This dissertation reports on precision measurements of the atomic structure of calcium ions (40Ca+), application of trapped 40Ca+ ions as a probe for a violation of fundamental symmetry and prospects of performing quantum simulations with trapped ion.We demonstrate a novel technique to perform spectroscopy on the dipole transition of 40Ca+ that circumvents usual difficulties from dark resonances and Doppler heating. The center of the atomic transition can be detected to a precision of 200 kHz or less with an integration time of 10 minutes. We apply this method to directly measure the influence of micromotion on the fluorescence spectra and confirm the dependence of the modulation index on the radial trap frequency. We measure the branching fraction of the excited 2P1/2 state of 40Ca+ to be 0.93565(7) using a simple experimental scheme readily applicable to many other ion species. Our result for 40Ca+ distinguishes well among various theoretically calculated values, which is important in guiding further developments of the theoretical work.We apply the Ramsey spectroscopy technique based on a pair of correlated ions to probe the effect of the violation of local Lorentz invariance (LLI). The energy difference between the two components of the Bell state |PsiB> = |mJ=5/2,mJ=-5/2>+|mJ=1/2,mJ=-1/2> in the D5/2 manifold of 40Ca+ is monitored for 12 hours. We found that the energy component related to the violation of LLI varies less than 17±22 mHz. Assuming a hydrogen-like model of 40Ca+, the measurement result provides us the bound of the LLI parameter C(2)0 to be 1.7±2.2x10-17.Based on numerical simulations, we show that the Aubry transition in the Frenkel-Kontorova model with trapped ion can be observed for practical experimental parameters such as the strength and wavelength of the optical lattice, which serves as an external perturbing periodic potential. Moreover, we also show that the normal mode structure of ion chain can change significantly as we vary the strength of the optical lattice.
This dissertation reports on precision measurements of the atomic structure of calcium ions (40Ca+), application of trapped 40Ca+ ions as a probe for a violation of fundamental symmetry and prospects of performing quantum simulations with trapped ion.We demonstrate a novel technique to perform spectroscopy on the dipole transition of 40Ca+ that circumvents usual difficulties from dark resonances and Doppler heating. The center of the atomic transition can be detected to a precision of 200 kHz or less with an integration time of 10 minutes. We apply this method to directly measure the influence of micromotion on the fluorescence spectra and confirm the dependence of the modulation index on the radial trap frequency. We measure the branching fraction of the excited 2P1/2 state of 40Ca+ to be 0.93565(7) using a simple experimental scheme readily applicable to many other ion species. Our result for 40Ca+ distinguishes well among various theoretically calculated values, which is important in guiding further developments of the theoretical work.We apply the Ramsey spectroscopy technique based on a pair of correlated ions to probe the effect of the violation of local Lorentz invariance (LLI). The energy difference between the two components of the Bell state |PsiB> = |mJ=5/2,mJ=-5/2>+|mJ=1/2,mJ=-1/2> in the D5/2 manifold of 40Ca+ is monitored for 12 hours. We found that the energy component related to the violation of LLI varies less than 17±22 mHz. Assuming a hydrogen-like model of 40Ca+, the measurement result provides us the bound of the LLI parameter C(2)0 to be 1.7±2.2x10-17.Based on numerical simulations, we show that the Aubry transition in the Frenkel-Kontorova model with trapped ion can be observed for practical experimental parameters such as the strength and wavelength of the optical lattice, which serves as an external perturbing periodic potential. Moreover, we also show that the normal mode structure of ion chain can change significantly as we vary the strength of the optical lattice.
This thesis reports on the setup of a new ion trap apparatus designed for experiments with single ⁴⁰Ca⁺ ions to perform molecular spectroscopy. The calcium ion is laser cooled, allowing for sympathetic cooling of the nonfluorescing molecular ion. The aim of these experiments is to explore loading and identifying molecular ions in RF-Paul traps, as well as developing new spectroscopic tools to measure transitions of molecular ions via the fluorescence of co-trapped ⁴⁰Ca⁺ ions. Ground state cooling of a mixed ion pair is implemented as a first step towards increasing the sensitivity of our technique to the level necessary to measure transitions with low scattering rates (like those present in molecular ions). Doppler cooling on the S(1/2)->P(1/2) transition of the calcium ion results in the formation of a Coulomb crystal, the behavior of which may be used to infer properties of the molecular ion. Following cooling, sideband spectroscopy on the narrow S(1/2)->D(5/2) quadrupole transition of calcium may be used to identify the mass of single molecular ions. This method is verified via a non-destructive measurement on ⁴⁰CaH⁺ and ⁴⁰Ca¹⁶O⁺. The normal modes of the Coulomb crystal can also be used to extract information from the target ion to the control ion. By driving the blue side of a transition, laser induced heating can be put into the two ion system, which leads to changes in fluorescence of the ⁴⁰Ca⁺ ion, first demonstrated with two Ca⁺ isotopes. Increasing the sensitivity of this technique requires ground state cooling of both the ⁴⁰Ca⁺ ion and the ion of interest, enabling the transfer of the ion's motional state into the ground state with high probability. This thesis demonstrates ground state cooling of the atomic ion and sympathetic cooling of a second ion (⁴⁴Ca⁺). Once in the ground state, heating of the Coulomb crystal by scattering photons off of the spectroscopy ion can be measured by monitoring the resolved motional sidebands of the S(1/2)->D(5/2) transition of ⁴⁰Ca⁺, allowing for spectral lines to be inferred. Future experiments will investigate this technique with molecular ions.
We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with nonclosed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a cotrapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the 2D(3/2)→2P(1/2) transition in calcium, resulting in a transition frequency of f=346 000 234 867(96) kHz. Furthermore, we determine the isotope shift of this transition and the 2S(1/2)→2P(1/2) transition for 42Ca+, 44Ca+, and 48Ca+ ions relative to 40Ca+ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data.
We present an experimental scheme to perform spectroscopy on ions and atoms with a lambda-level structure. By rapidly switching lasers between both transitions, we circumvent the complications of both dark resonances and the ac-Stark effect. We demonstrate the scheme on the 2 S 1/2 − 2 P 1/2 and 2 D 3/2 − 2 P 1/2 transitions in 40 Ca + and, within a measurement time of 10 min, extract the centre frequencies of both dipole transitions with a statistical uncertainty on the order of 200 kHz. We also apply this method to directly observe the micromotion modulated fluorescence spectra of both transitions and for the first time measure the dependence of the micromotion modulation index on the trap frequency for both transitions.
In the first part of this thesis, a method for determining transition dipole matrix elements is introduced. It combines measuring absorptive and dispersive atom-light interactions off-resonant to the transition in question and is thus resilient against various line-broadening effects. A single 40Ca+ ion confined in a Paul trap is used for implementing that method. Rather than counting individual photons, the method is based on discriminating atomic states of the ion’s level scheme, which circumvents many systematic error sources affecting other methods. The dipole matrix elements of the 42S1/2 ↔ 42P1/2, the 42S1/2 ↔ 42P3/2 and the 42P1/2 ↔ 32D3/2 transitions are determined. Moreover, the method allows also for the deduction of the radiative lifetime of the 42P1/2 state which reads 6.904(26)ns. This value is in agreement with recent theoretical calculations, and resolves a long-standing discrepancy between calculated values and experimental results. In the second part of the thesis, the design, construction, assembly and characterization of a segmented, microstructured Paul trap which can accommodate a fiber cavity for light-ion interaction is described. The trap features 31 segments, which allow for ion transport along the trap axis. Vertical interconnect accesses needed to be incorporated in the design of the conducting paths in order to electrically connect all segment electrodes to the outside. The trap is fabricated from alumina substrates and evaporatively coated with gold. To further characterize the trap, simulations of axial trap frequencies have been compared with measured values for different regions in the trap, also axial transport of single ions over a distance of ≈ 2.5 mm has been implemented. Coherent dynamics on the quadrupole transition of 40Ca+ have been used to perform sideband cooling and a single ion was cooled below the Doppler limit. The dynamics of carrier and red sideband transitions have been employed to measure the trap’s heating rate, which amounts to n = 16.5/ms at a trap frequency of 2π × 1.32 MHz.
This thesis describes work on numerical modelling of the 43Ca+ ion in a Paul trap using the optical Bloch equations. This is a challenging system to study, with many states involved in the internal dynamics. A major outcome is the development of a cooling scheme for the 146.09 gauss atomic clock transitions which makes use of a dark resonance. It is much more effective than methods that avoid coherent effects. The scheme is realised in experiment. Complicated fluorescence data is modelled very well, and predictions for the ion's motional temperature show good agreement with measured values. Data and fits for an ion that has been Doppler cooled below the Doppler limit are presented. I describe GLOBES, a set of routines that simulates an arbitrary ion in the presence of an arbitrary system of laser beams using the optical Bloch equations. Techniques used to efficiently calculate the steady state, analyse fluorescence scans and solve time-dependent problems for small and large times are discussed. A new routine SILVER IMPER that leapfrogs over the initial dynamics to model the approach to the steady state is introduced. Doppler cooling in 40Ca+ is analysed and two extensions made to the basic theory. The ‘excursion method’ of calculation takes account of the non-linear variation with velocity of the scattering rate. The ‘dynamic method’ allows for the fact that the ion may not be in equilibrium with the incident radiation during its oscillations, a necessity as the timescale of the external motion is of order the characteristic timescale of the internal motion for standard secular frequencies. This 'dynamic effect' is a general property of trapped ion systems and is also observed in a two-state system. A two-variable fluorescence scan taken from a four-laser, five-level system in 40Ca+ is analysed. Techniques to fit large data sets and automatically resolve resonant features are demonstrated. A general treatment of resonant behaviour in three, four and five level pump/probe systems is used to describe the data. This is verified by a second, tailor-made set of scans.
The experimental study at Wuhan Institute of Physics and Mathematics (WIPM), Chinese Academy of Scienses (CAS) on the precision spetroscopy based on single trapped Ca+ ion is described in this paper. A single Ca+ ion is trapped in a miniature Paul trap and laser cooled to Lamb-Dicke regime, and the ion can be trapped more than 2 months. The linewidth of the 729 nm laser for probing the Ca+ 4s2S1/2-3d2D5/2 clock transition is reduced to lessthan 1 Hz by locked to a super cavity, and the 729 nm laser can be locked more than 1 month continuously. Two similar Ca + ion optical frequency standards are set up for frequency comparison. The systematic uncertainty is evaluated to be <6 ´ 10−17 for both ftrquency standards. The frequency difference of two frequency standards is measured to be 3.0 (5.5) ´ 10−17 within 42 d. The Allan deviation for a single clock is measured to be 1×10−14τ−1/2 with a 3-d-continuous comparison, the stability for a reaches 7 ´ 10−17 at an averaging time of 20000 s. Meanwhile, the absolute frequency of the Ca+ 4s2S1/2-3d2D5/2 clock transition is measured to be 411042129776401.7(1.1) Hz with respect to the SI second through the Global Positioning System (GPSx). The precision spectroscopy experiments are carried out based on the single Ca+ ion system. The magic wavelengths for the Ca+ optical frequency standardare measured to be λ|mj|=1/2=395.7992(7) nm and λ|mj|=3/2=395.7990(7) nm, which agrees with theoretical calculation made by Tang et al. The lifetime of the 3d2D5/2 is measured to be 1174(10) ms, which is agree with the experimental measurement made by University of Oxford and University of Innsbruck and the recent theoretical calculation made by Sahoo.