knowledge of the atomic system: presently Ytterbium has the largest theoretical uncertainty on the BBR shift. Then, both for atomic physics and metrology, new measurements of the Ytterbium atomic properties are strongly demanded, such as the determination of transition matrix elements, lifetimes, branching ratios, polarizabilities and hyperfine constants. In this work we present a set of new measurements for the radiative decay and for the cold collisions trap losses in laser-cooled Ytterbium atoms. These data are relevant to the blackbody radiation shift evaluation and to the cold collisions shift theory.