The long term aim of this work is to study the suitability of using laser cooled Ca+ ions in Penning traps as the basic components of a quantum computer. A great deal of progress in the field of quantum computing has been made in recent years with laser cooled ions stored in radio frequency ion traps. Building a useful quantum computer with trapped ions is however extremely challenging. Penning traps offer some possible benefits over radio frequency traps. They also create some additional difficulties. The potential advantages and disadvantages of Penning traps are discussed throughout the thesis. We show that we are able to overcome the problems associated with laser cooling in Penning traps, and have trapped single ions for extended periods of time. Pairs of Ca+ ions have been aligned along the axis of a Penning trap, and have been optically resolved. A novel Penning trap array based on PCB boards has been developed. A prototype was built and tested, along with the electronics required to shuttle ions between different sub-traps. Ions have been shuttled a distance of 10 mm in 2.5 μs. A return trip efficiency of up to 75% was seen. A quantum effect – J-state mixing caused by large magnetic fields – has been observed for the first time in single atomic ions. The magnetic field causes a forbidden [Delta]J = 2 transition to become weakly allowed. This effect is of general interest in atomic physics, and is also very relevant for quantum computation studies. A quantitative prediction of the magnitude of the J-mixing effect has been derived theoretically. This is compared to experimental data, and is found to be in excellent qualitative and good quantitative agreement.
The long term aim of this work is to study the suitability of using laser cooled Ca+ ions in Penning traps as the basic components of a quantum computer. A great deal of progress in the field of quantum computing has been made in recent years with laser cooled ions stored in radio frequency ion traps. Building a useful quantum computer with trapped ions is however extremely challenging. Penning traps offer some possible benefits over radio frequency traps. They also create some additional difficulties. The potential advantages and disadvantages of Penning traps are discussed throughout the thesis. We show that we are able to overcome the problems associated with laser cooling in Penning traps, and have trapped single ions for extended periods of time. Pairs of Ca+ ions have been aligned along the axis of a Penning trap, and have been optically resolved. A novel Penning trap array based on PCB boards has been developed. A prototype was built and tested, along with the electronics required to shuttle ions between different sub-traps. Ions have been shuttled a distance of 10 mm in 2.5 μs. A return trip efficiency of up to 75% was seen. A quantum effect – J-state mixing caused by large magnetic fields – has been observed for the first time in single atomic ions. The magnetic field causes a forbidden [Delta]J = 2 transition to become weakly allowed. This effect is of general interest in atomic physics, and is also very relevant for quantum computation studies. A quantitative prediction of the magnitude of the J-mixing effect has been derived theoretically. This is compared to experimental data, and is found to be in excellent qualitative and good quantitative agreement.
Results demonstrating laser cooling and observation of individual calcium ions in a Penning trap are presented. We show that we are able to trap, cool, image and manipulate the shape of very small ensembles of ions sufficiently well to produce two-ion 'Coulomb crystals' aligned along the magnetic field of a Penning trap. Images are presented which show the individual ions to be resolved in a two-ion crystal. A distinct change in the configuration of such a crystal is observed as the experimental parameters are changed. These structures could eventually be used as building blocks in a Penning trap based quantum computer.
This thesis presents work aimed towards achieving sideband cooling of 40Ca+ ions in a Penning trap. The observation of an increase in the number of quantum jumps as a function of the trapping magnetic field is first presented. This observation is explained by the ion falling into a long-lived D5/2 state, out of which the ion is not being re-pumped. The ion can fall into this state due to mixing of the fine structure components with the same mJ quantum number induced by the applied magnetic field. A calculation of the mixing and shelving rate as a function of magnetic field strength is presented. This theory matches well with the experimental results observed. This work has been presented in a publication in which a perturbative analysis was used. An alternative analysis is presented here in which the full Hamiltonian is diagonalised. The essential conclusions however remain unchanged. This ‘J-state mixing’ effect means re-pumping from each of the six D5/2 state sub-levels of our ion is required for efficient laser cooling. This is achieved by the addition of a system comprising an 854 nm laser and a fibre EOM to provide the radiation required to re-pump these levels. The same EOM is then used to re-pump out of the four sub-levels of the D3/2 state using a single 866 nm laser. This is a great simplification of the experimental setup required to cool a 40Ca+ ion in a Penning trap which would otherwise require ten separate lasers to independently address each of the D sub-states. Achieving efficient repumping leads to the ability to perform pulsed spectroscopy on the quadrupole S1/2 → D5/2 transition in 40Ca+ . Preliminary results of this spectroscopy in a radio-frequency trap are presented.
For 35 years, laser-cooled trapped ions have been at the frontier of progress in quantum computing, quantum simulation and precision measurement, and remain one of the most valuable tools in these fields to this day. Most of these experiments are predicated upon or benefit from the ability to place ions in the motional quantum ground state, a technique that was first demonstrated in radiofrequency ion traps 25 years ago. For a range of crucial experiments that are impossible to conduct in radiofrequency traps or are not well suited to this architecture, Penning traps provide an important alternative. However, the performance of Penning traps had been limited by the fact that ground-state cooling was yet to be achieved in such a system. This thesis reports the first demonstration of resolved-sideband cooling in a Penning trap, for 40Ca+ions cooled with light at 729-nm, achieving a ground state occupation of 99% in one dimension. Demonstrations of the coherent manipulations possible at this level of confinement are presented. The ion heating rate is measured and although higher than might be expected given the unusually large ion-electrode distance remains amongst the lowest reported in any trap to date. Achieving this result required the development of a number of new experimental systems and major upgrades to the stability and reliability of the experiment, the details of which are also given. The thesis also presents theoretical work into the use of two-dimensional Coulomb crystals in a Penning trap as a resource for quantum information. Using the symmetries of the crystal, we find that it is possible to engineer complex entangled states, specifically two small quantum error correcting codes, using a very small number of global entangling pulses. Efficient entanglement protocols such as these are vital for the implementation of useful quantum error correction.
We report on the design and testing of an array of Penning ion traps made from printed circuit board. The system enables fast shuttling of ions from one trapping zone to another, which could be of use in quantum information processing. We describe simulations carried out to determine the optimal potentials to be applied to the trap electrodes for enabling this movement. The results of a preliminary experiment with a cloud of laser cooled calcium ions demonstrate a round-trip shuttling efficiency of up to 75%.
Laser cooled ions in a Penning trap can be isolated from the environment by placing them in vacuum and only interacting with them through optical and RF fields. The number of trapped particles can be varied from a single ion up to thousands. Confinement is provided by a static homogeneous magnetic field and a quadrupole electric potential. In the natural frame of the ions, this appears as a 3D simple harmonic potential. Therefore three dimensional structures can be formed in the absence of any additional RF field which may lead to heating as is the case with RF traps. There are 3N different motional modes for N particles. I present an analysis of the motion of a single particle showing that the energy levels for all three modes are equally spaced. I also describe the interaction between a trapped two level atom and an optical field. During my time in the lab the laser and computer control of the experiment has been significantly improved. In addition, an existing trap was modified to provide greater optical access and fluorescence collection. This allowed the vibrational levels superimposed on the internal states of a single 40Ca+ ion to be resolved via a narrow linewidth, electric quadrupole transition. This is the first observation of magnetron and modified cyclotron sidebands on an optical transition. When more than one calcium ion is laser cooled, and their temperature reduced below 5mK, they form a Coulomb crystal. The locations of the ions minimise the total potential energy which is comprised of the Coulomb repulsion and trap potential. The fluorescence collection optics have been arranged to resolve individual ions in these crystals. Information about the motion of the ions is deduced by comparing photos from the experiment to numerical simulations. Previously, only two ions have ever been aligned along the magnetic field in a Penning trap. I present strings of up to 29 particles and suggest the only limitation, apart from the electrode structure, is the overlap of the laser beams with the ions.
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.