Liang-Cheng Tu

The mass of the photon

Because classical Maxwellian electromagnetism has been one of the cornerstones of physics during the past century, experimental tests of its foundations are always of considerable interest. Within that context, one of the most important efforts of this type has historically been the search for a rest mass of the photon. The effects of a nonzero photon rest mass can be incorporated into electromagnetism straightforwardly through the Proca equations, which are the simplest relativistic generalization of Maxwell’s equations. Using them, it is possible to consider some far-reaching implications of a massive photon, such as variation of the speed of light, deviations in the behaviour of static electromagnetic fields, longitudinal electromagnetic radiation and even questions of gravitational deflection. All of these have been studied carefully using a number of different approaches over the past several decades. This review attempts to assess the status of our current knowledge and understanding of the photon rest mass, with particular emphasis on a discussion of the various experimental methods that have been used to set upper limits on it. All such tests can be most easily categorized in terms of terrestrial and extraterrestrial approaches, and the review classifies them as such. Up to now, there has been no conclusive evidence of a finite mass for the photon, with the results instead yielding ever more stringent upper bounds on the size of it, thus confirming the related aspects of Maxwellian electromagnetism with concomitant precision. Of course, failure to find a finite photon mass in any one experiment or class of experiments is not proof that it is identically zero and, even as the experimental limits move more closely towards the fundamental bounds of measurement uncertainty, new conceptual approaches to the task continue to appear. The intrinsic importance of the question and the lure of what might be revealed by attaining the next decimal place are as strong a draw on this question as they are in any other aspect of precise tests of physical laws.

A torsion balance for impulse and thrust measurements of micro-Newton thrusters

This paper reports the performance of a torsion-type thrust stand suitable for studies of micro-Newton thrusters, which is developed for ground testing the micro-Newton thruster in Chinese Test of the Equivalence Principle with Optical readout space mission. By virtue of specially suspending design and precise assembly of torsion balance configuration, the thrust stand with load capacity up to several kilograms is able to measure the impulse bit up to 1350 μNs with a resolution of 0.47 μNs, and the average thrust up to 264 μN with a resolution of 0.09 μN in both open and close loop operation. A pulsed plasma thruster, the preliminary prototype developed for Chinese TEPO space mission, is tested by the thrust stand, and the results reveal that the average impulse bit per pulse is measured to be 58.4 μNs with a repeatability of about 5%.

Implementation of the scale factor balance on two pairs of quartz-flexure capacitive accelerometers by trimming bias voltage

Gravity gradient measurement makes use of the difference between the outputs of pairs of linear accelerometers, which results in cancelling out the common mode accelerations caused by mounting platform and external environment. One of the key technologies is to match the acceleration-to-voltage or acceleration-to-current transfer functions of the pairs of the accelerometers to an extremely high degree of accuracy. The differential signals then make the gravity gradients observable. By using two pairs of the quartz-flexure accelerometers with a capacitive sensing and electrostatic closed-loop control, the electrostatic control bias voltages were trimming remotely and automatically in real time. Each pair of accelerometers was matched individually and then all four accelerometers were finally re-balanced. The experimental results show that the consistency of five digits is achieved at a noise level of ~5×10(-8) g/√Hz (1 g ≈ 9.8 m/s(2)) and the scale factors ranging from 0.25 to 0.32 V/mg. Further improvement to the achieved level of matching is limited by the intrinsic noise of the accelerometers used.

Feedback control of torsion balance in measurement of gravitational constant G with angular acceleration method

The performance of the feedback control system is of central importance in the measurement of the Newtons gravitational constant G with angular acceleration method. In this paper, a PID (Proportion-Integration-Differentiation) feedback loop is discussed in detail. Experimental results show that, with the feedback control activated, the twist angle of the torsion balance is limited to [Formula: see text] at the signal frequency of 2 mHz, which contributes a [Formula: see text] uncertainty to the G value.

Novel Capacitive Sensing System Design of a Microelectromechanical Systems Accelerometer for Gravity Measurement Applications

This paper presents an in-plane sandwich nano-g microelectromechanical systems (MEMS) accelerometer. The proof-mass fabrication is based on silicon etching through technology using inductive coupled plasma (ICP) etching. The capacitive detection system, which employs the area-changing sensing method, combines elementary capacitive pickup electrodes with periodic-sensing-array transducers. In order to achieve a large dynamic range with an ultrahigh resolution, the capacitive detection system employs two periodic-sensing-array transducers. Each of them can provide numbers for the signal period in the entire operating range. The suspended proof-mass is encapsulated between two glass caps, which results in a three dimensional structure. The measured resonant frequency and quality factor (Q) are 13.2 Hz and 47, respectively. The calibration response of a ±0.7 g input acceleration is presented, and the accelerometer system presents a sensitivity of 122 V/g and a noise floor of 30 ng/√Hz (at 1 Hz, and 1 atm). The bias stability for a period of 10 h is 30 μg. The device has endured a shock up to ±2.6 g, and the full scale output appears to be approximately ±1.4 g presently. This work presents a new opportunity for highly sensitive MEMS fabrication to enable future high-precision measurement applications, such as for gravity measurements.

Preliminary determination of Newtonian gravitational constant with angular acceleration feedback method

This paper describes the preliminary measurement of the Newtonian gravitational constant G with the angular acceleration feedback method at HUST. The apparatus has been built, and preliminary measurement performed, to test all aspects of the experimental design, particularly the feedback function, which was recently discussed in detail by Quan et al. The experimental results show that the residual twist angle of the torsion pendulum at the signal frequency introduces 0.4 ppm to the value of G. The relative uncertainty of the angular acceleration of the turntable is approximately 100 ppm, which is mainly limited by the stability of the apparatus. Therefore, the experiment has been modified with three features: (i) the height of the apparatus is reduced almost by half, (ii) the aluminium shelves were replaced with shelves made from ultra-low expansion material and (iii) a perfect compensation of the laboratory-fixed gravitational background will be carried out. With these improvements, the angular acceleration is expected to be determined with an uncertainty of better than 10 ppm, and a reliable value of G with 20 ppm or below will be obtained in the near future.

G measurements with time-of-swing method at HUST

We review the G measurements with time-of-swing method at HUST. Two independent experiments have been completed and an improved experiment is in progress. The first G value was determined as 6.6699(7)×10−11 m3 kg−1 s−2 with a relative standard uncertainty (ur) of 105 ppm by using a long period torsion pendulum and two cylindrical source masses. Later, this result was corrected to be 6.6723(9)×10−11 m3 kg−1 s−2 with ur=130 ppm after considering the density distribution of the cylinders and the air buoyancy, which was 360 ppm larger than the previous value. In 2009, a new experiment by using a simple block pendulum and spherical source masses with more homogeneous density was carried out. A series of improvements were performed, and the G value was determined to be 6.67349(18)×10−11 m3 kg−1 s−2 with ur=26 ppm. To reduce the anelasticity of the torsion fibre, fused silica fibres with Qs of approximately 5×104 are used to measure G in the ongoing experiment. These fibres are coated with thin layers of germanium and bismuth in turn to reduce the electrostatic effect. Some other improvements include the gravity compensation, reduction of the coating layer effect, etc. The prospective uncertainty of the next G value is 20 ppm or lower.

Low temperature fabrication and doping concentration analysis of Au/Sb ohmic contacts to n-type Si

This paper investigates low temperature ohmic contact formation of Au/Sb to n-type Si substrates through AuSb/NiCr/Au metal stacks. Liquid epitaxy growth is utilized to incorporate Sb dopants into Si substrate in AuSi melt. The best specific contact resistivity achieved is 0.003 Ω ⋅ cm2 at 425 oC. Scanning electron microscopy (SEM) reveals inverted pyramidal crater regions at the metal/semiconductor interface, indicating that AuSi alloying efficiently occurs at such sites. Secondary ion mass spectroscopy (SIMS) shows that Sb atoms are successfully incorporated into Si as doping impurities during the anneal process, and the Sb doping concentration at the contact interface is found to be higher than the solid solubility limit in a Si crystal. This ohmic contacts formation method is suitable for semiconductor fabrication processes with limited thermal budget, such as post CMOS integration of MEMS.

On the calculation of the gravitational torque in measuring G by a dynamic method

The authors of the paper [1], Grav. Cosmol. 16, 323 (2010), presented two methodologies for calculating the gravitational torque while measuring the gravitational constant G by a dynamic method. We have checked their calculations and found an evident error which directly leads a wrong conclusion in the paper. Besides, their discussion on the advantage of the methodology includes a logical contradiction.

A nano-g MEMS accelerometer for earthquake monitoring

This paper reports on an in-plane nano-g MEMS accelerometer using periodic-sensing-array capacitance displacement transducer. The parasitic capacitances and fringe effect are proved to have great influences on sensitivity by simulation. Benefiting from the large proof mass and optimized displacement transducers, the experimentally measured noise limited resolution is 30ng/√Hz at 1Hz, which is among the highest sensitivities reported to date. The earthquake occurred in Taiwan was detected during a continuous measurement.