T. Fordell

We report on a precision measurement of the differential static scalar polarizability $Δα_0$ of the ${}^{2}\!S_{1/2} \rightarrow {}^{2}\!D_{5/2}$ optical clock transition in the $^{88}$Sr$^{+}$ ion. The polarizability was determined from the 'magic' ion-trap drive frequency where the micromotion-induced second-order Doppler and quadratic Stark shifts cancel, using a single clock in an interleaved scheme by switching between minimized and large micromotion. By measuring at different Mathieu $q_z$ parameters, $Δα_0$ can be obtained without prior knowledge of the angle between the rf electric field and the trap axis, which would otherwise dominate the systematic uncertainty. For validation, measurements were carried out at different micromotion levels and by displacing the ion in opposite directions. The results show excellent consistency and our value, $Δα_0 = -4.8314(20)\times 10^{-40}\;\mathrm{J\, m^2/V^2} = -29.303(12)\;\mathrm{au}$, reduces the uncertainty by a factor of 3.5 compared to a previous measurement, while showing a discrepancy of $5 σ$. Our measurement reduces the polarizability-related uncertainty of the $^{88}$Sr$^{+}$ clock to $2.2\times 10^{-19}$ for a blackbody radiation temperature of 295 K -- a significant step towards total uncertainties ${<}1\times10^{-18}$. Using existing polarizability transfer schemes, the result can reduce the uncertainty also for other ion species.

The motion of an ion in a radiofrequency (rf) Paul trap is described by the Mathieu equation and the associated stability parameters that are proportional to the rf and dc electric field gradients. Here, a higher-order, iterative method to accurately solve the stability parameters from measured secular frequencies is presented. It is then used to characterize an endcap trap by showing that the trap's radial asymmetry is dominated by the dc field gradients and by measuring the relation between the applied voltages and the gradients. The results are shown to be in good agreement with an electrostatic finite-element-method simulation of the trap. Furthermore, a method to determine the direction of the radial trap axes using a 'tickler' voltage is presented and the temperature dependence of the rf voltage is discussed. As an application for optical ion clocks, the method is used to predict and minimize the electric quadrupole shift (EQS) using the applied dc voltages. Finally, a lower limit of 1070 for the cancellation factor of the Zeeman-averaging EQS cancellation method is determined in an interleaved low/high EQS clock measurement. This reduces the EQS uncertainty of our $^{88}$Sr$^+$ optical clock to ${\lesssim} 1\times 10^{-19}$ in fractional frequency units.

A frequency-stable, broadband laser is presented for experiments on trapped ions. Since the design is based on widely available semiconductor optical amplifier technology, similar lasers can be realized for virtually any wavelength in the near-infrared, and the coherence properties and output power allow for efficient second harmonic generation. No closed-loop frequency stabilization for addressing Doppler- or naturally-broadened, dipole-allowed transitions is needed, and the light source can be turned on and off during a measurement cycle with sub-microsecond response time. As a case study, a 921.7-nm laser with an output power of 20mW and a linewidth of 10GHz is realized, which is then frequency doubled to 460.9nm for excitation of strontium as the first step in photo-ionization. The excitation efficiency is compared to that achievable with a narrow-linewidth distributed Bragg reflector laser as well as to theory.

Many ion species commonly used for laser-cooled ion trapping studies have a low-lying metastable 2D3/2 state that can become populated due to spontaneous emission from the 2P1/2 excited state. This requires a repumper laser to maintain the ion in the Doppler cooling cycle. Typically the 2D3/2 state, or some of its hyperfine components if the ion has nuclear spin, has a higher multiplicity than the upper state of the repumping transition. This can lead to dark states, which have to be destabilized by an external magnetic field or by modulating the polarization of the repumper laser. We propose using unpolarized, incoherent amplified spontaneous emission (ASE) to drive the repumping transition. An ASE source offers several advantages compared to a laser. It prevents the buildup of dark states without external polarization modulation even in zero magnetic field, it can drive multiple hyperfine transitions simultaneously, and it requires no frequency stabilization. These features make it very compact and robust, which is essential for the development of practical, transportable optical ion clocks. We construct a theoretical model for the ASE radiation, including the possibility of the source being partially polarized. Using 88Sr+ as an example, the performance of the ASE source compared to a single-mode laser is analyzed by numerically solving the eight-level density matrix equations for the involved energy levels. Finally a reduced three-level system is derived, yielding a simple formula for the excited state population and scattering rate, which can be used to optimize the experimental parameters. The required ASE power spectral density can be obtained with current technology.