Optical spectroscopy in ion traps

Spectroscopic experiments in static or dynamic ion traps have produced results of extremely high precision. They have been, however, performed mainly on systems with simple electronic level schemes as available in singly charged ions of the earth-alkaline elements. In this contribution the most complex system investigated so far, Eu⁺, is used as example to discuss the possibility of spectroscopy on superheavy elements in traps.     

Quantum Games in ion traps

We propose a general, scalable framework for implementing two-choices-multiplayer Quantum Games in ion traps. In particular, we discuss two famous examples: the Quantum Prisoners' Dilemma and the Quantum Minority Game. An analysis of decoherence due to intensity fluctuations in the applied laser fields is also provided.     

Optimum electrode configurations for fast ion separation in microfabricated surface ion traps

For many quantum information implementations with trapped ions, effective shuttling operations are important. Here, we discuss the efficient separation and recombination of ions in surface ion trap geometries. The maximum speed of separation and recombination of trapped ions for adiabatic shuttling operations depends on the secular frequencies the trapped ion experiences in the process. Higher secular frequencies during the transportation processes can be achieved by optimising trap geometries. We show how two different arrangements of segmented static potential electrodes in surface ion traps can be optimised for fast ion separation or recombination processes. We also solve the equations of motion for the ion dynamics during the separation process and illustrate important considerations that need to be taken into account to make the process adiabatic.     

Crystal resonator design for space applications

Summary Crystal resonators may be used on various vehicles. They are submitted to accelerations, shocks, vibrations and to external pressure and temperature variations (acceleration variations may be some 10g, pressure variations may reach one atmosphere and temperature 100°C). The goal of this paper is to describe an attempt to reduce the various environmental effects especially by use of a mounting structure external to the resonator. Each effect needs a particular study. 1) Shocks and vibrations. A particular fixation structure has been designed. Resonators can support a shock equivalent to 1000g over 0.1 ms in any direction. Also the mounting structure resonant frequency can be rejected over 3000 Hz. 2)g sensitivity.g sensitivity has been reduced. Theoretical and experimental results are given. 3) External pressure and temperature variations. Crystal enclosure is submitted to variations of pressure and temperature which yield enclosure deformations. The study of the resonator dependence by respect to its enclosure has been performed. A quartz structure surrounding the vibrating crystal has been designed and specific enclosures have been tried thus yielding reduced mechanical strains due to external pressure and temperature variations. These structures are described and discussed. Based on the results of the previous study of a series of 10 sample resonators has been manufactured. The performances are presented and compared to results obtained with previous designs. The authors of this paper have agreed to not receive the proofs for correction.     

Paul阱中存储离子的研究

根据Paul离子阱结构及电场分布特点,列出阱内离子运动方程并求解,对其中离子运动、硅团簇离子碰撞解离反应进行了分析.     

The ion cyclotron resonator in the magnetosphere

Our concern here is to present the idea of the ion cyclotron resonator in the planetary magnetosphere and to discuss briefly the experimental status of the corresponding theory. The resonator confines the ion cyclotron waves to a thin equatorial zone, so that it keeps the wave field from coming into contact with the ionosphere, resulting in a decrease in energy losses. The properties of the resonator are illustrated by adopting a plausible distribution of the magnetic field in the equatorial zone, which yields an expression for the discrete spectrum of the waves just above the gyrofrequency of heavy ions. We show that the resonator is remarkable for many reasons, including the frequency dependence of its size and specific structure of the spectrum.     

Hyperfine structure andg-factor measurements in ion traps

We report about measurements on ground-state hyperfine splitting constants of stable Eu⁺ isotopes in radio frequency ion traps and experiments on the electronicg-factor of Ba⁺ in a Penning trap. From the precision of both measurements, which ranges between 3·10⁻⁶ and 5·10⁻⁷, we conclude that precise determination of the differential Bohr-Weisskopf effect in chains of isotopes will be possible in the near future.     

Quantum chaos of an ion trapped in a linear ion trap

We describe the transition to quantum chaos of an ion trapped in a linear ion trap and interacting with two laser fields. Under the conditions of adiabatic illumination of the upper level of the ion, and when the frequencies of the two laser beams are slightly different, the system is reduced to a quantum linear oscillator interacting with a monochromatic wave. The property of localization over the quantum resonance cells is proposed to exploit in order to facilitate the process of measurement of the probability distribution of an ion on the vibrational levels. In the regime of strong chaos the time-averaged values of the energy and dispersion of energy are computed and compared with the corresponding classical quantities for different values of the perturbation amplitude. In the exact resonance case, the classical analog of the system possesses an infinite inhomogeneous stochastic web. We analyze the quantum dynamics inside the inhomogeneous web. It is shown that the quantum system mimics on average the dynamics of the corresponding classical system. Formation of the quantum resonance cells is illustrated in the case of a finite detuning from the exact resonance, and under increasing of the wave amplitude. The parameters of the model and the initial conditions are close to the real physical situation which can be realized in the system of cold trapped ion perturbed by two lasers fields with close frequencies. (c) 2000 American Institute of Physics.     

Characteristics of electrical field and ion motion in surface-electrode ion traps

In this article, we calculated the potential function of the surface-electrode ion trap (SEIT) by using Green's function method, optimized trap size, obtained the coefficients of the multipoles and analyzed ion trajectories in the RF potential. The optimized SEIT not only increases its trapping well depth by a factor of about 15, but also has relatively good linearity of the field (or large quadrupole component). The current design of SEIT can work well either as the ion guide for ion transmission or as the ion trap for ion confinement. Our research can be used to calculate the potential function in the SEIT with different device parameters, understand ion motions in the traps and optimize instrument performance. The method for calculating potential function can be expanded to planar and halo ion traps.     

On the sensitivity of ion traps for spectroscopic applications

Ba⁺ ions, created by surface ionization near one endcap of an rf quadrupole trap were slowed down by collisions with the background gas. At He pressures of 10^?6 mbar or more 2% of the primary ions could be trapped. The sensitivity of ion detection by fluorescence radiation allows spectroscopic experiments, starting from less than 10⁷ particles. The observation of the ground-state hyperfine splitting of¹³⁷Ba⁺ is given as an example.     

Paul阱中离子运动及稳定性分析

Paul离子阱由于没有外加磁场所引起的塞曼效应的影响,已成为离子存储及研究离子的重要装置.根据在实验中所采用的Paul离子阱结构及电场分布特点,列出阱内离子运动方程并进行求解,对其中各种运动进行分析,同时还分析了离子存储稳定性.最后对所作的研究进行总结,得到如下结论:阱中离子的运动为谐振运动、基频微运动和高阶微振动.     

Recent developments in laser resonator design

The problems related to resonators suitable for generation of diffraction-limited beams of high power or energy, and a few of the most significant recent solutions, are reviewed. In particular, this paper is addressed to two promising resonator configurations developed mainly for Nd:YAG (yttrium aluminium garnet) lasers: dynamically stable resonators of minimum misalignment sensitivity for lasers with a strong thermal lensing in the active rod and unstable resonators with variable reflectivity output mirrors of super-Gaussian profile. For both cases experimental data and simple design guidelines are discussed.     

Proposal for measurement of harmonic oscillator berry phase in ion traps

We propose a scheme for measuring the Berry phase in the vibrational degree of freedom of a trapped ion. Starting from the ion in a vibrational coherent state we show how to reverse the sign of the coherent state amplitude by using a purely geometric phase. This can then be detected through the internal degrees of freedom of the ion. Our method can be applied to preparation of entangled states of the ion and the vibrational mode.     

Electron attachment to anionic clusters in ion traps

Ion traps are versatile tools for the investigation of gas-phase cluster ions, allowing, e.g., cluster-size selection and extended reaction times. Taking advantage of their particular storage capability of simultaneous trapping of electrons and clusters, Penning traps have been applied for the production of clusters with high negative charge states. Recently, linear radio-frequency quadrupole traps have been demonstrated to be another candidate to produce polyanionic clusters. Operation with rectangular, rather than harmonic, radio-frequency voltages provides field-free time slots for unhindered electron passage through the trap. Several aspects of electron-attachment techniques by means of Penning and radio-frequency traps are addressed and recent experimental results are presented.     

Suitability of linear quadrupole ion traps for large Coulomb crystals

Growing and studying large Coulomb crystals, composed of tens to hundreds of thousands of ions, in linear quadrupole ion traps presents new challenges for trap implementation. We consider several trap designs, first comparing the total driven micromotion amplitude as a function of location within the trapping volume; total micromotion is an important point of comparison since it can limit crystal size by transfer of radiofrequency drive energy into thermal energy. We also compare the axial component of micromotion, which leads to first-order Doppler shifts along the preferred spectroscopy axis in precision measurements on large Coulomb crystals. Finally, we compare trapping potential anharmonicity, which can induce nonlinear resonance heating by shifting normal mode frequencies onto resonance as a crystal grows. We apply a non-deforming crystal approximation for simple calculation of these anharmonicity-induced shifts, allowing a straightforward estimation of when crystal growth can lead to excitation of different nonlinear heating resonances. In the anharmonicity point of comparison, we find significant differences between the trap designs, with an original rotated-endcap trap performing better than the conventional in-line endcap trap.     

Observation of power-Law scaling for phase transitions in linear trapped ion crystals

We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to ten ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.     

Dynamics of a two-level trapped ion in a cavity

In the present paper we consider the case of a two-level ion in a cavity in the presence of a single mode field linearly polarized. We suppose that the ion is free to move along the polarization direction and trapped by a harmonic potential along the other two directions. By multiple path integration we derive the density matrix of the system and we study its dynamics. We assume an initial electromagnetic vacuum. This initial condition for the present system, compared with any other initial photonic state, gives new and higher order leading terms with respect to an expansion in powers of the inverse of the volume. Further after such an expansion there appears a first order term that originates from the combined interaction of the two-level system (qubit) with the quantum motion of the ion and the electromagnetic field in the cavity. We notice that the dynamics of the present system is very rich and can be studied exhaustively in the present framework.     

Higher dimensional entangled qudits in a trapped three-level ion

Quantum entangled states in a system of trapped three-level ion interacting with two laser beams in Λ (Lambda) configuration is investigated. We have characterized a typical family of initial conditions for their potential to generate quantum entanglement of internal and external degrees of freedom of the ion. It is found that entangled qudits, specifially qutrits and quadrits, can be optimally for a certain preparation of the ionic system. Analytical results, describing the quantum entangled state explicity, are presented. The amount of quantum entanglement is quantified directly by calculating the generalized concurrence for arbitrary qudits. It is obtained that higher dimensional entanglement can be established with the Lamb-Dicke parameter (LDP). The LDP dependence of Schmidt coefficients is shown.     

A single trapped ion in a finite range trap

This paper presents a method to describe dynamics of an ion confined in a realistic finite range trap. We model this realistic potential with a solvable one and we obtain dynamical variables (raising and lowering operators) of this potential. We consider coherent interaction of this confined ion in a finite range trap and we show that its center-of-mass motion steady state is a special kind of nonlinear coherent states. Physical properties of this state and their dependence on the finite range of potential are studied.     

Atomic parity violation in a single trapped radium ion

Atomic parity violation (APV) experiments are sensitive probes of the electroweak interaction at low energy. These experiments are competitive with and complementary to high-energy collider experiments. The APV signal is strongly enhanced in heavy atoms and it is measurable by exciting suppressed (M1, E2) transitions. The status of APV experiments and theory are reviewed as well as the prospects of an APV experiment using one single trapped Ra^?+? ion. The predicted enhancement factor of the APV effect in Ra^?+? is about 50 times larger than in Cs atoms. However, certain spectroscopic information on Ra^?+? needed to constrain the required atomic many-body theory, was lacking. Using the AGOR cyclotron and the TRI??P facility at KVI in Groningen, short-lived ^212???214Ra^?+? ions were produced and trapped. First ever excited-state laser spectroscopy was performed on the trapped ions. These measurements provide a benchmark for the atomic theory required to extract the electroweak mixing angle to sub-1% accuracy and are an important step towards an APV experiment in a single trapped Ra^?+? ion.