DISS. ETH NO. 23051 Transport Quantum Logic Gates for Trapped Ions A thesis submitted to attain the degree of DOCTOR OF SCIENCE of ETH ZURICH¨ (Dr. sc. ETH ZURICH)¨ presented by LUDWIG ERASMUS DE CLERCQ MSc. Phys., Univerity of Stellenbosch born on 15.01.1986 citizen of Republic of South Africa Accepted on the recommendation of Prof. Dr. J. P. Home Prof. Dr. T. Sch¨atz 2015 Abstract One of the most promising methods for scaling up quantum informa- tion processing with trapped ions is the quantum CCD architecture [Wineland 98, Kielpinski 02], in which ions are shuttled between many zones of a multiplexed ion trap processor. A primary element of this design is the parallel operation of gates in multiple regions, presenting a formidable challenge for scaling of optical control. In this thesis, I demon- strate a new route which could dramatically reduce these requirements, by transporting ions through laser beams [D. Leibfried 07]. The thesis covers the hardware, software and experiments which were required in order to achieve this goal. In order to perform these experiments I have developed several hard- ware and software solutions which are more widely applicable. Firstly, the Electronically Variable Interactive Lockbox (EVIL) which is widely used in our laboratory as a PI-controller. Secondly, the Direct Ether- net Adjustable Transport Hardware (DEATH) developed specifically for the transport experiments. Finally, I devised a simple method to cre- ate complex transport experiments which require control over multiple independent potential wells. The main achievement of this thesis is the demonstration of parallel quan- tum logic gates involving transport of ions. I have also demonstrated that these gates can be performed sequentially in order to create more com- plex operations by performing a Ramsey experiment. Additionally I have developed a novel method to estimate time-dependent coefficients of a Hamiltonian containing two non-commuting terms. The problem natu- rally arises when transporting an ion through a laser beam. The method is sensitive enough that we can detect the curvature of the wavefronts of the Gaussian laser beam. i Zusammenfassung Eine der vielversprechendsten Methoden, die Quanteninformationsver- arbeitung mit gefangenen Ionen zu skalieren, ist die quantenladungsge- kopplete Architektur (,,quantum charge-coupled device") [Wineland 98, Kielpinski 02], in welcher Ionen zwischen verschiedenen Zonen eines ge- multiplexten Ionenfallen-Prozessors hin und her bewegt werden. Ein wich- tiges Element dieses Designs ist die gleichzeitige Anwendung von Gatte- roperationen in verschiedenen Regionen des Chips, welches erhebliche Schwierigkeiten bei der Skalierung des optischen Aufbaus zur Steuerung der Ionen bereitet. In der vorliegenden Arbeit beschreibe ich einen neuen Weg, welcher diese Beschr¨ankungen stark vereinfacht, in dem Ionen durch statische Laserstrahlen transportiert werden [D. Leibfried 07]. Diese Dis- sertation beschreibt die Hard- und Software, sowie Experimente, welche ben¨otigt werden, um dieses Ziel zu erreichen. Um diese Experimente durchfuhren¨ zu k¨onnen, habe ich im Verlauf die- ser Arbeit verschiedene Hard- und Softwarel¨osungen entwickelt, welche auch anderweitig anwendbar sind. Nennenswert sind hier die elektro- " nisch verstellbare, interaktive Lockbox\(EVIL), welche in unserem La- bor als PI-Regler genutzt wird, sowie die direkt uber¨ Ethernet anpass- " bare Transport-Hardware\(DEATH), welche speziell fur¨ die Transport- Experimente entwickelt wurde. Schliesslich habe ich eine einfache Metho- de entwickelt, um komplexe Transport-Experimente zu realisieren, die Kontrolle uber¨ mehrere, voneinander unabh¨angige Potentialt¨opfe ben¨otigen. Die haupts¨achliche Leistung dieser Arbeit ist die Demonstration paralle- ler quantenlogischer Gatter, welche den Transport von Ionen beinhalten. In dem ich diese Methode genutzt habe, um ein Ramsey-Experiment durchzufuhren,¨ konnte ich ausserdem zeigen, dass Gatter sequenziell aus- gefuhrt¨ werden k¨onnen, um komplexere Operationen zu realisieren. Schliess- lich habe ich eine neue Technik entwickelt, die es erm¨oglicht, die zeitabh¨angigen Koeffizienten eines Hamiltonians, welcher zwei nicht-kommutierenden Terme beinhaltet, abzusch¨atzen. Eine solche Problemstellung taucht auf, wenn ein Ion durch einen Laserstrahl transportiert wird. Die Methode ist so empfindlich, dass die Krummung¨ der Wellenfront eines Gauss-Strahls nahe des Fokuses gemessen werden kann. iii Acknowledgments It has been very fun and educational working with everyone in the TIQI group. You all have been an inspiration to me and have driven me to perform cool experiments. Listening to progress of everyone on a weekly basis was so enlightening that I know everyone is always motivated to do their best to improve things in the laboratory. I wish to thank Prof. Dr. Jonathan Home, who has given me the op- portunity to carry out the research I have performed in his group. He has supervised this work and provided meaningful suggestions and dis- cussions on my topic of research. He always pushed me and motivated me to improve on data I have taken to achieve the best possible results for my experiments. The words "good progress" I will always associate with his name. Ben Keitch for always being willing to help and provide technical know- how, especially when I started in the group and needed it most. Vlad Negnevitsky who has truly helped me the most in becoming an engineer and together building the EVIL systems everyone is using in the laboratory. Apart from the engineering we had many fruitful discussions on physics. His willingness to help everyone who asks stands out in our group and he has made a difference in most projects. Hsiang-Yu Lo for getting me up and running in the laboratory and help- ing me with experiments whenever I needed it. Discussing basic questions we both had in ion trapping/physics in general and using our hands on occasion as vectors on an imagined Bloch-sphere has certainly been fun. You did an amazing job with the beryllium system, sorry that the parallel gates experiment have been running both times the lasers have broken... Daniel Kienzler, his designed and manufactured 3D Paul trap which all of the experimentalists in B20 are using on a daily basis. Matteo Marinelli for taking most of the data with me for the experiments contained in this thesis and walking home with me when we have missed the last bus. You have made great additions to Ionizer and without those my fish, fins and flare would never have existed. I have to admit everything was awesome. David Nadlinger, his work on the EVILs, DEATHs and control system which in some cases were in dire need of change. His work has made it much simpler to obtain good data for my experiments. We have worked a lot together throughout all your projects, or rather, it was great having to see you just excellently completing task without too much input. It has been fun working with you. Robin Oswald for making excellent upgrades to the way I have solved waveforms and for speeding up the extraction process we both have worked on for quite some time. You have a unique way of approach- ing problems which is refreshing and I believe you are an equally strong physicist and engineer. v Christa Fl¨uhmannfor her work on the 729 nm and the magnetic field sta- bilization which all of the users in B20 can only appreciate the amount of effort she has put in getting it running so well, thank you. I hope you do not play music through those sounds cards while performing experiments by accident. I also want to thank the experimentalists from our other laboratories in B25, Florian Leupold, Frieder Lindenfelser and Joseba Alonso for always being willing to listen and being able to lift up my mood. You guys have been great. Lastly I would like to thank my parents Wessel and Hilda de Clercq for always encouraging and supporting me trough all my studies and personal life. They have given and done more for me than any other and I am proud to be their son. vi Contents 1 Introduction1 1.1 Thesis layout............................ 4 2 The physics of ion trapping7 2.1 Linear Paul trap .......................... 7 2.2 Hamiltonian............................. 11 2.2.1 This work and analysis of motion............. 14 2.3 Two-photon stimulated Raman transitions............ 15 2.4 Final remarks............................ 17 3 General experimental overview 19 3.1 Trap................................. 19 3.2 Experimental setup overview ................... 20 3.3 Calcium and beryllium as qubits ................. 21 3.3.1 Calcium ion......................... 24 3.3.2 Beryllium ion........................ 24 3.4 Laser setups for transport experiments.............. 26 3.5 External Filters........................... 27 3.6 Experimental control........................ 28 3.7 Final remarks............................ 30 4 Electronically Variable Interactive Lock-box 33 4.1 Overview .............................. 33 4.2 Development history........................ 34 4.3 Projects on the EVIL ....................... 39 4.3.1 PI controller ........................ 41 4.3.2 Pulse shaping........................ 43 4.4 Bitstream.............................. 47 4.5 Software............................... 47 4.6 Future improvements and projects ................ 51 vii Contents 5 Voltage sources 53 5.1 Slow multi-channel device - AD5371 ............... 53 5.2 Other Technologies......................... 55 5.3 Considerations and requirements ................. 57 5.4 Hardware design - DEATH