We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser.We calculate the relative population probabilities at each level the...We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser.We calculate the relative population probabilities at each level theoretically with the density matrix method.In a steady state,5.8% atoms are at 7S1/2 level and 2.9% at 6P3/2 level,which builds up the population inversion between the two levels.We obtain the fluorescence spectra produced in thermal cesium cell in our experiment.The measured relative intensity of each available fluorescence spectral line in the experiment agrees very well with the theoretical result.The demonstrated population inversion between 7S1/2 and 6P3/2 levels can be used to construct an active optical clock of four-level system with a wavelength of 1469.9 nm.展开更多
The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-fiat module if Tor1r（M, N） is GV-torsion for all R-modules N. In this paper, we introduc...The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-fiat module if Tor1r（M, N） is GV-torsion for all R-modules N. In this paper, we introduce the w-operation in Gorenstein homological algebra. An R-module M is called Ding w-flat if there exists an exact sequence of projective R-modules ... → P1 → P0 → p0 → p1 → ... such that M Im（P0 → p0） and such that the functor HomR （-,F） leaves the sequence exact whenever F is w-flat. Several well- known classes of rings are characterized in terms of Ding w-flat modules. Some examples are given to show that Ding w-flat modules lie strictly between projective modules and Gorenstein projective modules. The Ding w-flat dimension （of modules and rings） and the existence of Ding w-flat precovers are also studied.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10874009 and 11074011)
文摘We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser.We calculate the relative population probabilities at each level theoretically with the density matrix method.In a steady state,5.8% atoms are at 7S1/2 level and 2.9% at 6P3/2 level,which builds up the population inversion between the two levels.We obtain the fluorescence spectra produced in thermal cesium cell in our experiment.The measured relative intensity of each available fluorescence spectral line in the experiment agrees very well with the theoretical result.The demonstrated population inversion between 7S1/2 and 6P3/2 levels can be used to construct an active optical clock of four-level system with a wavelength of 1469.9 nm.
文摘The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-fiat module if Tor1r（M, N） is GV-torsion for all R-modules N. In this paper, we introduce the w-operation in Gorenstein homological algebra. An R-module M is called Ding w-flat if there exists an exact sequence of projective R-modules ... → P1 → P0 → p0 → p1 → ... such that M Im（P0 → p0） and such that the functor HomR （-,F） leaves the sequence exact whenever F is w-flat. Several well- known classes of rings are characterized in terms of Ding w-flat modules. Some examples are given to show that Ding w-flat modules lie strictly between projective modules and Gorenstein projective modules. The Ding w-flat dimension （of modules and rings） and the existence of Ding w-flat precovers are also studied.
