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Review of Scientific Instruments

Active impedance matching of a cryogenic radio frequency resonator for ion traps

M. Schubert, L. Kilzer, T. Dubielzig, Meinhard Schilling, C. Ospelkaus, Benedikt Hampel

Published Sep 1, 2022• 3 citations
Publisher

Abstract

A combination of direct current (DC) fields and high amplitude radio frequency (RF) fields is necessary to trap ions in a Paul trap. Such high electric RF fields are usually reached with the help of a resonator in close proximity to the ion trap. Ion trap based quantum computers profit from good vacuum conditions and low heating rates that cryogenic environments provide. However, an impedance matching network between the resonator and its RF source is necessary, as an unmatched resonator would require higher input power due to power reflection. The reflected power would not contribute to the RF trapping potential, and the losses in the cable induce additional heat into the system. The electrical properties of the matching network components change during cooling, and a cryogenic setup usually prohibits physical access to integrated components while the experiment is running. This circumstance leads to either several cooling cycles to improve the matching at cryogenic temperatures or the operation of poorly matched resonators. In this work, we demonstrate an RF resonator that is actively matched to the wave impedance of coaxial cables and the signal source. The active part of the matching circuit consists of a varactor diode array. Its capacitance depends on the DC voltage applied from outside the cryostat. We present measurements of the power reflection, the Q-factor, and higher harmonic signals resulting from the nonlinearity of the varactor diodes. The RF resonator is tested in a cryostat at room temperature and cryogenic temperatures, down to 4.3 K. A superior impedance matching for different ion traps can be achieved with this type of resonator.

DOI
10.1063/5.0097583

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A combination of direct current (DC) fields and high amplitude radio frequency (RF) fields is necessary to trap ions in a Paul trap. Such high electric RF fields are usually reached with the help of a resonator in close proximity to the ion trap. Ion trap based quantum computers profit from good vacuum conditions and low heating rates that cryogenic environments provide. However, an impedance matching network between the resonator and its RF source is necessary, as an unmatched resonator would require higher input power due to power reflection. The reflected power would not contribute to the RF trapping potential, and the losses in the cable induce additional heat into the system. The electrical properties of the matching network components change during cooling, and a cryogenic setup usually prohibits physical access to integrated components while the experiment is running. This circumstance leads to either several cooling cycles to improve the matching at cryogenic temperatures or the operation of poorly matched resonators. In this work, we demonstrate an RF resonator that is actively matched to the wave impedance of coaxial cables and the signal source. The active part of the matching circuit consists of a varactor diode array. Its capacitance depends on the DC voltage applied from outside the cryostat. We present measurements of the power reflection, the Q-factor, and higher harmonic signals resulting from the nonlinearity of the varactor diodes. The RF resonator is tested in a cryostat at room temperature and cryogenic temperatures, down to 4.3 K. A superior impedance matching for different ion traps can be achieved with this type of resonator.
Trapping ions in Paul traps require high radio frequency voltages, which are generated using resonators. When operating traps in a cryogenic environment, an in-vacuum resonator showing low loss is crucial to limit the thermal load to the cryostat. In this study, we present a guide for the design and production of compact, shielded cryogenic resonators. We produced and characterized three different types of resonators and furthermore demonstrate efficient impedance matching of these resonators at cryogenic temperatures.
Trapped-ion qubits are one approach among many for achieving scalable quantum computers. An ion trap has to be operated with several dc and radio frequency (rf) signals to trap and control its qubits. Many ion trap setups are operated at cryogenic temperatures to reduce thermal influences, to reach very high vacuum, and to achieve high fidelity for quantum operations. A resonance circuit, consisting of a coil and the capacitance of the trap electrodes, is used to step-up a low power rf signal to high amplitudes in close proximity to the ion trap. These ac fields are used to confine ions70 μm70 \,{\rm \mu }\mathrm{m}70μmabove a surface ion trap chip. An increased quality factor (Q-factor) of the resonance circuit leads to a higher voltage gain, but the experiment also benefits from a better attenuation of parasitic frequency components in the confining electric field. The Q-factor is inversely proportional to the trap capacitance. Since ion traps are growing in size due to a larger number of qubits, the capacitance is increasing. Therefore, the development of a coil with low losses becomes even more important. In this work, we present the setup of a superconducting coil for a high-Q resonator, measurements of the Q-factor, and its temperature dependency. The coil is made of a niobium-titanium (NbTi) wire wound on a threaded bobbin made of ceramics and equipped with further thermalization structures. The superconducting resonator is a very promising approach to satisfy the needs for future trapped-ion quantum computing setups.
We report on the investigation and implementation of a lumped-component, radio-frequency resonator used in a cryogenic vacuum environment to drive an ion trap. The resonator was required to achieve the voltages necessary to trap (~100 V), while dissipating very little power. Ultimately, for an input voltage of 1.35 V, a voltage gain of 100 was measured at 5.7 K, using a design which dissipated only 18 mW. The resonator operated at a frequency of 7.64 MHz and had a Q of 700. Single (40)Ca(+) ions were confined in a trap driven by this device, providing proof of successful resonator operation at low temperature.
Radio-frequency reflectometry techniques enable high-bandwidth readout of semiconductor quantum dots. Careful impedance matching of the resonant circuit is required to achieve high sensitivity, which, however, proves challenging at cryogenic temperatures. Gallium arsenide--based voltage-tunable capacitors, so-called varactor diodes, can be used for in situ tuning of the circuit impedance but deteriorate and fail at temperatures below 10 K and in magnetic fields. Here, we investigate a varactor based on strontium titanate with a hyperabrupt capacitance-voltage characteristic, i.e., a capacitance tunability similar to the best gallium arsenide--based devices. The varactor design introduced here is compact, scalable, and easy to wire bond, with an accessible capacitance range from 45 pF to 3.2 pF. We tune a resonant inductor-capacitor circuit to perfect impedance matching and observe robust temperature- and field-independent matching down to 11 mK and up to 2 T in-plane field. Finally, we perform gate-dispersive charge sensing on a germanium-silicon core-shell nanowire hole double quantum dot, paving the way toward gate-based single-shot spin readout. Our results bring small magnetic field--resilient highly tunable varactors to mK temperatures, expanding the toolbox of cryo-radio-frequency applications.
Radio-frequency reflectometry allows for fast and sensitive electrical readout of charge and spin qubits hosted in quantum dot devices coupled to resonant circuits. Optimizing readout, however, requires frequency tuning of the resonators and impedance matching. This is difficult to achieve using conventional semiconductor or ferroelectric-based varactors in the detection circuit as their performance degrades significantly in the mK temperature range relevant for solid-state quantum devices. Here we explore a different type of material, strontium titanate, a quantum paraelectric with exceptionally large field-tunable permittivity at low temperatures. Using strontium titanate varactors we demonstrate perfect impedance matching and resonator frequency tuning at 6 mK and characterize the varactors at this temperature in terms of their capacitance tunability, dissipative losses and magnetic field sensitivity. We show that this allows us to optimize the radio-frequency readout signal-to-noise ratio of carbon nanotube quantum dot devices to achieve a charge sensitivity of 4.8 μμμe/Hz1/2^{1/2}1/2 and capacitance sensitivity of 0.04 aF/Hz1/2^{1/2}1/2.
Large surface-electrode ion traps with multiple trapping regions and junctions are a natural approach to scaling trapped ion quantum computers, supporting the connectivity and ion counts necessary for complex quantum algorithms. However, a major hurdle in this scaling is on-chip power dissipation from the applied RF voltage, which increases at a rate between linear and cubic relative to trap size, depending on whether the losses are dielectric or Ohmic. Here, we present two versions of a trap with features designed to reduce both types of RF power dissipation. The first variant contains a raised RF electrode that increases the electrode–ground distance to reduce capacitance. Different DC voltage sources are demonstrated on this trap to show that technical noise before the filter remains the dominant source of voltage noise and therefore motional heating. The second variant additionally includes a method for removing dielectric from beneath the RF electrode to further reduce dielectric losses. These traps were demonstrated at room temperature with 40Ca+ ions. The similar heating rates and heating rate axial frequency dependencies between 2.4 and 3.0 MHz illustrate that this dielectric modification is not detrimental to trap performance.