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Acta Physica Sinica

Density shift measurement and synchronous frequency comparison based on in situ imaging technique

Xiaohua Hu, Xiaotong Lu, Xiao-Fei Zhang, Hong Chang

Published Jan 1, 2022• 0 citations
Publisher

Abstract

Precision measurement of the density shift caused by the interaction among neutral atoms trapped in an optical lattice has important applications in the study of multi-body interaction and the realization of high-performance optical lattice clocks. The common methods of measuring the density are the self-comparison technique and frequency comparison between two optical lattice clocks. Both methods are based on the identical density shift coefficient and should interrelatedly operate the clock at high- and low-density state, respectively. The precision of self-comparison method is limited by the Dick effect. The synchronous frequency comparison between two optical lattice clocks can realize the precision beyond the Dick limit. However, both methods can only obtain the average density shift and ignore the fact that the magnitude of the density shift is different over the lattice sites as inhomogeneous density distribution in the lattice. In this paper, the synchronous frequency comparison technique based on in situ imaging is used to accurately measure the density shift coefficient of optical lattice clock. Atoms in the optical lattice are simultaneously and independently excited by the same clock laser beam, and the clock transition probability of 11 uncorrelated regions of the optical lattice is simultaneously detected by in situ imaging. Thus, the clock laser noise, which is the root cause of the Dick effect, is common-mode rejected as the frequency difference between uncorrelated regions is measured by the clock transition spectrum. Beyond the Dick-noise-limited stability, the stability of synchronous frequency comparison between uncorrelated regions is consistent with the limit resulting from the atom detection noise. Between the center and margin of the lattice, the differential shifts of the black-body radiation shift, lattice AC Stark shift, probe Stark shift, DC Stark shift, and quadratic Zeeman shift are all below 5 × 10–6 Hz, which is three orders of magnitude smaller than the density shift and can be ignored in this experiment. Benefitting from the inhomogeneous distribution of atom number and negligible external field gradient in the optical lattice, the compared frequency shift between uncorrelated regions indicates the density shift. By measuring the relationship between the density shift and atom difference, the density shift coefficient is determined as –0.101(3) Hz/atom/site (with a measurement time of 103 s), and the fractional measurement uncertainty of the mean density shift of our system is 1.5 × 10–17.

DOI
10.7498/aps.71.20220600

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Precision measurement of the density shift caused by the interaction among neutral atoms trapped in an optical lattice has important applications in the study of multi-body interaction and the realization of high-performance optical lattice clocks. The common methods of measuring the density are the self-comparison technique and frequency comparison between two optical lattice clocks. Both methods are based on the identical density shift coefficient and should interrelatedly operate the clock at high- and low-density state, respectively. The precision of self-comparison method is limited by the Dick effect. The synchronous frequency comparison between two optical lattice clocks can realize the precision beyond the Dick limit. However, both methods can only obtain the average density shift and ignore the fact that the magnitude of the density shift is different over the lattice sites as inhomogeneous density distribution in the lattice. In this paper, the synchronous frequency comparison technique based on in situ imaging is used to accurately measure the density shift coefficient of optical lattice clock. Atoms in the optical lattice are simultaneously and independently excited by the same clock laser beam, and the clock transition probability of 11 uncorrelated regions of the optical lattice is simultaneously detected by in situ imaging. Thus, the clock laser noise, which is the root cause of the Dick effect, is common-mode rejected as the frequency difference between uncorrelated regions is measured by the clock transition spectrum. Beyond the Dick-noise-limited stability, the stability of synchronous frequency comparison between uncorrelated regions is consistent with the limit resulting from the atom detection noise. Between the center and margin of the lattice, the differential shifts of the black-body radiation shift, lattice AC Stark shift, probe Stark shift, DC Stark shift, and quadratic Zeeman shift are all below 5 × 10–6 Hz, which is three orders of magnitude smaller than the density shift and can be ignored in this experiment. Benefitting from the inhomogeneous distribution of atom number and negligible external field gradient in the optical lattice, the compared frequency shift between uncorrelated regions indicates the density shift. By measuring the relationship between the density shift and atom difference, the density shift coefficient is determined as –0.101(3) Hz/atom/site (with a measurement time of 103 s), and the fractional measurement uncertainty of the mean density shift of our system is 1.5 × 10–17.
In this paper, we demonstrate in situ synchronous frequency comparison between distinct regions in a one-dimensional optical lattice. The synchronous comparison instability is well below the Dick limit and agrees with the limit induced by atomic detection noise. The absolute atom number is extracted from the synchronous comparison instability with an uncertainty below 3%. Surpassing the performance of absorption imaging, this method provides a way to directly and precisely determine the absolute atom number from detection noise. Taking advantage of the inhomogeneous density distribution over the whole lattice, the density shift can also be conveniently measured by this synchronous frequency comparison method. Inconsistent with the expectation of the linear relationship between density shift and atom number difference, nonlinearity is observed, indicating that the assumption of an identical density shift coefficient over the whole lattice is not always safe.
We present a synchronous frequency comparison method based on one cold-atom ensemble by using the dual-excitation spectrum technique, which can simultaneously detect the probabilities of two different clock transitions. We experimentally verify this synchronous frequency comparison method between |mF|=9/2 and |mF|=7/2 in a one-dimensional 87Sr optical lattice clock and the comparison instability is well below the Dick limit. We also extend the dual-excitation spectrum method to shorten the clock feedback cycle by a half in optical lattice clocks and experimentally demonstrate that the interleaved self-comparison instability is 1.4 times lower than that of the traditional operation method.
Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two 87Sr^{87}\mathrm{Sr}87Sr lattice systems using a laser with a thermal noise floor of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with $\ensuremath{\sim}{10}^{3}$ atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be $\ensuremath{-}3.11\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ with an uncertainty of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$.
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.
Frequency metrology underpins precise measurements. At the forefront of this field are optical clocks which can perform measurements that are accurate to more digits than those in the number representing seconds elapsed from the beginning of the universe. Frequency estimation errors in the operation of optical clocks lead to frequency instability, prohibiting them from reaching high accuracies on short to medium time scales, and limiting access to interesting measurements of the atomic environment and exotic external perturbations such as gravity fields or fields of fundamentally new physical origins. Optical lattice traps are typically employed in state-of-the-art optical clocks to suppress Doppler effects. By carefully tuning the optical lattice to the magic wavelength, unwanted Stark shifts can be suppressed significantly, allowing operation with thousands of atoms and minimising the fundamental source of frequency estimation errors, namely the quantum projection noise, to around 3 × 10−17 at 1 s. In this thesis, the status of the two Strontium optical lattice clocks at NPL, Sr1 and Sr2, is presented going over a few interesting measurement campaigns from the past years involving Sr1 and the latest experimental efforts to re-enable operation of Sr2. A model of clock stability is developed by incorporating known and new frameworks to characterise the relation between the operating parameters of optical clocks and their performance, with relevance to the NPL lattice clocks and beyond. In particular, a method is identified for addressing the main technical noise for optical lattice clocks, the Dick effect, which typically has a magnitude of 10−16 at 1 s and prevents optical lattice clocks from reaching the quantum projection noise level. By taking advantage of dynamical decoupling we can engineer an optimised duty cycle with benefits in general for systems limited by the optical coherence of the clock laser. Moreover, a study of other noise sources in the NPL lattice clocks is conducted using synchronous measurements between Sr1 and Sr2, revealing a large contribution from linear Zeeman shifts, also at the 10−16 level, and a plan to tackle them is detailed. A hybrid clock architecture is discussed showing how optical lattice clocks can improve the optical coherence of ion clocks thanks to their higher servo rate, and a preliminary experimental demonstration is reported. Finally, a new type of spectroscopy is presented which completely avoids aliasing of linear Zeeman shifts by simultaneously driving transitions with opposite Zeeman sensitivities. Such a technique also enables the continuous interrogation of atoms, a crucial missing component in the Dick-free conveyor belt lattice clock concept heralded as the next standard of stable optical clocks.
Abstract Optical clocks are the most precise measurement devices. Here we experimentally characterize one such clock based on the 1S0-3P0 transition of neutral 171Yb atoms confined in an optical lattice. Given that the systematic evaluation using an interleaved stabilization scheme is unable to avoid noise from the clock laser, synchronous comparisons against a second 171Yb lattice system were implemented to accelerate the evaluation. The fractional instability of one clock falls below 4 × 10−17 after an averaging over a time of 5,000 seconds. The systematic frequency shifts were corrected with a total uncertainty of 1.7 × 10−16. The lattice polarizability shift currently contributes the largest source. This work paves the way to measuring the absolute clock transition frequency relative to the primary Cs standard or against the International System of Units (SI) second.