Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result...Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result given by Takens to the cubic homogeneous parameterizedvector fields with six parameters.展开更多
High-precision sensing of vectorial forces has broad impact on both fundamental research and technological applications such as the examination of vacuum fluctuations and the detection of surface roughness of nanostru...High-precision sensing of vectorial forces has broad impact on both fundamental research and technological applications such as the examination of vacuum fluctuations and the detection of surface roughness of nanostructures.Recent years have witnessed much progress on sensing alternating electromagnetic forces for the rapidly advancing quantum technology-orders of magnitude improvement has been accomplished on the detection sensitivity with atomic sensors,whereas such high-precision measurements for static electromagnetic forces have rarely been demonstrated.Here,based on quantum atomic matter waves confined by a two-dimensional optical lattice,we perform precision measurement of static electromagnetic forces by imaging coherent wave mechanics in the reciprocal space.The lattice confinement causes a decoupling between real-space and reciprocal dynamics,and provides a rigid coordinate frame for calibrating the wavevector accumulation of the matter wave.With that we achieve a stateof-the-art sensitivity of 2.30(8)×10^(-26) N/√Hz.Long-term stabilities on the order of 10^(-28) N are observed in the two spatial components of a force,which allows probing atomic Van der Waals forces at one millimeter distance.As a further illustrative application,we use our atomic sensor to calibrate the control precision of an alternating electromagnetic force applied in the experiment.Future developments of this method hold promise for delivering unprecedented atom-based quantum force sensing technologies.展开更多
基金National Key Basic Research Special Fund(No.1998020307) National Natural Science Foundation of China(No.19990510).
文摘Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result given by Takens to the cubic homogeneous parameterizedvector fields with six parameters.
基金supported by the National Program on Key Basic Research Project of China (2018YFA0305601, 2021YFA07183012021YFA1400900)+4 种基金the National Natural Science Foundation of China (61727819, 11934002, and 11874073)Shanghai Municipal Science and Technology Major Project (2019SHZDZCX01)the Chinese Academy of Sciences Priority Research Program(XDB35020100)the Science and Technology Major Project of Shanxi (202101030201022)the Space Application System of China Manned Space Program
文摘High-precision sensing of vectorial forces has broad impact on both fundamental research and technological applications such as the examination of vacuum fluctuations and the detection of surface roughness of nanostructures.Recent years have witnessed much progress on sensing alternating electromagnetic forces for the rapidly advancing quantum technology-orders of magnitude improvement has been accomplished on the detection sensitivity with atomic sensors,whereas such high-precision measurements for static electromagnetic forces have rarely been demonstrated.Here,based on quantum atomic matter waves confined by a two-dimensional optical lattice,we perform precision measurement of static electromagnetic forces by imaging coherent wave mechanics in the reciprocal space.The lattice confinement causes a decoupling between real-space and reciprocal dynamics,and provides a rigid coordinate frame for calibrating the wavevector accumulation of the matter wave.With that we achieve a stateof-the-art sensitivity of 2.30(8)×10^(-26) N/√Hz.Long-term stabilities on the order of 10^(-28) N are observed in the two spatial components of a force,which allows probing atomic Van der Waals forces at one millimeter distance.As a further illustrative application,we use our atomic sensor to calibrate the control precision of an alternating electromagnetic force applied in the experiment.Future developments of this method hold promise for delivering unprecedented atom-based quantum force sensing technologies.
