A newly designed decoupling method for micro-Newton thrust measurement.

A decoupling method is proposed for micro-Newton thrust measurement with a torsion pendulum. The basic approach is to reduce the influences introduced by the propellant tube and wires of the thruster. A hollow aluminum tube is used to hang the torsion pendulum and is also chosen as the transport pipe for the propellant of the thruster. The electric control box of the thruster is mounted on the pendulum body, which is powered by an externally installed power supply through a liquid metal conductive unit. The control of the electric control box is performed through wireless transmission. With this design, the influences of the propellant tube and connection wires between the torsion pendulum and the outside device are reduced and the stability of the torsion spring constant of the system can be improved. The use of the liquid metal conductive unit reduces the coupling between the wires and the measurement system. The feasibility of the wireless transmission is analyzed. The error sources during the thrust measurement are analyzed, and the expected three σ uncertainty of the thrust is 0.032+(0.10%*F)2µN for the measurement of the cold gas thruster. The scheme provides a thrust measurement with higher precision and stability.

Effect of atom diffusion on the efficiency of Bragg diffraction in atom interferometers.

The transition efficiency of atomic Bragg diffraction as mirrors and beam splitters in Bragg atom interferometers plays an essential role in impacting the fringe contrast and measurement sensitivity. This can be attributed to the properties of atomic sources, Bragg pulse shapes, the pulse duration, and the relative position deviation of the atoms and Bragg pulses. Here, we investigate the effect of the atomic source's diffusion and velocity width on the efficiency of Bragg diffraction of the moving cold atomic cloud. The transfer efficiency of Bragg mirrors and beam splitters are numerically simulated and experimentally measured, which are well consistent in comparison. We quantify these effects of atomic diffusion and velocity width and precisely compute how Bragg pulses' efficiencies vary as functions of these parameters. Our results and methodology allow us to optimize the Bragg pulses at different atomic sources and will help in the design of large momentum transfer mirrors and beam splitters in atom interferometry experiments.

Impact of additional sidebands generated by a tapered amplifier on an atom interferometer.

Stimulated Raman transitions are often used in an atom interferometer (AI) for wave packet manipulation. Normally, two lasers with different frequencies contained in a Raman beam are combined first and then amplified by a single tapered amplifier (TA). This configuration can simplify the laser system of the AI, however, additional sidebands will be generated by the TA because of the nonlinear effect in the TA. In this work, the impact of additional sidebands generated with a single TA on the AI is studied. We first observe the additional sidebands in a Raman laser by a Fabry-Pérot interferometer (FPI), and the additional sidebands will be greatly suppressed by reducing the injection laser power of the TA. This is also confirmed by observing the position-dependent Raman transitions induced by additional sidebands at different injection power in an AI. However, the phase shifts induced by additional sidebands are not reduced obviously when the injection power of the TA is reduced. Therefore, it is necessary to separately amplify two lasers contained in the Raman laser by two TAs for a high precision AI. The spectroscopy of Raman laser generated by two TAs is also measured by the FPI, and the impact of additional sidebands on the AI is eliminated. This work has guiding significance for the design of the laser system in a high-precision AI.

A compound pendulum for thrust measurement of micro-Newton thruster.

A thrust stand is developed for testing micro-Newton level thrusters on the ground. The stand is composed of a compound pendulum that is symmetrically suspended by two thin beryllium copper strips, and it is precisely calibrated by gravity. The stiffness of the stand can be adjusted in 3 orders of magnitude by a counterweight. When the stiffness is larger than 1 Nm/rad, the stand demonstrates a fast response to thrust. The measured range of the stand reaches 1000 µN, and the noise is less than 0.1 µN/Hz within 1 mHz-1 Hz. To calibrate the resolution of the stand, an electrostatic force is applied to the stand with an actuator. The equivalent thrust is determined to be 0.09 µN with a standard uncertainty of 0.02 µN. Using the stand, a micro-Newton colloid thruster is tested. The output of the colloid thruster changes with the applied voltage as 0.015(1) µN/V. When changing the voltage by 50 V, the change in thrust is measured to be 0.7 µN with a standard uncertainty of 0.1 µN.

Characterizing atom clouds using a charge-coupled device for atom-interferometry-based G measurements.

Precise information of positions and sizes of atom clouds is required for atom-interferometry-based G measurements. In this work, characterizing atom clouds using a charge-coupled device (CCD) is presented. The parameters of atom clouds are extracted from fluorescence images captured by the CCD. For characterization, in-situ calibration of the magnification of the imaging system is implemented using the free-fall distance of atom clouds as the dimension reference. Moreover, influence of the probe beam on measuring the positions of atom clouds is investigated, and a differential measurement by reversing the direction of the probe beam is proposed to suppress the influence. Finally, precision at sub-mm level for characterizing atom clouds is achieved.

Influence of magnetic field on the seismometer in vibration correction for atom gravimeters.

Vibration correction provides a simple and flexible method of suppressing ambient vibration noise in transportable atom gravimeters. However, in the seismometers used for vibration correction, a spurious output may be induced by the magnetic field of the magnetic-optical trap, introducing errors to the gravity measurements. This paper evaluates the influence of the magnetic field on the seismometer and the corresponding errors in the gravity measurements. It is found that an error level of order 10 µGal may be present if the seismometer is not configured carefully. The dependence of the influence on the orientation of the seismometer and the lasting time of the magnetic field are investigated. The effective suppression of the influence by shielding the seismometer is also demonstrated. Our results focus attention on the possible errors related to seismometers in high-precision gravity measurements by using atom gravimeters.

Eliminating the phase shifts arising from additional sidebands in an atom gravimeter with a phase-modulated Raman laser.

The additional sidebands (ASBs) in a Raman laser will have a significant effect on the performance of atom gravimeters (AGs) based on phase-modulated Raman lasers. We propose a method of modulating the sideband-to-carrier ratio in Raman lasers to determine the magic time intervals where the phase shift induced by the ASB effect is minimized, and this method is demonstrated by experiments. Among these magic time intervals, some noise-immunity points are predicted. Based on the prediction and the result of the ASB effect changing with the interval time T between adjacent Raman pulses, an optimal magic time interval is selected. Therefore, the uncertainty to the gravity measurement induced by the ASB effect when the AG works at the magic time interval is reduced to 0.5 µGal. Furthermore, the ASB effect and its zero-phase points in four-pulse atom interferometers are also discussed. This work provides a clear way to eliminate the phase shift induced by the ASB effect in high-precision AGs employing phase-modulated Raman lasers.

Precision Magnetic Field Sensing with Dual Multi-Wave Atom Interferometer.

Precision magnetic field measurement is widely used for practical applications, fundamental research, and medical purposes, etc. We propose a novel quantum magnetometer based on atoms' multi-wave (3-wave and 5-wave) Ramsey interference. Our design features high phase sensitivity and can be applied to in situ measurements of the magnetic field inside vacuum chambers. The final state detection is designed to be achieved by Raman's two-photon transition. The analytical solution for applicable interference fringe is presented. Fringe contrast decay due to atom temperature and magnetic field gradient is simulated to estimate reasonable experimental conditions. Sensitivity functions for phase noise and magnetic field noise in a multi-wave system are derived to estimate the noise level required to reach the expected resolution. The validity of the model, dual-channel features on bias estimation, and the quasi-non-destructive detection feature are discussed.

Effects related to the temperature of atoms in an atom interferometry gravimeter based on ultra-cold atoms.

The temperature of atoms, coupled to several effects, plays an important role in high precision atom interferometry gravimeters. In this work, we present an ultra-cold 87Rb atom interferometry gravimeter, in which the atom source is produced by evaporative cooling in an all optical dipole trap to investigate the effects related to atom temperature. A condensate containing 4 × 104 atoms can be prepared within 3.2 s through an all-optical dipole trap composed of two reservoirs and a dimple. The fringe contrast of our atom interferometry gravimeter reaches up to 76(4)% due to the advantage of ultra-cold atom source even at a free evolution time of T=80 ms. A resolution of 6 µGal (1 µGal=1×10-8 m/s2) after 3000 s integration time with a sampling rate of 0.25 Hz is achieved in this atom gravimeter. The relationship between the fringe contrast and the atom temperature in the atom gravimeter is studied; in addition, the wavefront aberration effect in the atom gravimeter is also investigated by varying the temperature of atoms.

The influence of polarization misalignment for modulation transfer spectrum in atom gravimeter.

The accuracy of atom gravimeters is directly related to the Raman laser, which is used to manipulate the atomic wave packet, and the frequency of the Raman laser could be affected by temperature when the laser polarization is not along the preferred axis of the electro-optic crystal employed in the modulation transfer spectrum (MTS). This effect has been researched by modulating the laser polarization in the MTS in this work. The experimental results show that both the laser frequency and gravity measurement results have a sinusoidal dependence on temperature, and the period of the fluctuation is 0.8 °C. The systematic effect can reach 12.4 µGal when the polarization misalignment is 15°, which is a remarkable contribution to the absolute gravity measurement. The amplitude of this effect could be reduced by adjusting the laser polarization to the crystal's preferred axis. According to the result, the included angle between the laser polarization and the crystal's preferred axis should be smaller than 5° if 2 µGal accuracy is required.

A dual-magneto-optical-trap atom gravity gradiometer for determining the Newtonian gravitational constant.

As part of a program to determine the gravitational constant G using multiple independent methods in the same laboratory, an atom gravity gradiometer is being developed. The gradiometer is designed with two magneto-optical traps to ensure both the fast simultaneous launch of two atomic clouds and an optimized configuration of source masses. Here, the design of the G measurement by atom interferometry is detailed, and the experimental setup of the atom gravity gradiometer is reported. A preliminary sensitivity of 3 × 10-9 g/Hz to differential gravity acceleration is obtained, which corresponds to 99 E/Hz (1 E = 10-9 s-2) for the gradiometer with a baseline of 0.3 m. This provides access to measuring G at the level of less than 200 parts per million in the first experimental stage.

Measuring the effective height for atom gravimeters by applying a frequency jump to Raman lasers.

As the existence of the gravity gradient, the output of gravimeters is actually the gravitational acceleration at the reference instrumental height. Precise knowledge of the reference height is indispensable in the utilization of gravity measurements, especially for absolute gravimeters. Here, we present an interferometric method to measure the distance between the atomic cloud and a reflecting mirror directly, which consequently determines the reference height of our atom gravimeter. This interferometric method is based on a frequency jump of Raman lasers applied at the π pulse of the atom interferometer, which induces an additional phase shift proportional to the interested distance. An uncertainty of 2 mm is achieved here for the distance measurement, and the effect of the gravity gradient on absolute gravity measurements can thus be constrained within 1 µGal. This work provides a concrete-object-based measurement of the reference height for atom gravimeters.

Effects of wave-front tilt and air density fluctuations in a sensitive atom interferometry gyroscope.

We present a matter wave gyroscope with a Sagnac area of 5.92 cm2, achieving a short-term sensitivity of 167 nrad/s/Hz1/2. The atom interferometry gyroscope is driven by a π/2 - π - π - π/2 Raman pulse sequence based on an atom fountain with a parabolic trajectory. The phase-locked laser beams for Raman transitions partly propagate outside of the vacuum chamber and expose to the air when passing through the two arms of the vacuum chamber. This configuration leads to the tilt of the laser's wave-front and suffers the fluctuation of air density. The impacts on both the fringe contrast and long-term stability are experimentally investigated in detail, and effective schemes are developed to improve the performance of our atom gyroscope. The method presented here could be useful for developing large atom interferometry facilities with separated vacuum chambers.

Multi-wave atom interferometer based on Doppler-insensitive Raman transition.

An atom interferometer based on Doppler-insensitive Raman transition is proposed, which has sharply peaked interference fringes for multi-wave interference. We show that two sets of counter-propagating Doppler-insensitive Raman beam pairs can be used to construct a new type of multi-wave beam splitter, which can be used to construct an atom interferometer. Although the spacing between adjacent diffraction orders of the interferometer is small, they can be distinguished by the internal state of the atom. Our analysis shows that the width of the fringes of this atom interferometer is inversely proportional to the width (duration) of the beam splitter and the Rabi frequency of the Raman beams, that is, the interferometer can achieve high resolution at high light intensity and long pulse width.

Precision measurement of the Newtonian gravitational constant.

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10-11 m3 kg-1 s-2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.

A compact laser system for a portable atom interferometry gravimeter.

A compact laser system for a portable 87Rb atom interferometry gravimeter has been demonstrated in this work. This laser system is based on frequency doubling of a single seed laser at the wavelength of 1560 nm. The frequency of the seed laser is controlled by a digital unit with an analog feedback circuit. By using this frequency control method, the frequency of the laser system can be shifted over 1 GHz. Based on this method, the Raman frequency can be locked on the F = 3 → F' = 4 transition of 85Rb atoms. Moreover, the Raman sideband and the repumping laser are generated by a phase modulator, and it can generate different laser frequencies to meet the requirements of a typical atom interferometer. Additional sidebands in the Raman beam produced from the phase modulator are optimized and reduced, allowing us to observe atom interference with a free evolution time of 320 ms. The control unit including the laser system has been integrated into a box with a volume of 1.5 m × 0.6 m × 0.6 m, and the weight of which is only 150 kg. Using this compact optical scheme, our atomic gravimeter has achieved a sensitivity of 53 µGal/Hz1/2 and a resolution of better than 1 µGal (1 µGal = 1 × 10-8 m/s2) in an integration time of 3000 s.

Time base evaluation for atom gravimeters.

Time is an inevitable quantity involved in absolute gravity measurements, and 10 MHz frequency standards are usually utilized as time base. Here we investigate the influence of time base bias on atom-interferometry-based gravity measurements and present an onsite calibration of the time base bias relying on an atom gravimeter itself. With a microwave source referenced to the time base, the time base bias leads to a magnified frequency shift of the microwave source output. The shift is then detected by Ramsey spectroscopy with the clock transition of 87Rb atoms as a frequency discriminator. Taking advantage of available free-fall cold atoms and developed techniques of measuring the atom energy level shift in atom gravimeters, the calibration achieves an accuracy of 0.6 mHz for the time base. And the corresponding error for gravity measurements is constrained to 0.1 µGal, meeting the requirement of state-of-the-art gravimeters. The presented evaluation is important for the applications of atom gravimeters.

Measurements of the gravitational constant using two independent methods.

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10-11 and 6.674484 × 10-11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

Note: Effect of the parasitic forced vibration in an atom gravimeter.

The vibration isolator usually plays an important role in atom interferometry gravimeters to improve their sensitivity. We show that the parasitic forced vibration of the Raman mirror, which is induced by external forces acting on the vibration isolator, can cause a bias in atom gravimeters. The mechanism of how this effect induces an additional phase shift in our interferometer is analyzed. Moreover, modulation experiments are performed to measure the dominant part of this effect, which is caused by the magnetic force between the passive vibration isolator and the coil of the magneto-optic trap. In our current apparatus, this forced vibration contributes a systematic error of -2.3(2) × 10-7 m/s2 when the vibration isolator works in the passive isolation mode. Even suppressed with an active vibration isolator, this effect can still contribute -6(1) × 10-8 m/s2; thus, it should be carefully considered in precision atom gravimeters.

Test of the Universality of Free Fall with Atoms in Different Spin Orientations.

We report a test of the universality of free fall by comparing the gravity acceleration of the ^{87}Rb atoms in m_{F}=+1 versus those in m_{F}=-1, of which the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is η_{S}=(0.2±1.2)×10^{-7}. This also gives an upper limit of 5.4×10^{-6} m^{-2} for a possible gradient field of the spacetime torsion. The interferometer using atoms in m_{F}=±1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment.