Note: Measuring capacitance and inductance of a helical resonator and improving its quality factor by mutual inductance alteration

Design of a helical resonator with improved figure of merit

A helical resonator serves as a key element for the detection of the trapped charged particles in a Penning trap. In order to compare the performance of the helical resonators, the concept of figure of merit (FOM) was introduced by Ulmer et al. [Nucl. Instrum. Methods Phys. Res., Sect. A 705, 55-60 (2013)]. In this work, we optimized the geometrical parameters of a resonator by numerical simulations keeping its outer dimensions and the diameter of the copper wire fixed and obtained the best possible value of FOM under these constraints. The corresponding 95 MHz helical resonator has been designed and fabricated, and its measured value of FOM is in good agreement with the simulated values. An empirical relationship between the total length of the wire to make the helical coil and the resonance frequency has been obtained. The simulations show that the FOM increases considerably with the increase in the conductivity of the building material, and this would be useful in detecting the feeble trap signal in cryogenic environment.

A cryogenic radio-frequency ion trap for quantum logic spectroscopy of highly charged ions

A cryogenic radio-frequency ion trap system designed for quantum logic spectroscopy of highly charged ions (HCI) is presented. It includes a segmented linear Paul trap, an in-vacuum imaging lens, and a helical resonator. We demonstrate ground state cooling of all three modes of motion of a single ⁹Be⁺ ion and determine their heating rates as well as excess axial micromotion. The trap shows one of the lowest levels of electric field noise published to date. We investigate the magnetic-field noise suppression in cryogenic shields made from segmented copper, the resulting magnetic field stability at the ion position and the resulting coherence time. Using this trap in conjunction with an electron beam ion trap and a deceleration beamline, we have been able to trap single highly charged Ar¹³⁺ (Ar XIV) ions concurrently with single Be⁺ ions, a key prerequisite for the first quantum logic spectroscopy of a HCI. This major stepping stone allows us to push highly-charged-ion spectroscopic precision from the gigahertz to the hertz level and below.

Atomic flux distribution from a low-divergent dark wall oven

Nearly collimated atomic beam is of interest for a variety of experiments. This article reports a simple way of modifying the atomic beam distribution using a dark wall oven and describes detailed study of outcoming atoms' spatial distribution. A simple design is obtained by employing the fact that inhomogeneous thermal distribution along a capillary results due to its partial resistive heating. Based on this phenomenon, we have designed a dark wall oven consisting of a reservoir, collimator, and cold absorber at the exit end of atoms, where all three are fabricated out of a single stainless steel capillary. The nearly collimated spatial distribution of the atoms resulting due to the absorber eliminating the atoms diverging above a certain angle is modeled and experimentally verified. A divergence as minimum as 1.2(1)° corresponding to a half angle θ_1/2 = 0.9(1)° is measured at an oven temperature of 250 °C that produces an atomic flux of about 8 × 10⁹ atoms s^-1. Total flux as estimated using our measured spatial distribution of atoms matches well with the numerically simulated values of it for the dark wall oven.

Estimation of the ion-trap assisted electrical loads and resulting BBR shift

Capacitive, inductive and resistive loads of an ion-trap system, which can be modelled as LCR circuits, are important to know for building a high accuracy experiment. Accurate estimation of these loads is necessary for delivering the desired radio frequency (RF) signal to an ion trap via an RF resonator. Of particular relevance to the trapped ion optical atomic clock, determination of these loads lead to accurate evaluation of the Black-Body Radiation (BBR) shift resulting from the inaccurate machining of the ion-trap itself. We have identified different sources of these loads and estimated their values using analytical and finite element analysis methods, which are found to be well in agreement with the experimentally measured values. For our trap geometry, we obtained values of the effective inductive, capacitive and resistive loads as: 3.1 μH, 3.71 (1) μH, 3.68 (6) μH; 50.4 pF, 51.4 (7) pF, 40.7 (2) pF; and 1.373 Ω, 1.273 (3) Ω, 1.183 (9) Ω by using analytical, numerical and experimental methods, respectively. The BBR shift induced by the excess capacitive load arising due to machining inaccuracy in the RF carrying parts has been accurately estimated, which results to a fractional frequency shift of 6.6 × 10⁻¹⁷ for an RF of 1 kV at 2π × 15 MHz and with ±10 μm machining inaccuracy. This needs to be incorporated into the total systematic uncertainty budget of a frequency standard as it is about one order of magnitude higher than the present precision of the trapped ion optical clocks.