Stabilization and Control In a Linear Ion Trap A thesis submitted for the degree of Doctor of Philosophy John-Patrick Stacey Trinity Term Wadham College 2003 Oxford Abstract 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 40Ca+, 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 pho- ton 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 sub- stantial 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 abun- dances 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 re- duced; and most importantly, the photoionization is isotope selective. Evidence is presented which suggests that even with an non-enriched source, the rare isotope 43Ca 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. i Acknowledgements I would like to begin by thanking Prof Andrew Steane, my supervisor. His enthusiasm and advice have been indispensable in completing the work presented here: from the quick fixes to the bigger pictures, and all the details in between. I must also express my gratitude to Prof Derek Stacey. It has been a pleasure and a privilege to work alongside them both. I feel I must mention the other members of the ion-trapping group, if only to ensure that they’ll let me back into the department. I am grateful to Dr. David Lucas for his companionship and his tirelessness both in the office and while running experiments. Drs. Matthew McDonnell and Charles Donald, and more recently Simon Webster and Jonathan Home, have all contributed to- wards making my time as a DPhil student worthwhile. Spending several years in the same office as them has necessarily honed my wit as well as my wits, and I will miss having someone to insult. Thanks also to Drs. Angel Ramos and Marek Saˇ sura,ˇ and to Dr. David Stevens. My construction work and time in the basement of the Clarendon Laboratory would not have been the same without the presence of Graham Quelch and George Matthews. Between them they have no doubt saved several of my fingers during machining or drilling. Also I appreciate the hard work carried out by the occupants of the main Clarendon Workshop on my behalf, and also by David T Smith, Johan Fopma and everyone in the Central Electronics Group. Thanks also to everyone else in the department—academic, administrative and support staff—who have been consistently helpful and generous with their time. My undergraduate tutor, Dr. Geoff Brooker, might be considered to be indirectly to blame for everything presented here. His tuition was inspirational, and showed me just how enjoyable physics could be. He has recently offered advice on the work in this thesis, for which I am also grateful. I must also mention Michael Bancroft, who provided so much encouragement at school: thank you. After so many years in Oxford I have friends far too numerous to thank here individually. DougSoc, that indescribable, inscrutable society of either ‘weirdos and oddballs’ or ‘intellectual giants at play:’ I’m glad I have been able to come out to play with you all so many times, and I’m grateful for the skinned knees and grass stains it left me with. Members of Wadham, past and present: my friendships with you are what turned my occupation of just another collection of limestone quadrangles into something worthwhile. Friends from Queen Elizabeth’s Grammar School: if these acknowledgements were being read out at Speech Night, we’d all be asleep by now, or running a book on what time it will all finish. I miss your companionship, now we have all dispersed. The emotional and financial support of my family has been generous and inexhaustible. I am grateful for the support, love and pride of my parents and my Grandfather, and of my late Grand- mother. Thank you so much; I love you all and owe you a debt I can never repay. It only remains for me to thank Kate: for the freaky faces she pulls and the squeaky noises she makes; for the late-night telephone calls and the animal impressions; my prop, my friend, my darlen. ii CONTENTS Doctoral thesis, John-Patrick Stacey Contents Abstract i Acknowledgements ii 1 Introduction 1 1.1 A brief history of spectroscopy . 1 1.2 Computation theory and practice . 2 1.2.1 Classical computation and information theory . 2 1.2.2 Quantum computational theory . 2 1.2.3 Physical implementations of a quantum computer . 3 1.2.3.1 Ion traps . 4 1.2.3.2 Cavity QED . 4 1.2.3.3 Optical lattices . 5 1.2.3.4 NMR and other nuclear systems . 5 1.2.3.5 Solid-state quantum dots . 6 1.2.3.6 Miscellaneous other proposals . 6 1.2.4 Milestones in implementation . 7 1.3 Quantum computation in the Oxford Ion Trap . 7 1.4 Structure of the thesis . 8 2 Overview 9 2.1 Introduction . 9 2.2 Brief discussion of the experiment . 9 2.2.1 Principle of ion trapping . 10 2.2.2 The Cirac–Zoller scheme in the Oxford ion trap . 11 2.2.3 Manipulating the state of the ions . 11 2.2.3.1 Laser cooling and fluorescence . 11 2.2.3.2 State preparation . 12 2.2.3.3 Shelving and deshelving . 12 2.2.3.4 Two-photon transitions: EIT and dark resonances . 12 2.2.3.5 Photoionization . 13 2.2.4 Improvements required in the Oxford ion trap . 13 2.3 Physical properties of 40Ca+ . 14 2.3.1 Properties of the element and preparation of the ion . 14 2.3.2 Electronic structure of 40Ca+ . 15 2.3.3 Transition wavelengths and rates . 16 iii CONTENTS Doctoral thesis, John-Patrick Stacey 2.4 The ion trap and vacuum system . 16 2.4.1 Electrode structure . 16 2.4.2 The form of the Paul trapping potential . 17 2.4.3 Surrounding components and vacuum can . 17 2.5 Lasers . 18 2.5.1 Laser diodes . 18 2.5.2 The 794 nm master/slave system . 19 2.5.3 397 nm light and the 397 cooling laser . 19 2.5.4 The 866 nm laser . 20 2.5.5 The 854 nm/850 nm lasers . 20 2.5.6 The 389 nm, 393 nm and 423 nm lasers . 20 2.5.7 Directions of laser beams in the vacuum can . 21 2.6 Frequency references and measurement . 21 2.6.1 Absolute frequency measurement . 21 2.6.2 Signals from gas lamps . 23 2.6.3 Etalons for laser locking . 23 2.7 Cameras and imaging . 24 2.8 Quantum computation in the ion trap . 25 2.8.1 Introduction . 25 2.8.2 Qubit states and scalability . 25 2.8.3 Initialization and temperature . 26 2.8.4 Decoherence rates . 26 2.8.5 Logic gates within the 40Ca+ manifold . 26 2.8.6 State measurement . 27 I Shelving one Qubit State .