Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the
6S1/2 and
5D5/2 states to 0.1% precision. We find $R={\ensuremath{\Delta}}_{S}/{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at 514.531 nm where ${\ensuremath{\Delta}}_{S,D}$ are the light shifts of the $m=\ifmmode\pm\else\textpm\fi{}1/2$ splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of
R would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.
Abstract In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift and the parity-violating amplitude of the clock transition, and can be used as probes to test quantum electrodynamic effects, especially at the
10−3-
10−4 level. We developed a universal experimental approach to precise determination of the dipole transition matrix element with a energy level of two transition channels at various atomic species by using the quantum shelving technique. In which, the time-increased pulses were utilized to induce quantum shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited
2P1/2 state to the
2S1/2 ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this method to single Yb
+ ion, and determined the
6p 2P1/2 -
5d 2D3/2 transition matrix element of 2.9395(21)~
ea0, which represents an order of magnitude improvement over previous determination. By combining our result with the
6p 2P1/2 lifetime of 8.12(2)~ns, we extracted the
6s 2S1/2 -
6p 2P1/2 transition matrix element to be 2.4695(31)~
ea0.
We report an experimental determination of the ground-state hyperfine constant
A of the
25Mg+ ions by measuring the $|{S}_{1/2},F=2,m=0\ensuremath{\rangle}$ to $|{S}_{1/2},F=3,m=0\ensuremath{\rangle}$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=\ensuremath{-}596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.
We have measured the ratio
R of the vector ac Stark effect (or light shift) in the
6S1∕2 and
5D3∕2 states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found $R={\ensuremath{\Delta}}_{S}∕{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at
514.531nm where ${\ensuremath{\Delta}}_{S,D}$ are the vector light shifts of the
6S1∕2 and
5D3∕2 $m=\ifmmode\pm\else\textpm\fi{}1∕2$ splittings due to circularly polarized light, and now we report the value at
1111.68nm,
R=+0.4176(8). These observations together yield a value of the $⟨5D\ensuremath{\Vert}er\ensuremath{\Vert}4F⟩$ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.
We report an improved measurement of the Land\'e
gJ factor of the
5D5/2 state of singly ionized barium. Measurements were performed on single Doppler-cooled
138Ba
+ ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the
6S1/2 and
5D5/2 states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 $\ensuremath{\mu}$m. By calculating the ratio of the two Zeeman splittings, and using the measured Land\'e
gJ factor of the
6S1/2 state, we find a value of 1.200 372
(4stat)(7sys) for
gD5/2.
We have used stored ion methods to improve resolution and sensitivity in optical spectroscopy. Single atomic ions have been confined by electric and magnetic fields, cooled by laser radiation pressure to temperatures on the order of 1 mK, and probed spectroscopically with narrowband lasers. The absorption resonance of a single Hg + ion has been observed by a decrease in the transmitted light intensity. An ultraviolet transition in Hg + has been observed with a linewidth of only 30 kHz. Quantum jumps to and from metastable levels of Hg + have been observed and used to determine radiative decay rates and to infer the existence of photon antibunching. Quantum jumps have also been observed in single Mg + ions.