Jointly published with Canopus Academic Publishing Limited, UK
2016, IV, 300 p.
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This book will describe recent theoretical advances of cold atom physics in optical lattices, concentrating on strongly correlated systems and possible applications in quantum information processing. Furthermore, the latest experiments aiming towards realizing these theoretical ideas will be discussed. The book will present in detail recently developed quantum optical tools for manipulating atoms in optical lattices and show how they can be used to realize a large range of well controlled many body Hamiltonians. Connections and differences to standard condensed matter physics will be explained. Finally, it will discuss how the ability to dynamically change parameters in these Hamiltonians on time scales much shorter than typical decoherence times can be exploited to realize quantum information processing devices with neutral atoms in optical lattices.
Content Level »Research
Keywords »Canopus - atom optics - cold atoms - optical lattices - quantum information - qubits
1 Introduction Part I Few Atom Physics 2 Optical potentials 2.2 Periodic Lattice Structures 2.3 Lattice engineering 3 Single Atom Dynamics 3.1 Intraband Dynamics 3.2 Interband Dynamics 3.3 Additional Trap Potential 4 Atom atom interactions in optical lattices 4.1 Interatomic Potentials 4.2 s-wave Scattering 4.3 Feshbach Resonances 4.4 Losses 5 Bose-Einstein Condensates in Optical Lattices 5.1 The Gross-Pitaevskii Equation 5.2 Double Well Potential 5.3 Translationally Invariant Lattices 5.4 Harmonically Trapped Lattices Part II Many Atom Physics 6 Hubbard Models in Optical Lattices 6.1 Derivation of the Bose-Hubbard Model 6.2 Superfluid to Mott Insulator transition 6.3 Gutzwiller Ansatz 6.4 Phase diagram 6.5 Tonks-Girardeau Limit 6.6 Multi component Hubbard model 7 Loading of Degenerate Atomic Gases Into Optical Lattices 7.1 Adiabatic Switching on a Lattice 7.2 Defect suppressed lattices 7.3 Irreversible Loading and Cooling Schemes 8 Condensed matter models 8.1 Spin Models in Multicomponent Systems 8.2 Effective magnetic fields 8.3 Atomic Quantum Dots 8.4 Lattice Immersions 8.5 Unitary Dynamics and Numerical Methods 8.6 Detection Methods 9 Quantum information processing in optical lattices 9.1 diVincenzo Criteria in Optical Lattices 9.2 Entanglement Engineering 9.3 Graph States and One Way Computing 9.4 Quantum Random Walks 10 Summary and outlook