Cold trapped ions can be excellent sensors for ultra-precision detection of physical quantities,which strongly depends on the measurement situation at hand.The stylus ion trap,formed by two concentric cylinders over a...Cold trapped ions can be excellent sensors for ultra-precision detection of physical quantities,which strongly depends on the measurement situation at hand.The stylus ion trap,formed by two concentric cylinders over a ground plane,holds the promise of relatively simple structure and larger solid angle for optical access and fluorescence collection in comparison with the conventional ion traps.Here we report our fabrication and characterization of the first stylus ion trap constructed in China,aiming for studying quantum optics and sensing weak electric fields in the future.We have observed the stable confinement of the ion in the trapping potential for more than two hours and measured the heating rate of the trap to be dε/dt=7.10±0.13 meV/s by the Doppler recooling method.Our work starts a way to building practical quantum sensors with high efficiency of optical collection and with ultimate goal for contributing to future quantum information technology.展开更多
In this paper,we use the method of representation of Lie group to study a class of nonhomoge-neous convolution operator on the nilpotent Lie group H^n×R^k,and give a criteerion of their hypocllipticity.
Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of genera...Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation -ΔH^nu=|u|^p-1u,x∈H^n has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.展开更多
In this paper,we use the representation of nilpotent Lie group method to give a sufficient and necessary condition for subellipticity of Left invarient differental operators on nilpotent Lipgroup G^2n+k.
In this paper,we prove one case of conjecture given by Hernandez and Leclerc.We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quant...In this paper,we prove one case of conjecture given by Hernandez and Leclerc.We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group Uq(3).As a conclusion,for every exchange relation of cluster algebra,there exists an exact sequence of the full subcategory corresponding to it.展开更多
In this paer we will study the wellposed of the inital value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis L=(-1)^k/2^k ∑j=1...In this paer we will study the wellposed of the inital value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis L=(-1)^k/2^k ∑j=1^1 aj(Zj^k Zj^-k+Zj^-kZj^k)+(-i)^3k rS^k(where aj>0,r∈R)on the Heisenboerg group,then obtain the explicit expression of the fundamental solutions for the generalized heat operator δ/δt+L and the operator L.展开更多
基金Project supported by the Special Project for Research and Development in Key Areas of Guangdong Province,China (Grant No.2020B0303300001)the National Natural Science Foundation of China (Grant Nos.U21A20434,12074346,12074390,11835011,11804375,and 11804308)+2 种基金the Fund from the Key Laboratory of Guangzhou for Quantum Precision Measurement (Grant No.202201000010)the Science and Technology Projects in Guangzhou (Grant No.202201011727)the Nansha Senior Leading Talent Team Technology Project (Grant No.2021CXTD02)。
文摘Cold trapped ions can be excellent sensors for ultra-precision detection of physical quantities,which strongly depends on the measurement situation at hand.The stylus ion trap,formed by two concentric cylinders over a ground plane,holds the promise of relatively simple structure and larger solid angle for optical access and fluorescence collection in comparison with the conventional ion traps.Here we report our fabrication and characterization of the first stylus ion trap constructed in China,aiming for studying quantum optics and sensing weak electric fields in the future.We have observed the stable confinement of the ion in the trapping potential for more than two hours and measured the heating rate of the trap to be dε/dt=7.10±0.13 meV/s by the Doppler recooling method.Our work starts a way to building practical quantum sensors with high efficiency of optical collection and with ultimate goal for contributing to future quantum information technology.
基金Supported by the National Natural Science Foundation (10471034) Supported by the Provincial Foundationof Outstanding Young Scholars of Henan (0512000100) Supported by the Foundation of Henan University (05YBZR013)
基金Supported in part by National Natural Science Foundation of China under Grant No. 10971071the Outstanding Youth Fund of Henan Province under Grant No. 0512000100Innovation Fund of Colleges and Universities in Henan Province
文摘In this paper, we construct a new algebra structure 7-twisted affine Lie algebra ■[θ] and study itsvertex operator representations.
文摘In this paper,we use the method of representation of Lie group to study a class of nonhomoge-neous convolution operator on the nilpotent Lie group H^n×R^k,and give a criteerion of their hypocllipticity.
文摘Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation -ΔH^nu=|u|^p-1u,x∈H^n has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.
文摘In this paper,we use the representation of nilpotent Lie group method to give a sufficient and necessary condition for subellipticity of Left invarient differental operators on nilpotent Lipgroup G^2n+k.
基金Project supported by the National Natural Science Foundation of China(Grant No.11475178)
文摘In this paper,we prove one case of conjecture given by Hernandez and Leclerc.We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group Uq(3).As a conclusion,for every exchange relation of cluster algebra,there exists an exact sequence of the full subcategory corresponding to it.
文摘In this paer we will study the wellposed of the inital value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis L=(-1)^k/2^k ∑j=1^1 aj(Zj^k Zj^-k+Zj^-kZj^k)+(-i)^3k rS^k(where aj>0,r∈R)on the Heisenboerg group,then obtain the explicit expression of the fundamental solutions for the generalized heat operator δ/δt+L and the operator L.
