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Transitions between Magnetic Sublevels of the Hyperfine Structure Under Modulation of the External Magnetic Field

N. N. Yakobson

Published Apr 1, 1965• 0 citations
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In this paper, we theoretically calculate the natural lifetime of the $5s5p\phantom{\rule{4pt}{0ex}}^{3}\mathrm{P}_{0}^{o}$ state of the $^{87}\mathrm{Sr}$ atom and evaluate the effect of an external magnetic field on the lifetimes of Zeeman sublevels. Using the multiconfiguration Dirac-Hartree-Fock method, the hyperfine-induced $5s5p^{3}\mathrm{P}_{0}^{o}--5{s}^{2}\phantom{\rule{0.28em}{0ex}}^{1}\mathrm{S}_{0}$ clock transition rate of $^{87}\mathrm{Sr}$ is estimated as $6.39(37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to a lifetime of 156(9) s. Our result closely agrees with previous measurements after correcting the decay rate due to the black-body radiation effect. Additionally, the transition rates of Zeeman sublevels are calculated as a function of the magnetic-field strength. Our theoretical results reveal that transition rates between different excited Zeeman states are discrepant, and the lifetime of magnetic sublevel $+{M}_{F}^{e}\phantom{\rule{4pt}{0ex}}(\ensuremath{-}{M}_{F}^{e}$; the superscript $e$ refers to the excited state, i.e., the $5s5p\phantom{\rule{0.28em}{0ex}}^{3}\mathrm{P}_{0}^{o}$ state) will increase (decrease) with the magnetic-field strength. Moreover, we measure the coupling strength between the clock laser and the $^{87}\mathrm{Sr}$ atoms, and our findings align well with theoretical estimations regarding changes in normalized coupling strength with external magnetic-field strength.

Physical Review A•Jul 28, 2023•5 citations
An extremely thin cell with a wedge gap was developed that makes it possible to form a column of Rb atom vapor with thickness in the range from 100 to 600 nm. It is experimentally shown that the use of this cell, along with commercially available diode lasers, allows one to spectrally resolve individual transitions between the Zeeman sublevels of the hyperfine structure of the 87Rb D 1 line (transitions F g =1, 2→F e =1, 2) in the resonance fluorescence spectrum in the presence of an external magnetic field (B≈200 G). This makes it possible to realize systems consisting of nondegenerate atomic levels. For comparison, it is shown that transitions between the Zeeman sublevels in the fluorescence spectrum obtained with the aid of a conventional cell (1–10 cm long) in an external magnetic field with B∼200 G remain completely masked by the Doppler-broadened profile. The results obtained can be used for the creation of a simple magnetometer based on an extremely thin cell with Rb vapor for the measurement of magnetic fields with a submicron local spatial resolution.
Laser pumping magnetometers using alkali vapors as sensing medium can reach very high sensitivities in magnetic fields covering the range from the earth magnetic field to biological magnetic fields. In this paper, the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling are discussed. The hyperfine structure is further split into Zeeman sublevels for the effects of magnetic field. The electrons transition is made by using laser pumping and RF magnetic field in the hyperfine structure. The results of magne-to-optical double resonance is obtained. The accurate value of the external magnetic field could be measured by the resonant frequency.
In this paper, we theoretically calculate the natural lifetime of the 5s5p3P0o5s5p\phantom{\rule{4pt}{0ex}}^{3}\mathrm{P}_{0}^{o}5s5p3P0o​ state of the 87Sr^{87}\mathrm{Sr}87Sr atom and evaluate the effect of an external magnetic field on the lifetimes of Zeeman sublevels. Using the multiconfiguration Dirac-Hartree-Fock method, the hyperfine-induced 5s5p3P0o−−5s21S05s5p^{3}\mathrm{P}_{0}^{o}--5{s}^{2}\phantom{\rule{0.28em}{0ex}}^{1}\mathrm{S}_{0}5s5p3P0o​−−5s21S0​ clock transition rate of 87Sr^{87}\mathrm{Sr}87Sr is estimated as $6.39(37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to a lifetime of 156(9) s. Our result closely agrees with previous measurements after correcting the decay rate due to the black-body radiation effect. Additionally, the transition rates of Zeeman sublevels are calculated as a function of the magnetic-field strength. Our theoretical results reveal that transition rates between different excited Zeeman states are discrepant, and the lifetime of magnetic sublevel $+{M}_{F}^{e}\phantom{\rule{4pt}{0ex}}(\ensuremath{-}{M}_{F}^{e}$; the superscript eee refers to the excited state, i.e., the 5s5p3P0o5s5p\phantom{\rule{0.28em}{0ex}}^{3}\mathrm{P}_{0}^{o}5s5p3P0o​ state) will increase (decrease) with the magnetic-field strength. Moreover, we measure the coupling strength between the clock laser and the 87Sr^{87}\mathrm{Sr}87Sr atoms, and our findings align well with theoretical estimations regarding changes in normalized coupling strength with external magnetic-field strength.