We demonstrate a method to determine dipole matrix elements by comparing measurements of dispersive and absorptive light ion interactions. We measure the matrix element pertaining to the Ca II H line, i.e., the 4(2)S(1/2)↔4(2)P(1/2) transition of (40)Ca(+), for which we find the value 2.8928(43) ea(0). Moreover, the method allows us to deduce the lifetime of the 4(2)P(1/2) state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a long-standing discrepancy between calculated values and experimental results.
We demonstrate a method to determine dipole matrix elements by comparing measurements of dispersive and absorptive light ion interactions. We measure the matrix element pertaining to the Ca II H line, i.e., the 4(2)S(1/2)↔4(2)P(1/2) transition of (40)Ca(+), for which we find the value 2.8928(43) ea(0). Moreover, the method allows us to deduce the lifetime of the 4(2)P(1/2) state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a long-standing discrepancy between calculated values and experimental results.
In the first part of this thesis, a method for determining transition dipole matrix elements is introduced. It combines measuring absorptive and dispersive atom-light interactions off-resonant to the transition in question and is thus resilient against various line-broadening effects. A single 40Ca+ ion confined in a Paul trap is used for implementing that method. Rather than counting individual photons, the method is based on discriminating atomic states of the ion’s level scheme, which circumvents many systematic error sources affecting other methods. The dipole matrix elements of the 42S1/2 ↔ 42P1/2, the 42S1/2 ↔ 42P3/2 and the 42P1/2 ↔ 32D3/2 transitions are determined. Moreover, the method allows also for the deduction of the radiative lifetime of the 42P1/2 state which reads 6.904(26)ns. This value is in agreement with recent theoretical calculations, and resolves a long-standing discrepancy between calculated values and experimental results. In the second part of the thesis, the design, construction, assembly and characterization of a segmented, microstructured Paul trap which can accommodate a fiber cavity for light-ion interaction is described. The trap features 31 segments, which allow for ion transport along the trap axis. Vertical interconnect accesses needed to be incorporated in the design of the conducting paths in order to electrically connect all segment electrodes to the outside. The trap is fabricated from alumina substrates and evaporatively coated with gold. To further characterize the trap, simulations of axial trap frequencies have been compared with measured values for different regions in the trap, also axial transport of single ions over a distance of ≈ 2.5 mm has been implemented. Coherent dynamics on the quadrupole transition of 40Ca+ have been used to perform sideband cooling and a single ion was cooled below the Doppler limit. The dynamics of carrier and red sideband transitions have been employed to measure the trap’s heating rate, which amounts to n = 16.5/ms at a trap frequency of 2π × 1.32 MHz.
We report a precise determination of the lifetime of the (4p)2P3/2 state of 40Ca+, ${\ensuremath{\tau}}_{{P}_{3/2}}=6.639(42)\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, using a combination of measurements of the induced light shift and scattering rate on a single trapped ion. Good agreement with the result of a recent high-level theoretical calculation, 6.69(6) ns [M. S. Safronova et al., Phys. Rev. A 83, 012503 (2011)], but a 6-$\ensuremath{\sigma}$ discrepancy with the most precise previous experimental value, 6.924(19) ns [J. Jin et al., Phys. Rev. Lett. 70, 3213 (1993)], is found. To corroborate the consistency and accuracy of the new measurements, relativistically corrected ratios of reduced-dipole-matrix elements are used to directly compare our result with a recent result for the P1/2 state, yielding a good agreement. The application of the present method to precise determinations of radiative quantities of molecular systems is discussed.
We report the experimental determination of the 4s2S1/2 $\ensuremath{\leftrightarrow}$ 3d2D5/2 quadrupole transition matrix element in 40Ca+ by measuring the branching fraction of the 3d2D5/2 state decaying into the ground state 4s2S1/2 and the lifetime of the 3d2D5/2 state, using a technique of a highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching fraction and improved lifetime are, respectively, 0.998(12) and 1.1649(44) s, which yield the value of the quadrupole transition matrix element (in absolute value) of 9.733(52) ea02 with an uncertainty of 0.54%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.
Abstract We present for the first time a direct measurement of the lifetime ratio between the 3 d 2 D 3 / 2 and 3 d 2 D 5 / 2 metastable states in a single trapped 40 Ca + . A high-efficiency quantum state detection technique is adopted to monitor the quantum jumps, and a high precision and synchronized measurement sequence is used for laser control to study the rule of spontaneous decay. Our method shows that the lifetime ratio is a constant and is irrelevant to the dwell time; it is only determined by the spontaneous decay probabilities of the two metastable states at one random decay time, independent of the lifetimes of the two metastable states. Systematic errors such as collisions with background gases, heating effects, impurity components, the shelving and pumping rates and the photon counts are analyzed, and the lifetime ratio between the 3 d 2 D 3 / 2 and 3 d 2 D 5 / 2 states is directly measured to be 1.0257(43) with an uncertainty of 0.42%. Our result is in good agreement with the most precise many-body atomic structure calculations. Our method can be used to obtain the lifetime of a state which is usually difficult to measure and can be used to determine the magnetic dipole transition matrix elements in heavy ions such as Ba + and Ra + , and can also be universally applied to lifetime ratio measurements of other single atoms and ions with a similar structure.
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 6p2P1/2 - 5d2D3/2 transition matrix element of 2.9395(21)~ea0, which represents an order of magnitude improvement over previous determination. By combining our result with the 6p2P1/2 lifetime of 8.12(2)~ns, we extracted the 6s2S1/2 - 6p2P1/2 transition matrix element to be 2.4695(31)~ea0.
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⟩ in 138Ba+. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be 3.3227(12), corresponding to a P1/2 excited-state radiative lifetime of 7.8663(56)~ns. Combining our experimental results with a prior model for the differential scalar polarizability Δα0(ω), we extract the static value 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+ 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.