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Register a new userFormulation to test gravitational redshift based on the tri-frequency combination of ACES frequency links
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Atomic Clock Ensemble in Space (ACES) is an ESA mission mainly designed to test gravitational redshift with high-performance atomic clocks in space and on the ground. A crucial part of this experiment lies in its two-way Microwave Link (MWL), which uses the uplink of carrier frequency 13.475 GHz (Ku band) and downlinks of carrier frequencies 14.70333 GHz (Ku band) and 2248 MHz (S band) to transfer time and frequency. The formulation based on the time comparison has been studied for over a decade. However, there are advantages of using frequency comparison instead of time comparison to test gravitational redshift. Hence, we develop a tri-frequency combination (TFC) method based on the measurements of the frequency shifts of three independent MWLs between ACES and a ground station. The potential scientific object requires stabilities of atomic clocks at least $3times10^{-16}$/day, so we must consider various effects, including the Doppler effect, second-order Doppler effect, atmospheric frequency shift, tidal effects, refraction caused by the atmosphere, and Shapiro effect, with accuracy levels of tens of centimeters. The ACES payload will be launched as previously planned in the middle of 2021, and the formulation proposed in this study will enable testing gravitational redshift at an accuracy level of at least $2times10^{-6}$, which is more than one order higher than the present accuracy level of $7times10^{-5}$.
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We investigate the performance of the upcoming ACES (Atomic Clock Ensemble in Space) space mission in terms of its primary scientific objective, the test of the gravitational redshift. Whilst the ultimate performance of that test is determined by the systematic uncertainty of the on-board clock at 2-3 ppm, we determine whether, and under which conditions, that limit can be reached in the presence of colored realistic noise, data gaps and orbit determination uncertainties. To do so we have developed several methods and software tools to simulate and analyse ACES data. Using those we find that the target uncertainty of 2-3 ppm can be reached after only a few measurement sessions of 10-20 days each, with a relatively modest requirement on orbit determination of around 300 m.
We show that Wolf et al.s 2011 analysis in Class. Quant. Grav. v28, 145017 does not support their conclusions, in particular that there is no redshift effect in atom interferometers except in inconsistent dual Lagrangian formalisms. Wolf et al. misapply both Schiffs conjecture and the results of their own analysis when they conclude that atom interferometers are tests of the weak equivalence principle which only become redshift tests if Schiffs conjecture is invalid. Atom interferometers are direct redshift tests in any formalism.
We carried out a computer simulation of a large gravitational wave (GW) interferometer using the specifications of the LIGO instruments. We find that if in addition to the carrier, a single sideband offset from the carrier by the fsr frequency (the free spectral range of the arm cavities) is injected, it is equally sensitive to GW signals as is the carrier. The amplitude of the fsr sideband signal in the DC region is generally much less subject to noise than the carrier, and this makes possible the detection of periodic signals with frequencies well below the so-called seismic wall.
Aims. We study the 2D spectral line profile of HARPS (High Accuracy Radial Velocity Planet Searcher), measuring its variation with position across the detector and with changing line intensity. The characterization of the line profile and its variations are important for achieving the precision of the wavelength scales of 10^{-10} or 3.0 cm/s necessary to detect Earth-twins in the habitable zone around solar-like stars. Methods. We used a laser frequency comb (LFC) with unresolved and unblended lines to probe the instrument line profile. We injected the LFC light (attenuated by various neutral density filters) into both the object and the reference fibres of HARPS, and we studied the variations of the line profiles with the line intensities. We applied moment analysis to measure the line positions, widths, and skewness as well as to characterize the line profile distortions induced by the spectrograph and detectors. Based on this, we established a model to correct for point spread function distortions by tracking the beam profiles in both fibres. Results. We demonstrate that the line profile varies with the position on the detector and as a function of line intensities. This is consistent with a charge transfer inefficiency (CTI) effect on the HARPS detector. The estimate of the line position depends critically on the line profile, and therefore a change in the line amplitude effectively changes the measured position of the lines, affecting the stability of the wavelength scale of the instrument. We deduce and apply the correcting functions to re-calibrate and mitigate this effect, reducing it to a level consistent with photon noise.
Gravitational waves are perturbations of the metric of space-time. Six polarizations are possible, although general relativity predicts that only two such polarizations, tensor plus and tensor cross are present for gravitational waves. We give the analytical formulas for the antenna response functions for the six polarizations which are valid for any equal-arm interferometric gravitational-wave detectors without optical cavities in the arms.The response function averaged over the source direction and polarization angle decreases at high frequencies which deteriorates the signal-to-noise ratio registered in the detector. At high frequencies, the averaged response functions for the tensor and breathing modes fall of as $1/f^2$, the averaged response function for the longitudinal mode falls off as $1/f$ and the averaged response function for the vector mode falls off as $ln(f)/f^2$.
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