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Työväentutkimus Vuosikirja

Quantum Simulations of Atom-Photon Interactions

Martti Havukainen

Published Oct 1, 1999• 0 citations
OpenAlex

Abstract

ISBN 951-45-8709-X (PDF version) Helsingin yliopiston verkkojulkaisut Helsinki 1999 Preface This work has been done at Helsinki Institute of Physics (HIP). I am most grateful to Prof. Stig Stenholm for his guidance and giving me possibility to do this work. I am also greatly indebted to Doc. K.-A. Suominen. Part of the work was done in his group. I also thank Prof. V. Bužek and G. Drobny ́ for collaboration and for their hospitality during my visit in Bratislava. I want to thank my parents and little sister about everything. I also thank the members of the group of Quantum Optics who have helped me in numerous problems. Finally I thank all my friends especially in our bowling and minigolf group. They have helped me during my studies and together we have had many tight matches. I also want to thank the Center for Scientific Computing (CSC) for offering their computer facilities for this work. With gratitude I acknowledge the financial support provided by the Academy of

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We study (1 + 1)-dimensional SU(N ) spin systems in the presence of global SU(N ) rotation and lattice translation symmetries.Knowing the mixed anomaly of the two symmetries at low energy, we identify, by anomaly matching argument, a topological index for spin model-the total number of Young-tableaux boxes of spins per unit cell modulo N -characterizing the "ingappability" of the system.A nontrivial index implies either a ground-state degeneracy in a gapped phase, which can be thought of as a field-theory version of the Lieb-Schultz-Mattis (LSM) theorem, or a restriction of the possible universality classes in a critical phase, regarded as the symmetry-protected critical phases.As an example of the latter case, we show only a class of SU(N ) Wess-Zumino-Witten theories can be realized in the low-energy limit of the given lattice model in the presence of the symmetries.Similar constraints also apply when a higher global symmetry emerges in the model with a lower symmetry.We also predict a general constraint on the structure factor which is measurable in experiments.To generalize to higher dimensions, we introduce a new boundary condition which renders the flux-insertion argument for the LSM-type theorems in two or higher dimensional lattices free from the specific choice of system sizes.It also enables a formulation of the LSM-type theorems in arbitrary dimensions in terms of the anomaly in field theories of bulk correspondences.Moreover, by our new boundary condition, we also show that the higher-form U(1) LSM theorem and U(1) and SU(N ) LSM theorems in arbitrary higher dimensions have unified form in the bulk viewpoint.At last, we also discuss the discrete-symmetry LSM-type ingappabilities in the lattice language and we find that projective symmetry representations per unit cell implies that the system cannot be gapped with a unique translation-symmetric ground state.I would like to express my sincere gratitude to all those having helped me during my Master and Doctoral courses at the University of Tokyo.First of all, I would like to thank my parents who have supported me financially and encouraged me to do whatever I am keen on in the past 28 years.Also, I am grateful to every one that has taught me great knowledges on life and study at various steps.More specifically, I have to appreciate the guidance and kind supports by my supervisor, Professor Masaki Oshikawa who has given me patient guidance on study and kind financial supports.Moreover, I would thank Prof. Masahiro Sato for his cooperation in our paper, "Theory of electron spin resonance in one-dimensional topological insulators with spinorbit couplings: Detection of edge states".I am also grateful for Dr. Chang-Tse Hsieh for his collaboration on our work "Anomaly Matching and Symmetry-Protected Critical Phases in SU (N ) Spin Systems in 1+1 Dimensions", on which this Thesis is largely based, and Dr. Yoshiki Fukusumi on the work "Bosonization in a background U (1) gauge field".I would also thank Prof. Yuji Tachikawa and Prof. David Tong for patient and kind help on resolving my confusion during study.I would also like to acknowledge with much appreciation the help from our group members.

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ISBN 951-45-8709-X (PDF version) Helsingin yliopiston verkkojulkaisut Helsinki 1999 Preface This work has been done at Helsinki Institute of Physics (HIP). I am most grateful to Prof. Stig Stenholm for his guidance and giving me possibility to do this work. I am also greatly indebted to Doc. K.-A. Suominen. Part of the work was done in his group. I also thank Prof. V. Bužek and G. Drobny ́ for collaboration and for their hospitality during my visit in Bratislava. I want to thank my parents and little sister about everything. I also thank the members of the group of Quantum Optics who have helped me in numerous problems. Finally I thank all my friends especially in our bowling and minigolf group. They have helped me during my studies and together we have had many tight matches. I also want to thank the Center for Scientific Computing (CSC) for offering their computer facilities for this work. With gratitude I acknowledge the financial support provided by the Academy of
Approved by Supervising Committee: For my parents. Thank you for your love and support. Acknowledgments First of all, I would like to thank my supervisor, Prof. Mark Raizen. Mark, you allowed me great freedom in my work and put a lot of trust in me. Nevertheless, you were always there with good advice and great ideas when I needed you. I am very proud that I was given the opportunity to work in your group. Thank you for supporting me during my time in Austin and beyond. I am equally thankful to my fellow group members and friends Adam Libson, Dr. Ed Narevicius and Christian Parthey. Everything we accomplished during the last one and a half years was a group effort and they are the main reason I am writing this thesis using the pronoun “we”. Adam, although you sometimes “unnerved ” us with your constant fear of leaks or fatal rotor destruction, I wouldn’t have wanted to work with anybody else than you on this project. You often foresaw problems we would have easily
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We study (1 + 1)-dimensional SU(N ) spin systems in the presence of global SU(N ) rotation and lattice translation symmetries.Knowing the mixed anomaly of the two symmetries at low energy, we identify, by anomaly matching argument, a topological index for spin model-the total number of Young-tableaux boxes of spins per unit cell modulo N -characterizing the "ingappability" of the system.A nontrivial index implies either a ground-state degeneracy in a gapped phase, which can be thought of as a field-theory version of the Lieb-Schultz-Mattis (LSM) theorem, or a restriction of the possible universality classes in a critical phase, regarded as the symmetry-protected critical phases.As an example of the latter case, we show only a class of SU(N ) Wess-Zumino-Witten theories can be realized in the low-energy limit of the given lattice model in the presence of the symmetries.Similar constraints also apply when a higher global symmetry emerges in the model with a lower symmetry.We also predict a general constraint on the structure factor which is measurable in experiments.To generalize to higher dimensions, we introduce a new boundary condition which renders the flux-insertion argument for the LSM-type theorems in two or higher dimensional lattices free from the specific choice of system sizes.It also enables a formulation of the LSM-type theorems in arbitrary dimensions in terms of the anomaly in field theories of bulk correspondences.Moreover, by our new boundary condition, we also show that the higher-form U(1) LSM theorem and U(1) and SU(N ) LSM theorems in arbitrary higher dimensions have unified form in the bulk viewpoint.At last, we also discuss the discrete-symmetry LSM-type ingappabilities in the lattice language and we find that projective symmetry representations per unit cell implies that the system cannot be gapped with a unique translation-symmetric ground state.I would like to express my sincere gratitude to all those having helped me during my Master and Doctoral courses at the University of Tokyo.First of all, I would like to thank my parents who have supported me financially and encouraged me to do whatever I am keen on in the past 28 years.Also, I am grateful to every one that has taught me great knowledges on life and study at various steps.More specifically, I have to appreciate the guidance and kind supports by my supervisor, Professor Masaki Oshikawa who has given me patient guidance on study and kind financial supports.Moreover, I would thank Prof. Masahiro Sato for his cooperation in our paper, "Theory of electron spin resonance in one-dimensional topological insulators with spinorbit couplings: Detection of edge states".I am also grateful for Dr. Chang-Tse Hsieh for his collaboration on our work "Anomaly Matching and Symmetry-Protected Critical Phases in SU (N ) Spin Systems in 1+1 Dimensions", on which this Thesis is largely based, and Dr. Yoshiki Fukusumi on the work "Bosonization in a background U (1) gauge field".I would also thank Prof. Yuji Tachikawa and Prof. David Tong for patient and kind help on resolving my confusion during study.I would also like to acknowledge with much appreciation the help from our group members.