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Precision determination of dipole transition matrix elements with a single trapped ion

Hua Guan

Published Oct 10, 2023• 0 citations
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Abstract

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 $^{2}\!P_{1/2}$ state to the $^{2}\!S_{1/2}$ 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 $6p~^{2}\!P_{1/2}$ - $5d~^{2}\!D_{3/2}$ transition matrix element of 2.9395(21)~$ea_{0}$, which represents an order of magnitude improvement over previous determination. By combining our result with the $6p~^{2}\!P_{1/2}$ lifetime of 8.12(2)~ns, we extracted the $6s~^{2}\!S_{1/2}$ - $6p~^{2}\!P_{1/2}$ transition matrix element to be 2.4695(31)~$ea_{0}$.

DOI
10.21203/rs.3.rs-3374534/v1

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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 10−310^{-3}10−3-10−410^{-4}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 2 ⁣P1/2^{2}\!P_{1/2}2P1/2​ state to the 2 ⁣S1/2^{2}\!S_{1/2}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 2 ⁣P1/26p~^{2}\!P_{1/2}6p 2P1/2​ - 5d 2 ⁣D3/25d~^{2}\!D_{3/2}5d 2D3/2​ transition matrix element of 2.9395(21)~ea0ea_{0}ea0​, which represents an order of magnitude improvement over previous determination. By combining our result with the 6p 2 ⁣P1/26p~^{2}\!P_{1/2}6p 2P1/2​ lifetime of 8.12(2)ns, we extracted the 6s 2 ⁣S1/26s~^{2}\!S_{1/2}6s 2S1/2​ - 6p 2 ⁣P1/26p~^{2}\!P_{1/2}6p 2P1/2​ transition matrix element to be 2.4695(31)ea0ea_{0}ea0​.
In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift of the clock transition and the amplitude of the related parity-violating 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 precisely determine the dipole transition matrix elements by using the shelving technique, for the species where two transition channels are involved, in which the excitation pulses with increasing duration were utilized to induce shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited P1/22 state to the S1/22 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 technique to a single Yb+ ion, and determined the 6p P1/22-5d D23/2 transition matrix element 2.9979(20) ea0, which indicates an order of magnitude improvement over existing reports. By combining our result with the 6p P1/22 lifetime of 8.12(2) ns, we extracted the 6s S1/22-6p P1/22 transition matrix element to be 2.4703(31) ea0. The accurately determined dipole transition matrix elements can serve as a benchmark for the development of high-precision atomic many-body theoretical methods.
We present a method to precisely determine the 2D3/2^{2}D_{3/2}2D3/2​ state lifetime of a single trapped 174Yb+^{174}\mathrm{Yb}^{+}174Yb+ ion. This method is based on the detection of photons emitted from excited states, where a highly synchronized measurement sequence for laser control and an intensity-alternating sequence for atomic excitation and photon counting are used to minimize systematic errors. This method is easy to implement and is immune to fluctuations of magnetic field, laser intensity, and frequency detuning. Combined with the real-time approach of background photon correction, the radiative lifetime of the 2D3/2^{2}D_{3/2}2D3/2​ state is determined to be $54.83\ifmmode\pm\else\textpm\fi{}0.18$ ms, which represents an order of magnitude improvement in measurement precision. The accurately determined lifetime sets a benchmark for many-body atomic theories and is particularly useful to determine the coherence time limit of the optical clock.
Measurement of the reduced dipole matrix element in Ba+^++
We present a high-precision measurement of the reduced electric-dipole matrix element ⟨P1/2∥r∥S1/2⟩\langle P_{1/2}\|r\|S_{1/2}\rangle⟨P1/2​∥r∥S1/2​⟩ in 138Ba+^{138}\mathrm{Ba}^+138Ba+. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be 3.322 7(12)3.322\,7(12)3.3227(12), corresponding to a P1/2P_{1/2}P1/2​ excited-state radiative lifetime of 7.866 3(56)7.866\,3(56)7.8663(56)~ns. Combining our experimental results with a prior model for the differential scalar polarizability Δα0(ω)Δα_0(ω)Δα0​(ω), we extract the static value Δα0(0)=−73.09(12)Δα_0(0) = -73.09(12)Δα0​(0)=−73.09(12)a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature Ba+\mathrm{Ba}^+Ba+ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.
We report a measurement of the ratio of electric dipole transition matrix elements of cesium for the $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ transitions. We determine this ratio of matrix elements through comparisons of two-color, two-photon excitation rates of the 7s2S1/27s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}7s2S1/2​ state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of $R\ensuremath{\equiv}\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}/\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=1.5272(17)$ is in excellent agreement with a theoretical prediction of R=1.5270(27)R=1.5270(27)R=1.5270(27). Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of RRR. Combined with our recent determination of the lifetime of the 7s2S1/27s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}7s2S1/2​ state, we determine reduced matrix elements for these two transitions, $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}=\ensuremath{-}6.489(5)\phantom{\rule{4pt}{0ex}}{a}_{0}$ and $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=\ensuremath{-}4.249(4)\phantom{\rule{4pt}{0ex}}{a}_{0}$. These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.
We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba+ ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S(1/2) ground state or the 5D(3/2) metastable state. The ion is exposed to an rf field, and a probing/shelving mechanism detects whether spin-flip transitions have taken place. We have observed rf transitions with linewidths of 15 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba+ will permit a precise determination of the ratio of transition matrix elements.
We present a measurement of the branching ratios from the 6P3∕26{P}_{3∕2}6P3∕2​ state of BaII\mathrm{Ba}\phantom{\rule{0.2em}{0ex}}\mathrm{II}BaII into all dipole-allowed decay channels (6S1∕26{S}_{1∕2}6S1∕2​, 5D3∕25{D}_{3∕2}5D3∕2​, and 5D5∕25{D}_{5∕2}5D5∕2​). Measurements were performed on single 138Ba+^{138}{\mathrm{Ba}}^{+}138Ba+ ions in a linear Paul trap with a frequency-doubled mode-locked Ti:sapphire laser resonant with the $6{S}_{1∕2}\ensuremath{\rightarrow}6{P}_{3∕2}$ transition at 455nm455\phantom{\rule{0.3em}{0ex}}\mathrm{nm}455nm by detection of electron shelving into the dark 5D5∕25{D}_{5∕2}5D5∕2​ state. By driving a $\ensuremath{\pi}$ Rabi rotation with a single femtosecond pulse, an absolute measurement of the branching ratio to 5D5∕25{D}_{5∕2}5D5∕2​ state was performed. Combined with a measurement of the relative decay rates into 5D3∕25{D}_{3∕2}5D3∕2​ and 5D5∕25{D}_{5∕2}5D5∕2​ states performed with long trains of highly attenuated 455nm455\phantom{\rule{0.3em}{0ex}}\mathrm{nm}455nm pulses, it allowed the extraction of the absolute ratios of the other two decays. Relative strengths normalized to unity are found to be $0.756\ifmmode\pm\else\textpm\fi{}0.046$, $0.0290\ifmmode\pm\else\textpm\fi{}0.0015$, and $0.215\ifmmode\pm\else\textpm\fi{}0.0064$ for 6S1∕26{S}_{1∕2}6S1∕2​, 5D3∕25{D}_{3∕2}5D3∕2​, and 5D5∕25{D}_{5∕2}5D5∕2​, respectively. This approximately constitutes a threefold improvement over the best previous measurements and is a sufficient level of precision to compare to calculated values for dipole matrix elements.