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Register a new userDetermination of a high spatial resolution geopotential model using atomic clock comparisons
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Recent technological advances in optical atomic clocks are opening new perspectives for the direct determination of geopotential differences between any two points at a centimeter-level accuracy in geoid height. However, so far detailed quantitative estimates of the possible improvement in geoid determination when adding such clock measurements to existing data are lacking. We present a first step in that direction with the aim and hope of triggering further work and efforts in this emerging field of chronometric geodesy and geophysics. We specifically focus on evaluating the contribution of this new kind of direct measurements in determining the geopotential at high spatial resolution (~ 10 km). We studied two test areas, both located in France and corresponding to a middle (Massif Central) and high (Alps) mountainous terrain. These regions are interesting because the gravitational field strength varies greatly from place to place at high spatial resolution due to the complex topography. Our method consists in first generating a synthetic high resolution geopotential map, then drawing synthetic measurement data (gravimetry and clock data) from it, and finally reconstructing the geopotential map from that data using least squares collocation. The quality of the reconstructed map is then assessed by comparing it to the original one used to generate the data. We show that adding only a few clock data points (less than 1 % of the gravimetry data) reduces the bias significantly and improves the standard deviation by a factor 3. The effect of the data coverage and data quality on the results is investigated, and the trade-off between the measurement noise level and the number of data points is discussed.
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We compare two optical clocks based on the $^2$S$_{1/2}(F=0)to {}^2$D$_{3/2}(F=2)$ electric quadrupole (E2) and the $^2$S$_{1/2}(F=0)to {}^2$F$_{7/2}(F=3)$ electric octupole (E3) transition of $^{171}$Yb$^{+}$ and measure the frequency ratio $ u_{mathrm{E3}}/ u_{mathrm{E2}}=0.932,829,404,530,965,376(32)$. We determine the transition frequency $ u_{E3}=642,121,496,772,645.10(8)$ Hz using two caesium fountain clocks. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant $alpha$ to $1.0(1.1)times10^{-18}/mathrm{yr}$ and of the proton-to-electron mass ratio $mu$ to $-8(36)times10^{-18}/mathrm{yr}$. Using the annual variation of the Suns gravitational potential at Earth $Phi$, we improve limits for a potential coupling of both constants to gravity, $(c^2/alpha) (dalpha/dPhi)=14(11)times 10^{-9}$ and $(c^2/mu) (dmu/dPhi)=7(45)times 10^{-8}$.
According to general relativity theory (GRT), the geopotential difference (GD) can be determined by comparing the change in time difference between precise clocks using the precise point positioning (PPP) time transfer technique, referred to as the relativistic PPP time comparison approach. We focused on high-precision time comparison between two precise clocks for determining the GD using the relativistic PPP time transfer,and conducted simulation experiments to validate the approach. In the experiments, we consider three cases to evaluate the performance of the approach using clocks with different stabilities, namely, the frequency stabilities of the clocks equipped at three selected ground stations are respectively (Case 1), (Case 2), and (Case 3) at time period. Conclusions are drawn from the experimental results. First, high-precision clocks can significantly improve the accuracy for PPP time transfer, but the improvement is limited by measurement noises. Compared to Case 1, the long-term stabilities of OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. The frequency stabilities of Cases 1-3 are approximately 4.28*10-16, 4.00*10-17, and 3.22*10-17 at 10-day averaging time for OPMT-BRUX, respectively, and for PTBB-BRUX, these values are approximately 3.73*10-16, 8.17*10-17, and 4.64*10-17. Second, the geopotential difference between any two stations can be determined at the decimeter level, with its accuracy being consistent with the stabilities of the time links in Cases 1-3. In Case 3, the determined geopotential differences between OPMT and BRUX deviate from the EIGEN-6C4 model values by -0.64 m2/s2 with an uncertainty of 1.11 m2/s2, whereas the deviation error between PTBB and BRUX is 0.76 m2/s2 with an uncertainty of 1.79 m2/s2. The approach proposed in this study can be also applied to testing GRT.
Modern optical atomic clocks along with the optical fiber technology currently being developed can measure the geoid, which is the equipotential surface that extends the mean sea level on continents, to a precision that competes with existing technology. In this proceeding, we point out that atomic clocks have the potential to not only map the sea level surface on continents, but also look at variations of the geoid as a function of time with unprecedented timing resolution. The local time series of the geoid has a plethora of applications. These include potential improvement in the predictions of earthquakes and volcanoes, and closer monitoring of ground uplift in areas where hydraulic fracturing is performed.
Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.
We demonstrate a high-performance coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique (PPOP) in the pulsed regime, allowing the detection of high-contrast and narrow Ramsey-CPT fringes. The impact of several experimental parameters onto the clock resonance and short-term fractional frequency stability, including the laser power, the cell temperature and the Ramsey sequence parameters, has been investigated. We observe and explain the existence of a slight dependence on laser power of the central Ramsey-CPT fringe line-width in the pulsed regime. We report also that the central fringe line-width is commonly narrower than the expected Ramsey line-width given by $1/(2T_R)$, with $T_R$ the free-evolution time, for short values of $T_R$. The clock demonstrates a short-term fractional frequency stability at the level of $2.3 times 10^{-13}~tau^{-1/2}$ up to 100 seconds averaging time, mainly limited by the laser AM noise. Comparable performances are obtained in the conventional continuous (CW) regime, if use of an additional laser power stabilization setup. The pulsed interaction allows to reduce significantly the clock frequency sensitivity to laser power variations, especially for high values of $T_R$. This pulsed CPT clock, ranking among the best microwave vapor cell atomic frequency standards, could find applications in telecommunication, instrumentation, defense or satellite-based navigation systems.
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