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Physical Review A

Stability analysis in an optical lattice clock using the four-path measurement

Xiaotong Lu, Feng Guo, Jingjing Xia, Yanyan Liu, Benquan Lu, Hong Chang

Published Feb 13, 2024• 1 citation
Publisher

Abstract

In this paper, we propose a method for identifying the contribution of various sources of noise to the instability of an optical lattice clock. These sources include Dick noise, quantum projection noise, shot noise, and technical noise. By measuring the clock instability at four different sets of parameters, we can determine the frequency fluctuations due to each type of noise separately. Furthermore, we can accurately extract the absolute number of atoms, the photon number detected per atom by the photoelectric detector, and the root mean square fluctuations of the atom number. We demonstrate the effectiveness of our approach through numerical simulations, showcasing the ability to determine these parameters with an uncertainty of less than 10%. Specifically, a remarkable uncertainty of 1% can be achieved when determining the atom number.

DOI
10.1103/physreva.109.023111

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Optical lattice clocks demonstrate advantages in metrology and frontier physics because of their high stability.Here, we present approaches to enhancing the stability by decoupling the noise related to the short-term and long-term stability.For the short-term stability, we optimize the clock laser by decoupling the frequency noise, and optimize each noise contribution individually until it is below the thermal noise limit.For the long-term stability, we introduce a method to decouple the instability caused by systematic effects.Having identified that the collision frequency shift was the main limiting factor in our systems, we thus optimized the atom number fluctuations in optical lattices.Through targeted optimization, we achieve a synchronous comparison of two clocks with an average stability of 3.2 × 10 -16 = τ p and a long-term stability of 2.4 × 10 -18 at 8000 s.This work provides an analytical framework for enhancing optical clock stability.

Chinese Optics Letters•Jan 1, 2025•2 citations
In this paper, we propose a method for identifying the contribution of various sources of noise to the instability of an optical lattice clock. These sources include Dick noise, quantum projection noise, shot noise, and technical noise. By measuring the clock instability at four different sets of parameters, we can determine the frequency fluctuations due to each type of noise separately. Furthermore, we can accurately extract the absolute number of atoms, the photon number detected per atom by the photoelectric detector, and the root mean square fluctuations of the atom number. We demonstrate the effectiveness of our approach through numerical simulations, showcasing the ability to determine these parameters with an uncertainty of less than 10%. Specifically, a remarkable uncertainty of 1% can be achieved when determining the atom number.
We propose a method that enables the precise determination of the number of atoms in a Dick-noise-free optical lattice clock, by effectively addressing quantum projection noise. Our approach relies on conducting stability measurements at three distinct parameter sets, allowing us to differentiate between quantum projection noise, photon shot noise, and technical noise. Importantly, it enables accurate extraction of the atom number, even in the presence of photon shot noise and technical noise. We utilize numerical simulations to validate our approach, optimize the modulation parameters for minimal uncertainty, and investigate the impact of atom number fluctuations on the determinacy of our results. The numerical results show the validity of our method and demonstrate an estimated uncertainty in the atom number that is below 4% with 6.7 h measurement, provided that the standard deviation of atom number fluctuation is kept below 0.14 times the average atom number.
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.
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 an analysis of the different types of noise from the detection and interrogation laser in our strontium lattice clock. We develop a noise model showing that in our setup quantum projection noise-limited detection is possible if more than 130 atoms are interrogated. Adding information about the noise spectrum of our clock laser with sub-${10}^{\ensuremath{-}16}$ fractional frequency instability allows one to infer the clock stability for different modes of operation. Excellent agreement with experimental observations for the instability of the difference between two interleaved stabilizations is found. We infer a clock instability of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}/\sqrt{\ensuremath{\tau}}$ as a function of averaging time $\ensuremath{\tau}$ expressed in seconds for normal clock operation.
SummaryThe short-term frequency instability of the best optical atomic clock lies in the mid 10−17. However, the Dick effect is still an obstacle for a single operational clock closely followed by the quantum projection noise. To improve the frequency stability of the strontium optical lattice clock, we present a quantum non-demolition detection scheme based on the cavity mediated interaction between the atoms and a probe light that has a large-frequency detuning to the atomic resonance, aiming to bring the detection scheme proposed in [1] to the quantum regime. We obtained a rather small photon scattering rate, measured to be less than 0.1 photon/μs/atom, which allows us to not only preserve the atoms in the lattice but also the atomic wave function as long as the total probe time is on the order of a few microseconds. The detection noise for the number of atoms is 48/√photons atoms, implying that the frequency stability can surpass the standard quantum limit when the number of trapped atoms is larger than 2.3×104with spin squeezing protocols.
Optical lattice clocks demonstrate advantages in metrology and frontier physics because of their high stability.Here, we present approaches to enhancing the stability by decoupling the noise related to the short-term and long-term stability.For the short-term stability, we optimize the clock laser by decoupling the frequency noise, and optimize each noise contribution individually until it is below the thermal noise limit.For the long-term stability, we introduce a method to decouple the instability caused by systematic effects.Having identified that the collision frequency shift was the main limiting factor in our systems, we thus optimized the atom number fluctuations in optical lattices.Through targeted optimization, we achieve a synchronous comparison of two clocks with an average stability of 3.2 × 10 -16 = τ p and a long-term stability of 2.4 × 10 -18 at 8000 s.This work provides an analytical framework for enhancing optical clock stability.