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Measurement of reduced dipole matrix elements in 40Ca+ and construction of a scalable light-ion interface

M. Hettrich

Published Jan 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.18725/oparu-4182

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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.
We demonstrate a method to determine dipole matrix elements by comparing measurements of dispersive and absorptive light ion interactions. We measure the matrix element pertaining to the Ca II H line, i.e., the 4(2)S(1/2)↔4(2)P(1/2) transition of (40)Ca(+), for which we find the value 2.8928(43) ea(0). Moreover, the method allows us to deduce the lifetime of the 4(2)P(1/2) state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a long-standing discrepancy between calculated values and experimental results.
This dissertation describes a prototype experiment aiming at the realization of scalable quantum information. The essential feature is the usage of a novel microstructured ion trap derived from the Paul trap. It allows for storing and manipulating a large number of ions, as compared to conventional linear Paul traps. This thesis describes how the way is paved towards the realization of quantum information experiments in this ion trap. An analysis of the electrostatic properties of the ion trap is presented, which is laying the foundation for understanding the limits of confinement stability and effects beyond standard Paul trap behavior. The focus of this work lies on the realization and characterization of single and dual qubit operations, which are achieved by means of (semiclassical) atom-light interaction. In our experiment, the qubit is implemented in the Zeeman sublevels of the ion’s ground state, i.e. in the spin of the bright electron of a 40Ca+ ion. The main body of this thesis then describes the realization of the necessary steps of preparation, manipulation and readout of this qubit. The preparation includes optical pumping and cooling close to the motional quantum ground state by means of sideband cooling. Several possible techniques for these steps are tested and analyzed. Coherent manipulations are carried out by means of stimulated Raman transitions. Here, a strong emphasis is put on the characterization of the various decoherence mechanisms, which are dominated by the motional excitation of the ion due to thermalization of the ion with the trap electrodes, and by imperfections in the ion-laser interactions. As by-product of the latter investigation, a new measurement scheme for the experimental determination of atomic dipole matrix elements is presented.
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.
Laser-cooled ions in linear Paul Traps are one of the most promising candidates for a quantum computer. This thesis reports on the construction and operation of a segmented Paul trap. The trap was fabricated in UHV-compatible printed-circuit-board (PCB) technology and consists of 15 segments with a minimum segment width of 0,5 mm. With the large number of segments it is unique in Europe. Although a PCB-trap may not be suitable for large-scale quantum computers, the advantage of such a trap is fast and reliable fabrication with low fabrication costs. Therefore this technology is ideal for rapid testing of new trap geometries and ion shuttling methods. Experiments were carried out with individual laser-cooled 40Ca+ ions stored in the trap and observed by detecting their fluorescence. Measured trap frequencies agree to numerical simulations at the level of a few percent, demonstrating the fabrication accuracy of the segmented trap. Compensation voltages are used to cancel stray fields. The long time stability of these compensation voltages over many months is comparable to a conventional unsegmented trap. To determine the short time stability of the PCB-trap, the heating rate of the motional mode of an ion was measured by detecting fluoresence during Doppler cooling of heated ions. The observed heating rate was much higher than expected due to a massive deposition of calcium on the trap electrodes. Transport dynamics of a single trapped ion was investigated by shuttling the ion between trap locations 2mm apart. A non-adiabatic transport in roughly two oscillation periods in the axial trap potential was achieved. The quality of a transport function was evaluated with two different methods: the success probability and the excess energy of the ion after transport. The measurements were compared with numerical simulations of the classical energy transfer due to the transport. Finally, a string of ions held in a common trap was separated into two distinct traps.
Scalability and the implementation of fault tolerant quantum gates are the two main challenges which must be overcome in order to unlock the vast potential of quantum computing. This thesis describes work with calcium ions trapped in both microscopic and macroscopic linear Paul traps addressing both of these issues. We describe the assembly of a microstructured multi-zone ion trap which forms part of our group's contribution to the European "Microtrap" collaboration. We report the successful trapping of ions and characterization of the trap as well as a measurement of the heating rate. In miniaturized trap structures such as this one, background scattered light from the cooling beam causes difficulties. We introduce and demonstrate experimentally two techniques to overcome this problem. The first achieves background-free detection of ions using different repumping methods to enable the filtering out of the excitation wavelength. The second makes possible background-free readout of trapped ion qubits by separating in time the excitation and detection steps The second half of the thesis describes our experimental efforts towards implementing a two-qubit entangling gate with a mixed-species crystal. We describe the setup and characterization of a new macroscopic trap including the trapping and coherent manipulation of the internal states of both 40Ca+ and 43Ca+ ions. We accomplish the simultaneous independent readout of two qubits implemented in a 40Ca+ - 43Ca+ ion pair. We also present the setup and characterization of two injection-locked frequency-doubled Raman lasers and demonstrate coherent manipulation as well as a measurement of the off-resonant photon scattering error they introduce. Finally, we use them to achieve sideband cooling to the motional ground state of a mixed species ion crystal.
Miniaturized ion trap arrays with many trap segments present a promising architecture for scalable quantum information processing. The miniaturization of segmented linear Paul traps allows partitioning the microtrap into different storage and processing zones. The individual position control of many ions—each of them carrying qubit information in its long-lived electronic levels—by the external trap control voltages is important for the implementation of next generation large-scale quantum algorithms. We present a novel scalable microchip multi-segmented ion trap with two different adjacent zones, one for the storage and another dedicated to the processing of quantum information using single ions and linear ion crystals. A pair of radio-frequency-driven electrodes and 62 independently controlled dc electrodes allows shuttling of single ions or linear ion crystals with numerically designed axial potentials at axial and radial trap frequencies of a few megahertz. We characterize and optimize the microtrap using sideband spectroscopy on the narrow S1/2↔D5/2 qubit transition of the 40Ca+ ion, and demonstrate coherent single-qubit Rabi rotations and optical cooling methods. We determine the heating rate using sideband cooling measurements to the vibrational ground state, which is necessary for subsequent two-qubit quantum logic operations. The applicability for scalable quantum information processing is proved.