Two-phase driving of a linear radio-frequency ion trap

TL;DR

This work addresses axial micromotion caused by end-cap capacitance in linear RF ion traps and shows that single-phase driving amplifies axial distortions. It introduces a two-phase driving scheme based on a double-helical resonator with opposite helicity, yielding two RF outputs 180° apart and a common inductance; the mutual inductance M and coil self-inductance L define a coupling κ ≈ 0.03. A lumped-element circuit model and COMSOL simulations reproduce resonance shifts after adding a bias tee, matching measurements within ~10% for the lower-frequency resonance. Experimentally, they trap and cool a Yb$^{+}$ ion chain with radial frequencies exceeding $1.2$ MHz and demonstrate reduced axial micromotion, enabling a path toward compact fiber-coupled quantum information nodes.

Abstract

A linear radio-frequency Paul trap is traditionally driven with one diagonal pair of electrodes grounded and the other connected to a high-voltage radio-frequency source. This method simplifies impedance matching of the voltage source to the trap. However, for several architectures it leads to increasing the axial micromotion amplitude, for example, when the capacitance between radio-frequency and end-cap electrodes is not negligible. Here, we present a technique to generate two high-voltage radio-frequency signals \SI{180}{\degree} out of phase to drive a linear Paul trap with opposite voltages between neighbouring electrodes. Using this, we have successfully trapped and cooled a chain of Ytterbium ions in a linear radio-frequency Paul trap.

Figures (11)

• Figure 1: Different driving schemes of a linear radio-frequency ion trap, and their pseudopotentials. a) Single-phase driving where a diagonal pair of radio-frequency electrodes are connected to high-voltage radio-frequency source, and the other pair is grounded. b) The pseudopotential in the z-r plane close to the trap center for single-phase drive. Observe the imballance between x-y directions. c) The pseudopotential in the x-y plane close to the trap center for single-phase drive. Observe the induced pseudopotential component along the trap axis (z axis). d) Two-phase driving scheme where the two diagonal pairs are both connected to the radio-frequency voltage source, but with 180° phase difference. In this scheme, the voltage of the two pairs oscillate about the reference ground potential. e) The pseudopotential in the z-r plane close to the trap center for two-phase drive. f) The pseudopotential in the x-y plane close to the trap center for two-phase drive. One can observe the deformation of the potential in the two-phase drive scheme is minimised. The pseudopotentials are numerically simulated using software_comsol with a radio-frequency input $V_{pp} = 800V$ for the trap shown in Figure \ref{['fig:trap_photo']}.
• Figure 2: Design of the two-phase helical resonator. The resonator consists of two helical inner conductors in a copper shield, but with opposite helicity. The two opposite ends are grounded to the shield using thread and nuts, and the free ends offer the two outputs for the trap. Radio-frequency power can be fed into the system on either side using the feed antennas. The large coils are held in place using PVC spacers.
• Figure 3: Lowest two frequency eigenmodes of the electromagnetic field inside the coupled resonator. The eigenmodes were simulated using a FEM software software_comsol, and one cross-section of the electromagnetic field is shown here. a) The lower-frequency mode is the asymemetric mode with the two outputs of the resonator oscillating out of phase. It is the desired mode to operate the radio-frequency ion trap. b) The higher-frequency mode is the symmetric mode where the two outputs of the resonator oscillate in phase. The heat map show the absolute value of the electric field, for an arbitrary starting condition of the solver. Red arrows show the electric field direction, and the green streamline shows the magnetic field distribution for the two modes.
• Figure 4: A simple lumped-element model of the coupled resonator system. The two inductors of inductance L are coupled at the opposite ends due to the opposite helicity by an inductive coupling M. Furthermore, there is a coupling capacitance $C_c$ that connects the two outputs ($N_1$, $N_2$) of the two resonators.
• Figure 5: The complete equivalent circuit of our system. The orange region contains the two-phase helical resonator, similar to Figure \ref{['fig:lumped_circuit_simple']}. Here we include one of the feed antennas with an antenna-resonator coupling given by $M_f$. The yellow region includes the resonator with the silver-coated wires providing the two-phase outputs to the bias tee. The blue region depicts the bias tee with the four independent DC inputs, and the two pick-off antennas. The pick-off antennas are two open ended PCB traces with a SMA connector (see Figure \ref{['fig:bias_tee_design']}). This region contains all the real electronic components that are soldered onto the PCB. All other inductors, capacitors, and resistors are parasitic components describing various connecting wires and the ambience. The green region contains the ion trap with the vacuum chamber and its feed-through. The white region between the bias tee and the vacuum chamber shows the connection between the bias tee and the vacuum feed-through.