Developments of the micro-Gal level gravimeter based on atom interferometry are reviewed, and the recent progress and results of our group are also presented. Atom interferometric gravimeters have shown high resolutio...Developments of the micro-Gal level gravimeter based on atom interferometry are reviewed, and the recent progress and results of our group are also presented. Atom interferometric gravimeters have shown high resolution and accuracy for gravity measurements. This kind of quantum sensor has excited world-wide interest for both practical applications and fundamental research.展开更多
We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop(PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz ove...We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop(PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator(OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer(DDS) which is also referenced to the 100 MHZ OCXO to generate the final6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are-47 d Bc/Hz,-77 dBc/Hz,-104 dBc/Hz and-121 dBc/Hz at1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than 5.0 × 10^-14τ^1/2 when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.展开更多
Performance test of a high precise accelerometer or an inertial sensor on the ground is inevitably limited by the seismic noise. A torsion pendulum has been used to investigate the performances of an electrostatic acc...Performance test of a high precise accelerometer or an inertial sensor on the ground is inevitably limited by the seismic noise. A torsion pendulum has been used to investigate the performances of an electrostatic accelerometer, where the test mass is suspended by a fiber to compensate for its weight, and this scheme demonstrates an advantage, compared with the high-voltage levitation scheme, in which the effect of the seismic noise can be suppressed for a few orders of magnitude in low frequencies. In this work, the capacitive electrode cage is proposed to be suspended by another pendulum, and theoretical analysis shows that the effects of the seismic noise can be further suppressed for more than one order by suspending the electrode cage.展开更多
Over the past 50 years, lunar laser ranging has made great contributions to the understanding of the Earth–Moon system and the tests of general relativity. However, because of the lunar libration, the Apollo and Luno...Over the past 50 years, lunar laser ranging has made great contributions to the understanding of the Earth–Moon system and the tests of general relativity. However, because of the lunar libration, the Apollo and Lunokhod corner-cube retroreflector（CCR） arrays placed on the Moon currently limit the ranging precision to a few centimeters for a single photon received. Therefore, it is necessary to deploy a new retroreflector with a single and large aperture to improve the ranging precision by at least one order of magnitude. Here we present a hollow retroreflector with a 170-mm aperture fabricated using hydroxide-catalysis bonding technology. The precisions of the two dihedral angles are achieved by the mirror processing with a sub-arc-second precision perpendicularity, and the remaining one is adjusted utilizing an auxiliary optical configuration including two autocollimators. The achieved precisions of the three dihedral angles are 0.10 arcsecond,0.30 arc-second, and 0.24 arc-second, indicating the 68.5% return signal intensity of ideal Apollo 11/14 based on the far field diffraction pattern simulation. We anticipate that this hollow CCR can be applied in the new generation of lunar laser ranging.展开更多
We investigated the sensitivities of atom interferometers in the usual fringe-scanning method （FSM） versus the fringe- locking method （FLM）. The theoretical analysis shows that for typical noises in atom interfero...We investigated the sensitivities of atom interferometers in the usual fringe-scanning method （FSM） versus the fringe- locking method （FLM）. The theoretical analysis shows that for typical noises in atom interferometers, the FSM will degrade the sensitivity while the FLM does not. The sensitivity-improvement factor of the FLM over the FSM depends on the type of noises, which is validated by numerical simulations. The detailed quantitative analysis on this fundamental issue is presented, and our analysis is readily extendable to other kinds of noises as well as other fringe shapes in addition to a cosine one.展开更多
In a test of the weak equivalence principle （WEP） with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the fre...In a test of the weak equivalence principle （WEP） with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the free oscillation signal and employ the correlation method to estimate the amplitude of the modulation signal. The data analysis of an experiment shows that the uncertainties of amplitude components of the modulation signal obtained by the correlation method are in agreement with those due to white noise. The power spectral density of the modulation signal obtained by the correlation method is about one order higher than the thermal noise limit. It indicates that the correlation method is an effective way to estimate the amplitude of the modulation signal and it is instructive to conduct a high-accuracy WEP test.展开更多
In the torsion pendulum experiments, the thermal noise sets the most fundamental limit to the accurate estimation of the amplitude of the signal with known frequency. The variance of the conventional method can meet t...In the torsion pendulum experiments, the thermal noise sets the most fundamental limit to the accurate estimation of the amplitude of the signal with known frequency. The variance of the conventional method can meet the limit only when the measurement time is much longer than the relaxation time of the pendulum. By using the maximum likelihood estimation and the equation-of-motion filter operator, we propose an optimal(minimum variance, unbiased) amplitude estimation method without limitation of the measurement time, where thermal fluctuation is the leading noise. While processing the experimental data tests of the Newtonian gravitational inverse square law, the variance of our method has been improved than before and the measurement time of determining the amplitude with this method has been reduced about half than before for the same uncertainty. These results are significant for the torsion experiment when the measurement time is limited.展开更多
Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in t...Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio ？t/（1/λ） where ？t is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time ？t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio ？t/（1/λ） is less than 1, the uncertainty remains substantially unchanged.展开更多
The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effe...The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effect with a simplified theoretical model of the time-propagation operator. According to the typical parameters, we find that this effect should be taken into account when the gravimeter reaches an accuracy of 10^-10g, and the larger the pulse duration is, the more obvious the systematic effect will be. Finally, we make a simple discussion on the possibility of testing this effect.展开更多
In the measurement of G with the angular acceleration method,the improved correlation method developed by Wu et al.（Wu W H,Tian Y,Luo J,Shao C G,Xu J H and Wang DH 2016 Rev.Sci.Instrum.87 094501） is used to accurate...In the measurement of G with the angular acceleration method,the improved correlation method developed by Wu et al.（Wu W H,Tian Y,Luo J,Shao C G,Xu J H and Wang DH 2016 Rev.Sci.Instrum.87 094501） is used to accurately estimate the amplitudes of the prominent harmonic components of the gravitational background signal with time-varying frequency.Except the quadratic slow drift,the angular frequency of the gravitational background signal also includes a cosine oscillation coming from the useful angular acceleration signal,which leads to a deviation from the estimated amplitude.We calculate the correction of the cosine oscillation to the amplitude estimation.The result shows that the corrections of the cosine oscillation to the amplitudes of the fundamental frequency and second harmonic components obtained by the improved correlation method are within respective errors.展开更多
Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the th...Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.展开更多
Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE(Gravity Recovery and Climate Experiment)Follow-On-like missions and gravitational wave detectors.For such accu...Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE(Gravity Recovery and Climate Experiment)Follow-On-like missions and gravitational wave detectors.For such accuracy of modern space missions,a precise relativistic model of light propagation is required.With the post-Newtonian approximation,we utilize the Synge world function method to study the light propagation in the Earth’s gravitational field,deriving the gravitational delays up to order c^(−4).Then,we investigate the influences of gravitational delays in three inter-satellite laser ranging techniques,including one-way ranging,dual one-way ranging,and transponder-based ranging.By combining the parameters of Kepler orbit,the gravitational delays are expanded up to the order of e^(2)(e is the orbital eccentricity).Finally,considering the GRACE Follow-On-like missions,we estimate the gravitational delays to the level of picometer.The results demonstrate some high-order gravitational and coupling effects,such as c^(−4)-order gravitational delays and coupling of Shapiro and beat frequency,which may be non-negligible for higher precision laser ranging in the future.展开更多
We report construction of an iodine-stabilized laser frequency standard at 532 nm based on modulation transfer spectroscopy(MTS)technology with good reproducibility.A frequency stability of 2.5×10^(-14)at 1 s ave...We report construction of an iodine-stabilized laser frequency standard at 532 nm based on modulation transfer spectroscopy(MTS)technology with good reproducibility.A frequency stability of 2.5×10^(-14)at 1 s averaging time is achieved,and the frequency reproducibility has a relative uncertainty of 3.5×10^(-13),demonstrating the great stability of our setup.The systematic uncertainty of the iodine-stabilized laser frequency standard is evaluated,especially the contribution of the residual amplitude modulation(RAM).The contribution of the RAM in MTS cannot be evaluated directly.To solve this problem,we theoretically deduce the MTS signal with RAM under large modulation depth,and prove that the non-symmetric shape of the MTS signal is directly related to the MTS effect.The non-symmetric shape factor can be calibrated with a frequency comb,and in real experiments,this value can be obtained by least-squares fitting of the MTS signal,from which we can infer the RAMinduced frequency shift.The full frequency uncertainty is evaluated to be 5.3 kHz(corresponding to a relative frequency uncertainty of 9.4×10^(-12)).The corrected transition frequency has a difference from the BIPM-recommended value of 2 kHz,which is within 1σ uncertainty,proving the validity of our evaluation.展开更多
We theoretically investigate the application of the fringe-locking method（FLM） in the dual-species quantum test of the weak equivalence principle（WEP）.With the FLM,the measurement is performed invariably at the mi...We theoretically investigate the application of the fringe-locking method（FLM） in the dual-species quantum test of the weak equivalence principle（WEP）.With the FLM,the measurement is performed invariably at the midfringe,and the extraction of the phase shift for atom interferometers is linearized.For the simultaneous interferometers,this linearization enables a good common-mode rejection of vibration noise,which is usually the main limit for high precision WEP tests of the dual-species kind.We note that this method also allows for an unbiased determination of the gravity accelerations difference,which meanwhile is ready to be implemented.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.41127002,11204094,11205064,and 11474115)the National High Technology Research and Development Program of China(Grant No.2011AA060503)
文摘Developments of the micro-Gal level gravimeter based on atom interferometry are reviewed, and the recent progress and results of our group are also presented. Atom interferometric gravimeters have shown high resolution and accuracy for gravity measurements. This kind of quantum sensor has excited world-wide interest for both practical applications and fundamental research.
基金Supported by the National Key Research and Development Program of China under Grant No 2017YFA0304400the National Natural Science Foundation of China under Grant Nos 91336213,11703031,U1731132 and 11774108
文摘We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop(PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator(OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer(DDS) which is also referenced to the 100 MHZ OCXO to generate the final6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are-47 d Bc/Hz,-77 dBc/Hz,-104 dBc/Hz and-121 dBc/Hz at1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than 5.0 × 10^-14τ^1/2 when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.
基金Supported by the National Natural Science Foundation of China under Grant No 11235004
文摘Performance test of a high precise accelerometer or an inertial sensor on the ground is inevitably limited by the seismic noise. A torsion pendulum has been used to investigate the performances of an electrostatic accelerometer, where the test mass is suspended by a fiber to compensate for its weight, and this scheme demonstrates an advantage, compared with the high-voltage levitation scheme, in which the effect of the seismic noise can be suppressed for a few orders of magnitude in low frequencies. In this work, the capacitive electrode cage is proposed to be suspended by another pendulum, and theoretical analysis shows that the effects of the seismic noise can be further suppressed for more than one order by suspending the electrode cage.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11655001 and 11605065)
文摘Over the past 50 years, lunar laser ranging has made great contributions to the understanding of the Earth–Moon system and the tests of general relativity. However, because of the lunar libration, the Apollo and Lunokhod corner-cube retroreflector（CCR） arrays placed on the Moon currently limit the ranging precision to a few centimeters for a single photon received. Therefore, it is necessary to deploy a new retroreflector with a single and large aperture to improve the ranging precision by at least one order of magnitude. Here we present a hollow retroreflector with a 170-mm aperture fabricated using hydroxide-catalysis bonding technology. The precisions of the two dihedral angles are achieved by the mirror processing with a sub-arc-second precision perpendicularity, and the remaining one is adjusted utilizing an auxiliary optical configuration including two autocollimators. The achieved precisions of the three dihedral angles are 0.10 arcsecond,0.30 arc-second, and 0.24 arc-second, indicating the 68.5% return signal intensity of ideal Apollo 11/14 based on the far field diffraction pattern simulation. We anticipate that this hollow CCR can be applied in the new generation of lunar laser ranging.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41127002,11574099,41504034,and 11474115)the National Basic Research Program of China(Grant No.2010CB832806)
文摘We investigated the sensitivities of atom interferometers in the usual fringe-scanning method （FSM） versus the fringe- locking method （FLM）. The theoretical analysis shows that for typical noises in atom interferometers, the FSM will degrade the sensitivity while the FLM does not. The sensitivity-improvement factor of the FLM over the FSM depends on the type of noises, which is validated by numerical simulations. The detailed quantitative analysis on this fundamental issue is presented, and our analysis is readily extendable to other kinds of noises as well as other fringe shapes in addition to a cosine one.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160,91636221,and 11605065)
文摘In a test of the weak equivalence principle （WEP） with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the free oscillation signal and employ the correlation method to estimate the amplitude of the modulation signal. The data analysis of an experiment shows that the uncertainties of amplitude components of the modulation signal obtained by the correlation method are in agreement with those due to white noise. The power spectral density of the modulation signal obtained by the correlation method is about one order higher than the thermal noise limit. It indicates that the correlation method is an effective way to estimate the amplitude of the modulation signal and it is instructive to conduct a high-accuracy WEP test.
基金Project supported by the National Natural Science Foundation of China(Grant No.11575160)
文摘In the torsion pendulum experiments, the thermal noise sets the most fundamental limit to the accurate estimation of the amplitude of the signal with known frequency. The variance of the conventional method can meet the limit only when the measurement time is much longer than the relaxation time of the pendulum. By using the maximum likelihood estimation and the equation-of-motion filter operator, we propose an optimal(minimum variance, unbiased) amplitude estimation method without limitation of the measurement time, where thermal fluctuation is the leading noise. While processing the experimental data tests of the Newtonian gravitational inverse square law, the variance of our method has been improved than before and the measurement time of determining the amplitude with this method has been reduced about half than before for the same uncertainty. These results are significant for the torsion experiment when the measurement time is limited.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175160,11275075,and 11575160)
文摘Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio ？t/（1/λ） where ？t is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time ？t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio ？t/（1/λ） is less than 1, the uncertainty remains substantially unchanged.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11625417,11727809,11474115,91636219,and 91636221)the Post-doctoral Science Foundation of China(Grant No.2017M620308)
文摘The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effect with a simplified theoretical model of the time-propagation operator. According to the typical parameters, we find that this effect should be taken into account when the gravimeter reaches an accuracy of 10^-10g, and the larger the pulse duration is, the more obvious the systematic effect will be. Finally, we make a simple discussion on the possibility of testing this effect.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160,11175160,11275075,and 11511130011)
文摘In the measurement of G with the angular acceleration method,the improved correlation method developed by Wu et al.（Wu W H,Tian Y,Luo J,Shao C G,Xu J H and Wang DH 2016 Rev.Sci.Instrum.87 094501） is used to accurately estimate the amplitudes of the prominent harmonic components of the gravitational background signal with time-varying frequency.Except the quadratic slow drift,the angular frequency of the gravitational background signal also includes a cosine oscillation coming from the useful angular acceleration signal,which leads to a deviation from the estimated amplitude.We calculate the correction of the cosine oscillation to the amplitude estimation.The result shows that the corrections of the cosine oscillation to the amplitudes of the fundamental frequency and second harmonic components obtained by the improved correlation method are within respective errors.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160 and 11275075)the Natural Science Foundation of Key Projects of Hubei Province,China(Grant No.2013CFA045)
文摘Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12247150,12305062,12175076,and 11925503)the Post-doctoral Science Foundation of China(Grant No.2022M721257)the Guangdong Major Project of Basic and Applied Basic Research(Grant No.2019B030302001).
文摘Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE(Gravity Recovery and Climate Experiment)Follow-On-like missions and gravitational wave detectors.For such accuracy of modern space missions,a precise relativistic model of light propagation is required.With the post-Newtonian approximation,we utilize the Synge world function method to study the light propagation in the Earth’s gravitational field,deriving the gravitational delays up to order c^(−4).Then,we investigate the influences of gravitational delays in three inter-satellite laser ranging techniques,including one-way ranging,dual one-way ranging,and transponder-based ranging.By combining the parameters of Kepler orbit,the gravitational delays are expanded up to the order of e^(2)(e is the orbital eccentricity).Finally,considering the GRACE Follow-On-like missions,we estimate the gravitational delays to the level of picometer.The results demonstrate some high-order gravitational and coupling effects,such as c^(−4)-order gravitational delays and coupling of Shapiro and beat frequency,which may be non-negligible for higher precision laser ranging in the future.
基金the National Key Research and Development Program of China(Grant No.2017YFA0304401)Key-Area Research and Development Program of GuangDong Province,China(Grant No.2019B030330001)the National Natural Science Foundation of China(Grant Nos.11174095,61875065,91536116,and 11804108).
文摘We report construction of an iodine-stabilized laser frequency standard at 532 nm based on modulation transfer spectroscopy(MTS)technology with good reproducibility.A frequency stability of 2.5×10^(-14)at 1 s averaging time is achieved,and the frequency reproducibility has a relative uncertainty of 3.5×10^(-13),demonstrating the great stability of our setup.The systematic uncertainty of the iodine-stabilized laser frequency standard is evaluated,especially the contribution of the residual amplitude modulation(RAM).The contribution of the RAM in MTS cannot be evaluated directly.To solve this problem,we theoretically deduce the MTS signal with RAM under large modulation depth,and prove that the non-symmetric shape of the MTS signal is directly related to the MTS effect.The non-symmetric shape factor can be calibrated with a frequency comb,and in real experiments,this value can be obtained by least-squares fitting of the MTS signal,from which we can infer the RAMinduced frequency shift.The full frequency uncertainty is evaluated to be 5.3 kHz(corresponding to a relative frequency uncertainty of 9.4×10^(-12)).The corrected transition frequency has a difference from the BIPM-recommended value of 2 kHz,which is within 1σ uncertainty,proving the validity of our evaluation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41127002,11574099,and 11474115)the National Basic Research Program of China(Grant No.2010CB832806)
文摘We theoretically investigate the application of the fringe-locking method（FLM） in the dual-species quantum test of the weak equivalence principle（WEP）.With the FLM,the measurement is performed invariably at the midfringe,and the extraction of the phase shift for atom interferometers is linearized.For the simultaneous interferometers,this linearization enables a good common-mode rejection of vibration noise,which is usually the main limit for high precision WEP tests of the dual-species kind.We note that this method also allows for an unbiased determination of the gravity accelerations difference,which meanwhile is ready to be implemented.
