Pan-Pan Wang’s research while affiliated with Huazhong University of Science and Technology and other places

The exploration of the surrounding world and the universe is an important theme in the legacy of humankind. The detection of gravitational waves is adding a new dimension to this grand effort. What are the fundamental physical laws governing the dynamics of the universe? What is the fundamental composition of the universe? How has the universe evolved in the past and how will it evolve in the future? These are the basic questions that press for answers. The space-based gravitational wave detector TianQin will tune in to gravitational waves in the millihertz frequency range ($10^{-4} \sim 1$ Hz, to be specific), opening a new gravitational wave spectrum window to explore many of the previously hidden sectors of the universe. TianQin will discover many astrophysical systems, populating the universe at different redshifts: some will be of new types that have never been detected before, some will have very high signal-to-noise ratios, and some will have very high parameter estimation precision. The plethora of information collected will bring us to new fronts on which to search for the breaking points of general relativity, the possible violation of established physical laws, the signature of possible new gravitational physics and new fundamental fields, and to improve our knowledge on the expansion history of the universe. In this white paper, we highlight the advances that TianQin can bring to fundamental physics and cosmology.

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.

Gravitational waves (GWs) have six possible polarization modes, and whose successful detection can effectively test the gravitational properties under the strong field theory and help distinguish between different theories of gravity. Space-based GW detectors can respond differently to different polarization modes and can be used to measure the polarization states of GWs. However, during the detection process, multiple noises can swamp the faint GW signals, thus, it is essential to develop highly sophisticated experimental techniques and data processing methods to suppress the noises. For the most dominant laser frequency noise, time-delay interferometry technique is employed to construct a virtual equal-arm interferometer by performing appropriate time-delay and linear combination of data streams. This ensures the laser frequency noise is suppressed below the noise floor composed of test-mass noise and shot noise. To present the responsiveness of the detector to the polarization modes of GW signals and to clarify the corresponding characteristic regularities. In this paper, we calculate and analyze the sensitivity functions of 45 core geometric time-delay interferometry technique (TDI) combinations under the six polarization modes allowed by the metric gravity theory. The analysis is based on arbitrary second-generation TDI that can be independently linearly expanded by first-generation generators. It turns out that the sensitivity functions of 45 TDI combinations in different polarization modes are classified into exactly the same 11 categories, and there are obvious characteristic patterns in the asymptotic behavior of these sensitivity functions. These results can help to measure the GW polarization states, understand the nature of fields beyond the gravitational field, and provide some support for distinguishing gravitational theories. In addition, the sensitivity functions of multi-type TDI combinations can be applied to the parameter estimation to improve the localization accuracy of all-sky GW sources.

Arm-locking technique has been a focus of attention as one of the means to suppress the laser phase noise in space-based gravitational wave detector. The main idea of the arm-locking technique is to transfer the stability of the detector arm length to laser frequency by introducing a feedback control loop. Generally, laser phase noise will be suppressed by an amount similar to the magnitude of the controller gain. However, on the one hand, clock-jitter noise and optical bench motion noise, as the noise floor of the arm-locking technique, need to be suppressed. On the other hand, limited by the Doppler frequency pulling, the gain of the controller generally cannot be too large. It means that even if we do not consider clock-jitter noise and optical bench motion noise, it is difficult to suppress laser phase noise below the noise floor only by arm-locking technique. In this work, we combine self-referenced optical frequency combs and arm-locking technique to generate clock signals that are coherently referenced to the closed-loop laser beams, so that the clock-jitter noise is also suppressed by about the level of controller gain. We conduct a simulation on the above configuration, and the results show that the performance of the arm-locking is no longer limited by clock-jitter noise in the low-frequency band. To address the issue of insufficient laser phase noise suppression by the arm-locking technique, we further investigate time-delay interferometry (TDI) combinations under outputs of arbitrary arm-locking configurations. We obtain the equations for eliminating laser phase noise. To ensure that the TDI combinations can directly operate in the time domain, we derive a restricted solution space by assuming a specific form for the solutions.

Short-range gravity experiments are more suitable for the testing of high-order Lorentz symmetry breaking effects. In our previous work, we proposed a new experimental design based on precision torsion balance technology to test the Lorentz violation force effect that varies inversely with the fourth power of distance (corresponding to mass dimension d = 6 term), and the corresponding experiment is currently underway. In this paper, we focus on analyzing the potential of this experimental scheme to test the Lorentz violation force that varies inversely with the sixth power of distance (corresponding to mass dimension d = 8 term). The results show that, compared with the current best limit, the new experimental scheme can improve the constraints on the Lorentz violation coefficients with d = 8 by at least one order of magnitude.

Space gravitational wave detection primarily focuses on the rich wave sources corresponding to the millihertz frequency band, which provide key information for studying the fundamental physics of cosmology and astrophysics. However, gravitational wave signals are extremely weak, and any noise during the detection process could potentially overwhelm the gravitational wave signals. Therefore, data pre-processing is necessary to suppress the main noise sources. Among the various noise sources, laser phase noise is dominant, approximately seven orders of magnitude larger in strength than typical gravitational wave signals, and requires suppression using time-delay interferometry (TDI) techniques, which involve combining raw data with time delays. This paper will be based on the basic principles of TDI to present methods for obtaining multi-type TDI combinations, including algebraic methods for solving indeterminate equations and geometric methods for symbolic search. Furthermore, the applicability of TDI under actual operating conditions will be considered, such as the arm locking in conjunction with the TDI algorithm. Finally, the sensitivity functions for different types of TDI combinations will be provided, which can be used to evaluate the signal-to-noise ratio (SNRs) of different TDI combinations.

Phase-locking configuration was proposed as a baseline optical implementation for the space-borne gravitational wave detectors. By assigning one laser as the reference, termed the master, the remaining five lasers, dubbed slaves, are no longer free-running but phase-locked to form a master-slave arrangement. As a baseline optical implementation for the space-borne gravitational wave detectors, such an approach addresses the relative central frequency drift occurring to individual lasers over time. It is crucial for the effectiveness of the interference measurements, as the resultant beat note frequencies are guaranteed to remain in the phasemeter range. Moreover, it aims to reduce hardware redundancy and effectively decrease the total number of independent laser noise and data streams. The present study focuses on the implication of the time-delay interferometry (TDI) algorithm when implementing the master-slave configuration governed by phase-locking. We examine the modifications to the data streams’ structure and the reduction in the number of independent optical links compared to the standard TDI formalism. From a geometric TDI perspective, we analyze the valid TDI combinations by exhausting the solution space up to sixteen links. We show that a geometric TDI combination can always be reiterated regarding the modified data streams associated with the phase-locking scheme, resulting in a size equal to or shorter than the original TDI solution. Notably, for a specific phase-locking scheme, it is demonstrated that an originally sixteen-link TDI combination typically shrinks down to its counterpart with a smaller number of links, effectively simplifying the solutions’ forms. The analysis can be extended to all six distinct phase-locking schemes, and the aim is to identify TDI combinations that offer enhanced performance.