Laser Cooling Mechanisms and Brownian Motors in Optical Lattices Peder Sj¨olund Department of Physics Ume˚a University 2007 The figure on the cover page shows fluorescence from about 100 million atoms as they fall through a resonant laser beam. 100 ms earlier, the atoms were trapped in an optical lattice, and from the curve, one can detect that the temperature of the sample was about 4 µK. Laser Cooling Mechanisms and Brownian Motors in Optical Lattices Peder Sjo¨lund ISBN 978-91-7264-321-5 (c) Peder Sjo¨lund, 2007 Ume˚aUniversity Department of Physics SE - 907 37 Ume˚a SWEDEN Printed by Larssons tryckeri Ume˚a 2007 Laser Cooling Mechanisms and Brownian Motors in Optical Lattices AKADEMISK AVHANDLING Som med vederbo¨rligt tillst˚and av Rektors¨ambetet vid Ume˚a Universitet fo¨r vinnande av filosofie doktorsexamen framla¨gges till offentlig granskning vid Institutionen f¨or Fysik. H¨orsal MA121, MIT-huset, Ume˚a Universitet Torsdagen den 31:a maj, 2007, kl. 10.00 av Fil. Lic. Peder Sjo¨lund Opponent: Dr. Chris Westbrook, Laboratoire Charles Fabry de l’Institut d’Optique, Campus Polytechnique, RD128, 91127 Palaiseau Cedex, France. Betygsn¨amnd: Professor Sven Mannervik Professor Stefan Kro¨ll Dr. Jyrki Piilo Examinator: Professor Anders Kastberg Abstract In this thesis, detailed experimental studies and numerical simulations are presented of laser cooling mechanisms in dissipative optical lattices and re- sults of the first realized three dimensional Brownian motor in optical lat- tices. A dissipative optical lattice is a periodic light shift potential, created in the interference patterns of laser beams. In this, atoms can be both cooled and trapped, and the most important relaxation mechanism is generally considered to be “Sisyphus cooling”. However, careful experimental and theoretical investigations indicate the presence of other cooling processes as well. This is studied by varying different parameters such as irradiance and frequency of the lattice light. The time evolution of atoms in optical lattices show strong evidence of a bimodal velocity distribution, where a population transfer between one mode containing “hot” atoms and one mode containing “cold” atoms is evident. The normal diffusion of atoms in optical lattices is characterized by isotrop random fluctuations and exhibit the nature of Brownian motion. We have realized a technique where this motion is rectified and controlled. This is done in a three dimensional double optical lattice. This Brownian motor has control properties for both its speed and its direction in three dimensions. Our three dimensional double optical lattice is created by using laser light, exploiting two transitions, in the D2 line of cesium. Two three di- mensional optical lattices are spatially overlapped; each optical lattice traps atoms in one of two hyperfine ground states. The controllability comes about by inducing phase shifts in the lattice laser beams, which displace the lattices relative to each other. This type of highly controlled Brownian motor is of fundamental interest since Brownian motion is present in almost all systems and for the role they play in protein motors and the function of living cells, and for the potential applications in nanotechnology. Brownian motors of this kind also open the way to possible studies of quantum Brow- nian motors and quantum resonances that are predicted for atomic ratchets. Optical lattices, and especially double optical lattices, have also been suggested as a platform for quantum state manipulations due to the good isolation from environment and ambient effects. Most of the work in this thesis is a first step towards the implementation of quantum manipulation schemes in a double optical lattice. i List of papers: This thesis is based on the following papers: I Generation of multiple power-balanced laser beams for quantum- state manipulation experiments with phase-stable double optical lattices S. J. H. Petra, P. Sjo¨lund and A. Kastberg J. Opt. A: Pure Appl. Opt., 8, 381, (2006) II Time dependence of laser cooling in optical lattices C. M. Dion, P. Sjo¨lund, S. J. H. Petra, S. Jonsell and A. Kastberg Europhys. Lett. 72, 369 (2005) III A nonadiabatic semi-classical method for dynamics of atoms in op- tical lattices S. Jonsell, C. M. Dion, M. Nyl´en, S. J. H. Petra, P. Sjo¨lund and A. Kastberg Eur. Phys. J. D, 39, 67 (2006) IV Comment on “Tunable Tsallis Distributions in Dissipative Optical Lattices” C. M. Dion, P. Sjo¨lund, S. J. H. Petra, S. Jonsell, A. Kastberg, L. Sanchez- Palencia, and R. Kaiser Submitted to Phys. Rev. Lett. V Bimodal distribution of laser-cooled atoms in optical lattices C. M. Dion, P. Sjo¨lund, S. Jonsell and A. Kastberg To be submitted VI Demonstration of a controllable three-dimensional Brownian mo- tor in symmetric potentials P. Sjo¨lund, S. J. H. Petra, C. M. Dion, S. Jonsell, M. Nyl´en, L. Sanchez- Palencia and A. Kastberg Phys. Rev. Lett. 96, 190602, (2006) VII Characterisation of a three-dimensional Brownian motor in optical lattices P. Sjo¨lund, S. J. H. Petra, C. M. Dion, H. Hagman, S. Jonsell and A. Kast- berg Accepted for publication in Eur. Phys. J. D ii VIII Controllable 3D atomic Brownian motor in optical lattices C. M. Dion, P. Sjo¨lund, S. J. H. Petra, S. Jonsell, M. Nyl´en, L. Sanchez- Palencia and A. Kastberg Submitted to Eur. Phys. J. Special Topics IX Multidimensional coupling in a controllable three-dimensional Brow- nian motor in optical lattices H. Hagman, C. M. Dion, P. Sjo¨lund, S. J. H. Petra and A. Kastberg To be submitted iii Comments to my participation in papers included in the thesis In general, I have been main responsible for the performed experiments, as well as for construction and developments of the experimental set-up. Analysis of both experimental data and numerical results have always been an effort shared among the people in the group. My specific contributions to papers in this thesis are the following: In paper I, I am responsible for the construction of the experimental setup and for collecting the experimental data. In papers II and IV, I was main responsible for all the experimental results, and for parts of the analyses of the experimental data. Paper V is the result of a joint collaboration between several groups and has been subject of many lengthy discussions. In paper III, I contributed by being involved in discussions and ideas. A part of the scientific focus of Paper III is based on ideas and experimental findings by me. In V, I contributed by analysing many of the numerical results and by being involved in discussions. The experimental results from paper II, III and IV done by me has served as an inspiration and background for the result and conclusions presented in paper V. For papers VI, VII and VIII, I was main responsible for collecting all the experimental data, writing parts in the papers and for the following analysis of the experimental data. I have also contributed and taken part in discus- sions concerning the numerical results. In paper IX, I am main responsible for the construction of the experimental set-up. I have taken part in all aspects of discussions of both the numerical and experimental results and for the planing of the experiment. iv Acknowledgements There are a number of people I would like to thank for good collaboration during my years as a Ph.D student. Anders Kastberg (Yoda) - for giving me the possibility to become a PhD-student in the cold matter and laser cooling group and for being a super-supervisor. You have been an excellent team leader and I thank you for the nice time we have had together. Espe- cially, I thank you for creating the good atmosphere in the group and for all the silly jokes. Stefan Petra - for being the best ”labmate” I could imagine and for a great time to- gether. In particular for all those hours, measuring in the dark and for fruitful scientific collaborations during several years. Svante Jonsell, Claude Dion, Mats Nyl´en, Laurent Sanchez-Palencia, Robin Kaiser - for a great team work and for given me insights in numerical simulations and other stuff. Magnus Rehn, Robert Saers - for being good friends and for sharing these years to- gether struggling with the labs. Johan Jersblad, Harald Ellmann - for giving me a nice start in the group. In partic- ular, I would like to thank Johan for all the experimental help in the beginning. Henning Hagman, Martin Z´elan - ”The young ones” I wish you all the best for the following years and upcoming work. Johan Svensson, Joakim Lundin, Anna Wallner, Florian Roth - for nice master projects and good company in the lab. Magnus Andersson, Erik Fa¨llman, J¨orgen Eriksson and all the nice people at the department - for being good friends and for always having something fun to tell. Lars Karlsson, Meena - for an indispensable help and expertise with electronics and for Tuesday 16.00 football. Martin Forsgren, Thomas Gustafsson, Lena A˚stro¨m - for the help and workmanship in the Physics Department work-shop. Margaretha Falgren, Ann-Charlott Dalberg, Lilian Andersson - for taking care of all the surrounding things such as economics, travels and teaching me to fill in different kinds of silly forms. Sonja Olofsson, Karin Rinnefeldt - for keeping the lab and my office clean. Annie Reiniusson - for being the best friend and co-worker during the years. Your friendship and support has meant a lot to me. Cenneth Sjo¨lund, Mona Sjo¨lund - my father and sister, for always being there. My close relatives and friends - for everything. v Contents 1 Introduction 1 2 Cooling and trapping of atoms 5 2.1 Introduction .