We demonstrate a simple electronic detection method for trapped ions in a linear Paul trap. Singly charged calcium ions are confined in a linear Paul trap and are driven by an ac electric field at their secular frequency. The collective motion of the ions causes induced current on the trap electrodes, and the current signal is detected by a tuned circuit. This paper describes the design of the tuned circuit and the performance of this detection method. This method can be applied to various species of ions in different trap geometries. It serves as a simple tool to probe the existing ions in the trap, while in some cases, optical detection is not feasible. This method is particularly suitable for demonstration in teaching laboratories where the ion trap systems and detection circuits can be constructed by undergraduate students.
We demonstrate a simple electronic detection method for trapped ions in a linear Paul trap. Singly charged calcium ions are confined in a linear Paul trap and are driven by an ac electric field at their secular frequency. The collective motion of the ions causes induced current on the trap electrodes, and the current signal is detected by a tuned circuit. This paper describes the design of the tuned circuit and the performance of this detection method. This method can be applied to various species of ions in different trap geometries. It serves as a simple tool to probe the existing ions in the trap, while in some cases, optical detection is not feasible. This method is particularly suitable for demonstration in teaching laboratories where the ion trap systems and detection circuits can be constructed by undergraduate students.
We demonstrate a linear radio-frequency trap for confining strontium ions that is simply constructed nearly entirely with commercial off-the-shelf components. The electrodes of this trap are spaced to allow tight radial confinement, and segmented to give tight axial confinement with minimal distortion of the radio-frequency field. The resulting secular frequencies of the trap are 1 MHz in the radial direction and 100 kHz in the axial direction, the ions can be imaged with 2–3 μm resolution, and we detect over 20 000 photons per second per ion. This article describes the construction of the vital parts of the trap system, the laser system and optics used to Doppler cool the ions and to observe quantum jumps, and the operation and behavior of the complete system.
This thesis describes experimental work towards developing a trapped ion quantum information processor. An existing ion trap apparatus was capable of trapping and laser-cooling single ions or small ion strings of 40 Ca+, and had been used for studies of quantum jumps and natural lifetime measurements in Ca. This thesis describes improvements in this apparatus, which have allowed the stability and the flexibility of experimental control of the ions to be greatly increased. This enabled experiments to read out the spin state of a single trapped ion, and to load ions with isotope selectivity through photoionization. The optical systems were improved by installation of new lasers, optical reference cavities, and a system of acousto-optic modulators for laser intensity switching and frequency control. The photon counting for fluorescence detection was improved, and a new photon time-of-arrival correlation circuit developed. This has permitted rapid and more sensitive detection of micromotion, and hence cancellation of stray fields in the trap. A study of resonant circuits in the low RF, high voltage (10 MHz, 1 kV) regime was carried out with a view to developing a new RF supply for the Paul trap with reduced noise and increased power. A new supply based on a helical resonator was built and used to trap ions. This technique has reduced noise and will permit higher secular frequencies to be attained in the future. A magnetic field B in the ion trap is used to define a quantization axis, and in one series of experiments was required to be of order 100 G to provide a substantial Zeeman splitting. A set of magnetic field coils to control the size and direction of B is described. The design of these posed some problems owing to an unforseen issue with the vacuum chamber. In short, it is magnetizable and acts to first approximation like a magnetic shield. The field coils had to be sufficiently substantial to produce the desired field at the ion even in the presence of this shielding effect, and dark resonance (and other) spectra with Zeeman splitting were obtained to calibrate the field using the ion as a probe. Finally, the thesis describes the successful loading of the ion trap by laser photoionization from a weak atomic beam. This involved two new lasers at 423 nm and 389 nm. Saturated absorption spectroscopy of neutral calcium is first described, then transverse excitation of an atomic beam in our vacuum chamber is used to identify all the main isotopes of calcium and confirm their abundances in our source (a heated sample of natural calcium). Finally, photoionization is used to load the trap. This has three advantages over electron-impact ionization. By avoiding an electron gun, we avoid charging of insulating patches and subsequent electric field drift as they discharge; the flux in the atomic beam and hence calcium (and other) deposits on the electrodes can be greatly reduced; and most importantly, the photoionization is isotope selective. Evidence is presented which suggests that even with an non-enriched source, the rare isotope 43 Ca can be loaded with reasonable efficiency. This isotope is advantageous for quantum information experiments for several reasons, but chiefly because its ground state hyperfine structure can act as a stable qubit.
Abstract A single-ion reservoir has been tested, and characterized in order to be used as a highly sensitive optical detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled40Ca+ion stored in a Paul trap with rotational symmetry. The performance is observed through the axial motion of the ion, which is equivalent to an underdamped and forced oscillator. Thus, the results can be projected also to Penning traps. We have found that, for an ion oscillator temperatureTaxial ≲ 10 mK in the forced-frequency rangeωz = 2π × (80,200 kHz), the reservoir is sensitive to a time-varying electric field equivalent to an electric force of 5.3(2) neV/μm, for a measured quality factorQ = 3875(45), and a decay time constantγz = 88(2) s−1. This method can be applied to measure optically the strength of an oscillating field or induced (driven) charge in this frequency range within times of tens of milliseconds. Furthermore the ion reservoir has been proven to be sensitive to electrostatic forces by measuring the ion displacement. Since the heating rate is below 0.3 μeV/s, this reservoir might be used as optical detector for any ion or bunch of charged particles stored in an adjacent trap.
Precise control of charged particles in radio-frequency (Paul) traps requires minimising excess micromotion induced by stray electric fields. We present a method to detect and compensate such fields through amplitude modulation of the radio-frequency trapping field. Modulation at frequencies close to the motional modes of the trapped particle excites coherent motion whose amplitude linearly depends on the stray field. In trapped-ion experiments, this motion can be detected by recording the arrival times of photons scattered during laser cooling. Only a single laser beam is required to resolve fields in multiple directions. In a demonstration using a 88Sr+ ion in a surface electrode trap, we achieve a sensitivity of 0.1Vm−1/Hz and a minimal uncertainty of 0.015Vm−1.
A three-dimensional linear Paul trap was modelled using COMSOL Multiphysics to study the confinement dynamics of a singly ionized calcium ion (Ca⁺) under time-dependent radio-frequency (RF) electric fields. Charged particle tracing module was used to simulate the ion trajectory inside the trap. The resulting trajectory data was exported to MATLAB, where Fast Fourier Transform (FFT) analysis was performed to extract the secular oscillation frequency of the trapped ion. The Secular frequency was observed to be approximately 500 kHz. The extracted secular frequency was then used to model the trapped ion as a quantum harmonic oscillator. Corresponding quantum wavefunctions and quantized motional energy levels were computed and visualized. The study demonstrates the connection between classical ion trapping dynamics and the quantum harmonic oscillator approximation commonly used in trapped-ion quantum systems.
For experiments with ions confined in a Paul trap, minimization of micromotion is often essential. In order to diagnose and compensate micromotion we have implemented a method that allows for finding the position of the radio-frequency (rf) null reliably and efficiently, in principle, without any variation of direct current (dc) voltages. We apply a trap modulation technique and focus-scanning imaging to extract three-dimensional ion positions for various rf drive powers and analyze the power dependence of the equilibrium position of the trapped ion. In contrast to commonly used methods, the search algorithm directly makes use of a physical effect as opposed to efficient numerical minimization in a high-dimensional parameter space. Using this method we achieve a compensation of the residual electric field that causes excess micromotion in the radial plane of a linear Paul trap down to $0.09\phantom{\rule{4pt}{0ex}}\text{V}\phantom{\rule{0.16em}{0ex}}{\text{m}}^{\ensuremath{-}1}$. Additionally, the precise position determination of a single harmonically trapped ion employed here can also be utilized for the detection of small forces. This is demonstrated by determining light pressure forces with a precision of 135 yN. As the method is based on imaging only, it can be applied to several ions simultaneously and is independent of laser direction and thus well suited to be used with, for example, surface-electrode traps.