arXiv subjects

Yu-Jie Tan

Publications and source records attributed to Yu-Jie Tan.

At least 19 recordsLinked to original sources

arXiv2026

Relativistic Modeling for Solid Earth Tide Estimation via Space-to-Ground Clock Comparison

With the rapid development of modern atomic clock technology, their unprecedented precision elevates them from timekeeping tools to gravitational potential sensors, thereby fostering the highly interdisciplinary field of Relativistic Geodesy. Given the potential for high-precision clock networks to detect periodic gravitational variations, it is imperative to assess their capability to invert solid Earth tide parameters via space-to-ground links in the presence of complex observational noise. To this end, we incorporate Earth's gravitational potential, direct lunisolar tidal potentials, and solid Earth tide effects into a high-precision relativistic framework for space-to-ground clock comparisons. By employing a three-link Doppler cancellation configuration to isolate the target signal, we perform numerical simulations for an inclined geosynchronous orbit satellite to analyze the effects of clock instability and colored precise orbit determination errors on parameter extraction. Our findings reveal that while high orbital altitudes cause severe collinearity between individual Love numbers, an effective parameter combining the $h_2$ and $k_2$ Love numbers successfully converges to a stable estimate within a 30-day continuous observation window. Furthermore, sensitivity analysis demonstrates that extraction accuracy is currently limited by clock stability rather than radial precise orbit determination errors.

gr-qc↗

arXiv2025

On angular dependent response to gravitational-wave signals for time-delay interferometry combinations

Space-based gravitational wave (GW) detectors are designed for wave sources in the millihertz band with different locations and orientations. Time-delay interferometry (TDI) technique is an indispensable ingredient in space-borne GW detection that effectively suppresses the laser phase noise. The abundant TDI solutions derived in the literature also feature distinct angular-dependent sensitivities. Because a GW source's angular location is unknown prior to the signals' detection, a solid-angle average is often performed when analyzing the sensitivity function of a given TDI combination. The present study explores the angular dependence of the detector's sensitivity. This detail is relevant, because once the initial detection is achieved, the source's location can be extracted and used to provide information on a refined TDI combination tailored for the specific GW source. As the TDI technique is a post-processing algorithm, such a procedure can be implemented in practice. We evaluate the angular dependence of the detector's response function to the GW signals for different TDI combinations as a function of the orientation angles. Moreover, we classify the response functions into seven categories at the low-frequency limit, leveraging the characteristics of the underlying geometrical TDI combinations. By further averaging out the azimuthal angle $\phi_D$ in the detector's plane, the main features of the resulting response functions and their zenithal dependence with respect to the GW source are scrutinized. The findings presented in this work provide pertinent insights for ongoing space-borne detector programs.

gr-qc↗

arXiv2025

Relativistic formulation for dual one-way Doppler Cancellation Scheme observables for gravitational redshift tests

Gravitational redshift is a fundamental prediction of general relativity and a sensitive probe of possible deviations from it. Motivated by recent progress in optical clocks and satellite-ground frequency transfer, we study a dual one-way optical Doppler-cancellation observable for space-based gravitational-redshift tests. The corresponding observable is constructed by combining oppositely directed one-way frequency observables, namely an uplink and a downlink whose measurements are recorded at the receiving terminals and combined in post-processing. We derive the corresponding relativistic observable up to order $c^{-3}$, as required for future $10^{-18}$-level clock comparisons. The resulting combination suppresses the first-order Doppler contribution to second order while retaining the gravitational-redshift signal. We analyze the dominant residual effects, including higher-order Doppler terms, atmospheric delay, Shpiro delay, tidal effects, clock synchronization etc. The formalism is applied to representative satellite-ground configurations, including an ACES/CSS-like low-Earth-orbit configuration and a geostationary Earth-orbit satellite. The results show that the dual one-way optical DCS configuration provides a useful relativistic framework and error-modeling reference for future $10^{-18}$-level space-based gravitational-redshift tests, while highlighting the need for stringent clock synchronization.

gr-qc↗

arXiv2025

Experimental demonstration of the clock asynchrony model in space-borne gravitational wave detection

Space-borne gravitational wave detection will open the observation window in the 0.1 mHz$-$1 Hz bandwidth, playing a crucial role in the development of cosmology and physics. Precise clock synchronization among satellites is essential for the accurate detection of gravitational wave signals. However, the independent clock counting mechanisms of each satellite pose a significant challenge. This work reports the mathematical model of clock asynchrony, which is mainly dominated by the constant term factor and the linear term factor. Moreover, it experimentally verifies the clock asynchronization technique based on a dual-phasemeter system. Through experimentation, the impacts of these two aspects of clock asynchrony were confirmed, and post-processing techniques were employed to reduce these impacts to as low as $\rm 2π\times 10^{-6} rad/Hz^{1/2}@ 3mHz$. Specifically, the constant term factor is measured by Time-delay Interferometry Ranging (TDIR), while the linear term factor can be gauged by clock transmission link. This study provides a reference for understanding the clock asynchrony mechanism and processing clock synchronization issues. Additionally, a low additional noise clock synchronization test system is introduced to support such measurements.

gr-qc↗

arXiv2025

Constraints on violation of Lorentz symmetry with clock-comparison redshift experiments

Lorentz symmetry is a cornerstone of both the General relativity and Standard Model and its experimental verification deepens our understanding of nature. This paper focuses on the investigation of Lorentz violations with the context of clock comparison experiments in the framework of Standard Model Extension (SME). Considering matter-gravity coupling sector, we provide a generic frame to study the sensitivities of Lorentz-violating coefficients for three distinct types of clock redshift tests, including the traditional gravitational redshift test, null-redshift test I and null-redshift test II. Each of these tests is sensitivity to different combinations of Lorentz-violating coefficients. By using the current clock comparison results, we estimate the limits of SME coefficients at level of parts in $10^{4}$ down to parts in $10^{7}$. Better sensitivity may be achieved in the clock comparisons by using the state-of-the-art optical clocks. Additionally considering relativistic factors in null-redshift I, the frequency comparison result of E2 and E3 transitions of Yb$^{+}$ can set the limit $c^{e}_{00}=(7.4\pm9.3)\times10^{-9}$ in the electron sector. Our analysis demonstrates that clock-comparison redshift experiments may contribute to explore the vast parameters space on searching for the Lorentz violation.

gr-qc↗

arXiv2025

Preliminary Sensitivity Study for a Gravitational Redshift Measurement with China's Lunar Exploration Project

General relativity (GR) is a highly successful theory that describes gravity as a geometric phenomenon. The gravitational redshift, a classic test of GR, can potentially be violated in alternative gravity theories, and experimental tests on this effect are crucial for our understanding of gravity. In this paper, considering the space-ground clock comparisons with free-space links, we discuss a high-precision Doppler cancellation-based measurement model for testing gravitational redshift. This model can effectively reduce various sources of error and noise, reducing the influences of the first-order Doppler effect, atmospheric delay, Shapiro delay, etc. China's Lunar Exploration Project (CLEP) is proposed to equip the deep-space H maser with a daily stability of $2\times10^{-15}$, which provides an approach for testing gravitational redshift. Based on the simulation, we analyze the space-ground clock comparison experiments of the CLEP experiment, and simulation analysis demonstrates that under ideal condition of high-precision measurement of the onboard H-maser frequency offset and drift, the CLEP experiment may reach the uncertainty of $3.7\times10^{-6}$ after a measurement session of 60 days. Our results demonstrate that if the issue of frequency offset and drift is solved, CLEP missions have a potential of testing the gravitational redshift with high accuracy. This manuscript has been accepted for publication in Classical and Quantum Gravity. DOI 10.1088/1361-6382/ad4ae2

gr-qc↗

arXiv2025

Progress of the TianQin project

TianQin is a future space-based gravitational wave observatory targeting the frequency window of $10^{-4}$ Hz $\sim 1$ Hz. A large variety of gravitational wave sources are expected in this frequency band, including the merger of massive black hole binaries, the inspiral of extreme/intermediate mass ratio systems, stellar-mass black hole binaries, Galactic compact binaries, and so on. TianQin will consist of three Earth orbiting satellites on nearly identical orbits with orbital radii of about $10^5$ km. The satellites will form a normal triangle constellation whose plane is nearly perpendicular to the ecliptic plane. The TianQin project has been progressing smoothly following the ``0123" technology roadmap. In step ``0", the TianQin laser ranging station has been constructed and it has successfully ranged to all the five retro-reflectors on the Moon. In step ``1", the drag-free control technology has been tested and demonstrated using the TianQin-1 satellite. In step ``2", the inter-satellite laser interferometry technology will be tested using the pair of TianQin-2 satellites. The TianQin-2 mission has been officially approved and the satellites will be launched around 2026. In step ``3", i.e., the TianQin-3 mission, three identical satellites will be launched around 2035 to form the space-based gravitational wave detector, TianQin, and to start gravitational wave detection in space.

gr-qc↗

arXiv2023

Testing Lorentz symmetry with space-based gravitational-wave detectors

Lorentz symmetry (LS), one of the most fundamental physical symmetries, has been extensively studied in the context of quantum gravity and unification theories. Many of these theories predict a LS violation, which could arise from the discreteness of spacetime, or extra dimensions. Standard-model extension (SME) is an effective field theory to describe Lorentz violation whose effects can be explored using precision instruments such as atomic clocks and gravitational-wave (GW) detectors. Considering the pure-gravity sector and matter-gravity coupling sector in the SME, we studied the leading Lorentz-violating modifications to the time delay of light and the relativistic frequency shift of the clock in the space-based GW detectors. We found that the six data streams from the GW mission can construct various combinations of measurement signals, such as single-arm round-trip path, interference path, triangular round-trip path, etc. These measurements are sensitive to the different combinations of SME coefficients and provide novel linear combinations of SME coefficients different from previous studies. Based on the orbits of TianQin, LISA, and Taiji missions, we calculated the response of Lorentz-violating effects on the combinations of the measurement signal data streams. Our results allow us to estimate the sensitivities for SME coefficients: $10^{-6}$ for the gravity sector coefficient $\bar{s}^{TT}$, $10^{-6}$ for matter-gravity coupling coefficients $(\bar{a}^{(e+p)}_{\text{eff}})_{T}$ and $\bar{c}^{(e+p)}_{TT}$, and $10^{-5}$ for $(\bar{a}^{n}_{\text{eff}})_{T}$ and $\bar{c}^{n}_{TT}$.

gr-qc↗

arXiv2023

Revisitation of algebraic approach for time delay interferometry

Time Delay Interferometry (TDI) is often utilized in the data pre-processing of space-based gravitational wave detectors, primarily for suppressing laser frequency noise. About twenty years ago, assuming armlengths remain constant over time, researchers presented comprehensive mathematical descriptions for the first-generation and modified first-generation TDI. However, maintaining a steady distance between satellites is pragmatically challenging. Hence, the operator equation that neutralizes laser frequency noise, though provided, was deemed difficult to resolve. In this paper, we solve this equation in the context of a non-static scenario where distances between spacecrafts vary over time. Surprisingly, contrary to what previous researchers thought, the study reveals that the equation has only the zero solution, which suggests that no nonzero TDI combination can entirely suppress laser frequency noise under time-varying armlengths. This necessitates the persistent search for second-generation TDI combinations through alternative methods besides directly solving the operator equation. We establish the connections between TDI combinations of different generations and propose a search strategy for finding higher-generation TDI combinations by using generators of lower-generation TDI. The findings contribute to the ongoing discussion on gravitational waves and provide a novel insight into the hurdles faced in space-based gravitational wave detection.

physics.ins-det↗

arXiv2023

Testing the polarization of gravitational wave background with LISA-TianQin network

While general relativity predicts only two tensor modes for gravitational wave polarization, general metric theories of gravity allows up to four additional modes, including two vector and two scalar modes. Observing the polarization modes of gravitational waves could provide a direct test of the modified gravity. The stochastic gravitational wave background (SGWB), which may be detected by space-based laser-interferometric detectors at design sensitivity, will provide an opportunity to directly measure alternative polarization. In this paper, we investigate the performance of the LISA-TianQin network for detecting alternative polarizations of stochastic backgrounds, and propose a method to separate different polarization modes. First, we generalize the small antenna approximation to compute the overlap reduction functions for SGWB with arbitrary polarization, which is suitable for any time-delay interferometry combination. Then we analyze the detection capability of LISA-TianQin for SGWB with different polarizations. Based on the LISA-TianQin orbital characteristics, we propose a method to distinguish different polarization modes from their mixed data. Compared with ground-based detectors, the LISA-TianQin network is more capable of resolving polarizations of SGWB. In particular, the LISA-TianQin network has the potential to resolve two scalar modes that ground-based detectors cannot.

gr-qc↗

arXiv2023

Electrostatic effect due to patch potentials between closely spaced surfaces

The spatial variation and temporal variation in surface potential are important error sources in various precision experiments and deserved to be considered carefully. In the former case, the theoretical analysis shows that this effect depends on the surface potentials through their spatial autocorrelation functions. By making some modification to the quasi-local correlation model, we obtain a rigorous formula for the patch force, where the magnitude is proportional to ${\frac{1}{{{a}^{2}}}{{(\frac{a}{w})}^{β(a/w)+2}}}$ with ${a}$ the distance between two parallel plates, ${w}$ the mean patch size, and $β$ the scaling coefficient from ${-2}$ to ${-4}$. A torsion balance experiment is then conducted, and obtain a 0.4 mm effective patch size and 20 mV potential variance. In the latter case, we apply an adatom diffusion model to describe this mechanism and predicts a ${f^{-3/4}}$ frequency dependence above 0.01 ${\rm mHz}$. This prediction meets well with a typical experimental results. Finally, we apply these models to analyze the patch effect for two typical experiments. Our analysis will help to investigate the properties of surface potentials.

cond-mat.soft↗

arXiv2022

Arm locking in conjunction with time-delay interferometry

A crucial challenge to the ongoing endeavor of spaceborne gravitational wave (GW) detection resides in the laser phase noise, typically 7 to 8 orders of magnitude above the inevitable noise. The arm locking technique was proposed to suppress the noise in pre-stabilized laser beams. Based on the feedback control theory, it is implemented by appropriate design of the signal routing architecture, particularly the controllers' transfer functions. Theoretically and experimentally, the technique has been demonstrated to be capable of suppressing the laser phase noise by approximately 2-4 orders of magnitude while taking into account various aspects such as the gain and distribution of nulls in the Bode plot and the laser frequency pulling associated with the Doppler frequency subtraction. Consequently, the resultant noise floor is composed of the sources attributed to the clock jitter, optical bench motion, test mass fluctuations, shot-noise phase fluctuations at the photodetectors, whereas the magnitudes of these noises largely remain unchanged during the process. Besides, the original GW signals are deformed through the arm-locking control loop and therefore bear specific features governed by the associated arm-locking scheme. Nonetheless, the remaining laser phase noise from the arm-locking feedback routing settles within the capability threshold of the time-delay interferometry (TDI). In this regard, it is generally understood that the output of arm locking furnishes the input of TDI, through which the residual noise is further reduced to the desired level at a post-processing stage. In this work, we investigate the specific schemes regarding how the arm locking output is processed further by the TDI algorithm. Specific forms of the TDI combinations are derived in accordance with suppressed laser phase noise and deformed signals of GW.

gr-qc↗

arXiv2022

Qusinormal oscillations and late-time tail of massless scalar perturbations of a magnetized black hole in Rastall gravity

In this paper, we study the quasinormal mode and late-time tail of charged massless scalar perturbations of a black hole in the generalized Rastall gravity. The black hole metric in question is spherically symmetric, accompanied by a power-Maxwell field surrounded by a quintessence fluid. It is shown that the massless scalar field, when {\it dressed up} with the magnetic field, acquires an effective mass which, in turn, significantly affects the properties of the resultant quasinormal oscillations and late-time tails. To be specific, the quasinormal frequencies become distorted and might even be unstable for particular spacetime configurations. Also, the exponent of the usual power-law tail is modified in accordance with the modification in the structure of the branch cut of the retarded Green's function. In particular, as the effective mass is generated dynamically due to the presence of the magnetic field, one may consider a process through which the field is gradually removed from the spacetime configuration. In this context, while the quasinormal oscillations converge to the case of massless perturbations, we argue that the properties of resultant late-time tails do not fall back to their massless counterpart. The relevant features are investigated by numerical and analytic approaches.

gr-qc↗

arXiv2022

Recent experimental progress on probing Lorentz Violation in pure gravity for d=6

Short-range experiment with striped design of the test and source masses offers uniquely sensitive probes for Lorentz Violation. In our previous work, we proposed to combine the horizontally and vertically striped experiments to constrain the violating parameters. Here, we further point out adopting the vertically striped structure with the experimental setup placed at two azimuth angles, which has more experimental operability. For the experiment, we have completed the assembly and measurement of the torsion pendulum.

hep-ph↗

arXiv2022

Full analytic expression of overlap reduction function for gravitational wave background with pulsar timing arrays

Pulsar timing array (PTA) is expected to detect gravitational wave background (GWB) in the nanohertz band within the next decade. This provides an opportunity to test the gravity theory and cosmology. A typical data analysis method to detect GWB is cross-correlation analysis. The overlap reduction function (ORF) plays an important role in the correlation data analysis of GWB. The present approach to dealing with the intricate integration in ORF is to use short-wave approximation to drop out the tricky terms. In this paper, we provide the full analytic expression of the ORF for PTA without any approximation for all possible polarizations allowed by modifications of general relativity. Compared with the numerical simulation and short-wave approximation, our results are more efficient and widely applicable. Especially for the scalar-longitudinal mode where the short-wave approximation is not available, our analytical expression is particularly significant.

gr-qc↗

arXiv2022

Geometric approach for the modified second generation time delay interferometry

The time delay interferometry (TDI) is an algorithm proposed to suppress the laser frequency noise in space-borne gravitational wave detectors. As a post-processing technique, it is implemented by constructing a virtual equal arm interferometer through an appropriate combination of the time-shifted data streams. Such an approach is tailored to the intrinsic feature of the space-based gravitational wave detection, namely, the distances between spacecraft are governed by the orbit dynamics and thus can not be held constant. Among different implementations, the geometric TDI was introduced as a method of exhaustion to evaluate the second-generation TDI combinations. The applications of the algebraic approach based on computational algebraic geometry, on the other hand, are mostly restricted to the first and the modified first-generation TDI. Besides, geometric TDI furnishes an intuitive physical interpretation about the synthesis of the virtual optical paths. In this paper, the geometric TDI is utilized to investigate the modified second-generation TDI combinations in conjunction with a ternary search algorithm. The distinction between the second-generation and modified second-generation TDI solutions is elaborated regarding the rate of change of the arm lengths with respect to the opposite cyclic directions. For the sixteen-link combinations, forty second-generation TDI solutions are recovered, among which nine of them are identified as the modified second-generation ones.

gr-qc↗

arXiv2021

Arm locking using laser frequency comb

In this work, we describe an updated version of single arm locking, and the noise amplification due to the nulls can be flexibly restricted with the help of optical frequency comb. We show that, the laser phase noise can be divided by a specific factor with optical frequency comb as the bridge. The analytical results indicate that, the peaks in the science band have been greatly reduced. The performance of the noise suppression shows that the total noise after arm locking can well satisfy the requirement of time delay interferometry, even with the free-running laser source. We also estimate the frequency pulling characteristics of the updated single arm locking, and the results suggest that the pulling rate can be tolerated, without the risk of mode hopping. Arm locking will be a valuable solution for the noise reduction in the space-borne GW detectors. We demonstrate that, with the precise control of the returned laser phase noise, the noise amplification in the science band can be efficiently suppressed based on the updated single arm locking. Not only our method allows the suppression of the peaks, the high gain, low pulling rate, it can also serve for full year, without the potential risk of locking failure due to the arm length mismatch. We finally discuss the unified demonstration of the updated single arm locking, where both the local and the returned laser phase noises can be tuned to generate the expected arm-locking sensor actually. Our work could provide a powerful method for the arm locking in the future space-borne GW detectors.

physics.optics↗

arXiv2021

Refined clock-jitter reduction in the Sagnac-type time-delay interferometry combinations

The ongoing development of the space-based laser interferometer missions is aiming at unprecedented gravitational wave detections in the millihertz frequency band. The spaceborne nature of the experimental setups leads to a degree of subtlety regarding the otherwise overwhelming laser frequency noise. The cancellation of the latter is accomplished through the time-delay interferometry technique. Moreover, to eventually achieve the desired noise level, the phase fluctuations of the onboard ultra-stable oscillator must also be suppressed. This can be fulfilled by introducing sideband signals which, in turn, give rise to an improved cancellation scheme accounting for the clock-jitter noise. Nonetheless, for certain Sagnac-type interferometry layouts, it can be shown that resultant residual clock noise found in the literature can be further improved. In this regard, we propose refined cancellation combinations for two specific clock noise patterns. This is achieved by employing the so-called geometric time-delay interferometry interpretation. It is shown that for specific Sagnac combinations, the residual noise diminishes significantly to attain the experimentally acceptable sensitivity level. Moreover, we argue that the derived combination, in addition to the existing ones in the literature, furnishes a general-purpose cancellation scheme that serves for arbitrary time-delay interferometry combinations. The subsequential residual noise will only involve factors proportional to the commutators between the delay operators. Our arguments reside in the form of the clock noise expressed in terms of the coefficients of the generating set of the first module of syzygies, the linear combination of which originally constitutes the very solution for laser noise reduction.

gr-qc↗