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Applied Physics Letters

Gravity measurement at the sub-millimeter scale with optical lattice clock

Sheng-Xian Xiao, Ying Liang, Ya Zhang, Tao Wang

Published Feb 26, 2024• 1 citation
Publisher

Abstract

Due to the excellent accuracy, the optical lattice clock (OLC) has not only achieved impressive results in frequency measurement but also gradually plays an important role in quantum precision measurement. In this paper, we propose a scheme for measuring gravity at the sub-millimeter scale extracted from the Rabi spectrum based on Super-Bloch oscillations of atoms in the OLC. Our proposal can be realized on the existing OLC platform without significant change. Under realistic existing experimental parameters of 87Sr OLC, we determine the optimal experimental conditions and obtain a sensitivity of 5μGal/Hz in the quantum projection noise limit, which is 50 times better than the previous method at the sub-millimeter scale under the same consideration. Another advantage of our proposal is that it is insensitive to the noise of the lattice laser, which contributes to the major uncertainty of the previous measurement (PRA 86, 033615). Our research will promote the development of OLC geoscopy.

DOI
10.1063/5.0192352

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Due to the excellent accuracy, the optical lattice clock (OLC) has not only achieved impressive results in frequency measurement but also gradually plays an important role in quantum precision measurement. In this paper, we propose a scheme for measuring gravity at the sub-millimeter scale extracted from the Rabi spectrum based on Super-Bloch oscillations of atoms in the OLC. Our proposal can be realized on the existing OLC platform without significant change. Under realistic existing experimental parameters of 87Sr OLC, we determine the optimal experimental conditions and obtain a sensitivity of 5μGal/Hz in the quantum projection noise limit, which is 50 times better than the previous method at the sub-millimeter scale under the same consideration. Another advantage of our proposal is that it is insensitive to the noise of the lattice laser, which contributes to the major uncertainty of the previous measurement (PRA 86, 033615). Our research will promote the development of OLC geoscopy.
Super-Bloch oscillations(SBOs) is giant Bloch oscillations (BOs) when applying both static and periodically driving force to free atoms in lattice at the condition that Bloch oscillations are close to integer times of driving frequencies. Rather than observe SBOs in real space, this paper presents a method to observe it using Rabi spectroscopy of Optical lattice clock(OLC). An effective model of OLC with atoms been added both static and time-periodical forces is derived. Based on that, we propose an experimental scheme and give the Rabi spectrum under lab achievable parameters. Utilizing the precision spectroscopy of OLC, force with a large range could be accurately measured by measuring the Period of SBOs. We also gave the best parameter condition of measuring gravity by calculating Fisher information. Our work paves the way to study other exotic dynamics behaviors in Floquet driving OLC.
Optical clocks operated on satellites are expected to open up new opportunities in time transfer, geodesy, fundamental physics, and satellite navigation. Here we demonstrate an important first step towards this goal: a modular, compact, optical lattice clock (OLC) system that achieves $2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ fractional uncertainty. The clock is operated with bosonic strontium and improves the performance of bosonic OLCs by a factor of 30. This has important implications for future use of bosonic OLCs in fundamental physics and metrology. We make use of the clock's metrological performance to measure, with independent clocks, the isotope shift of the $^{1}S_{0}\ensuremath{\rightarrow}^{3}P_{0}$ transitions of 88Sr^{88}\mathrm{Sr}88Sr and 87Sr^{87}\mathrm{Sr}87Sr, with an uncertainty of 12 mHz. The ratio of the transition frequencies is thus determined with $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ fractional uncertainty.
Optical atomic clocks have spurred a range of precision frequency comparison experiments and proposals including tests of general relativity, gravitational wave detection, and relativistic geodesy. Current measurements using optical atomic clocks are often limited by the coherence of the clock laser rather than the atomic samples used as a frequency reference. In order to overcome the performance limits imposed by clock laser coherence, we realize a multiplexed optical clock system where multiple spatially resolved ensembles each consisting of thousands of strontium atoms trapped in a 1D optical lattice function as separate atomic frequency references that can be simultaneously interrogated with a shared clock laser. This scheme allows us to make differential frequency comparisons with a quantum projection noise limited fractional instability of 9.7(4)×10−18/ √τ and a differential fractional uncertainty of 8.9×10−20 after 3.3 hours of averaging. We then use this system to perform a lab-based test of the gravitational redshift at the centimeter scale, where we measure a fractional frequency gradient of [−12.4±0.7stat ±2.5sys]×10−19/cm, consistent with the predicted value of 10.9×10−19/cm. Having demonstrated that our differential comparisons are no longer limited by the local oscillator, we turn to fundamental limits on atom–atom coherence. We perform a direct decay measurement of the natural lifetime of the excited clock state 3P0 in 87Sr, in which we use measurements of simultaneously loaded high and low density atomic ensembles and compare decay rates of 87Sr and 88Sr to help isolate natural lifetime decay from other population dynamics. We measure a lifetime of 167+79 −40, which is consistent with previously reported experimental and theoretical values. Lastly, we demonstrate a hyperfine-resolved readout scheme in 87Sr that converts depolarization errors during interrogation into erasure errors, extending coherence times between ensembles in our optical lattice clock up to 150s using spin-echo measurements. These results taken together demonstrate the advantages of differential clock measurements that aren’t limited by clock laser coherence and how to characterize and improve on the performance limits that arise in that regime.
We demonstrate the frequency comparison of two optical lattice clocks at the relative stabilities close to the quantum projection noise (QPN) limit of optical lattice clocks. This stable frequency comparison is accomplished by synchronous interrogations of two clocks by a common probe laser, which allows us to cancel out the probe laser's frequency noise. We perform the frequency comparison of a one-dimensional (1D) optical lattice clock with spin-polarized fermions 87Sr and a three-dimensional (3D) optical lattice clock with unity-occupation bosons 88Sr and achieve the Allan standard deviation of σγ(τ)=4×10-16 τ-1/2, which corresponds to the QPN limited stability for N=1,000 atoms and the spectrum linewidth γ=8 Hz. The relative stability reaches 1×10-17 with an averaging time of 1,600 s. Finally, we discuss the prospects to realize 10-18 fractional inaccuracies and the possible application of frequency comparison with synchronous interrogations to remote clocks' comparison for relativistic geodesy.
The optical lattice clocks were proved to be a powerful tool for precision measurement, like measuring the gravitational redshift at tiny gravity potential difference and monitoring the crustal deformations with ultrahigh accuracy. The Floquet optical lattice clock utilizes a time periodical acoustic wave acting on the optical lattice potential. Those atoms trapped in the lattice site will be compelled to move slightly with the modulated potential. These micromotions generate a series of Floquet quasi-energies which the atomic spectra would present for us. In virtue of Floquet engineering optical lattice theoretical model, the periodic acoustic wave signal acting on the lattice potential could be extracted. In this paper, we propose a novel way for acoustic sensing based on a 87Sr Floquet optical lattice clock. It may assist the traditional acoustic sensing technology based on fiber in achieving higher signal-noise ratio and accuracy. From the clockmaker's point of view, it may help us monitoring the environmental acoustic noise caused by vibrations and calibrate in time, especially when the optical clock operating in a movable carrier both on earth and space, what is even more important.
The quantum system under periodical modulation is the simplest path to understand the quantum nonequilibrium system because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase cannot be gauged out so that the physics can be dramatically changed. Here, we simultaneously modulate the frequency of the lattice laser and the Rabi frequency in an optical lattice clock (OLC) system. Thanks to the ultrahigh precision and ultrastability of the OLC, the relative phase could be fine-tuned. As a smoking gun, we observed the interference between two Floquet channels. Finally, by experimentally detecting the eigenenergies, we demonstrate the relation between the effective Floquet Hamiltonian and the one-dimensional topological insulator with a high winding number. Our experiment not only provides a direction for detecting the phase effect but also paves a way in simulating the quantum topological phase in the OLC platform.