The rapid development of quantum technologies has driven a revolution in related research areas such as quantum computation and communication, and quantum materials. The first prototypes of functional quantum devices are beginning to appear, frequently created using ensembles of atoms, which allow the observation of sensitive, quantum effects, and have important applications in quantum simulation and matter wave interferometry. This modern text offers a self-contained introduction to the fundamentals of quantum atom optics and atomic many-body matter wave systems. Assuming a familiarity with undergraduate quantum mechanics, this book will be accessible for graduate students and early career researchers moving into this important new field. A detailed description of the underlying theory of quantum atom optics is given, before development of the key, quantum, technological applications, such as atom interferometry, quantum simulation, quantum metrology, and quantum computing.
Author(s): Tim Byrnes, Ebubechukwu O. Ilo-Okeke
Publisher: Cambridge University Press
Year: 2021
Language: English
Pages: 300
Tags: Atomic Molecular Optics
Preface
Foreword
1 Quantum many-body systems
1.1 Introduction
1.2 Second quantization
1.3 Fock states
1.4 Multi-mode Fock states
1.5 Interactions
1.6 References and further reading
2 Bose-Einstein condensation
2.1 Introduction
2.2 Bose and Einstein's original argument
2.3 Bose-Einstein condensation for a grand canonical ensemble
2.4 Low-energy excited states
2.5 Superfluidity
2.6 References and further reading
3 The Order Parameter and Gross-Pitaevskii equation
3.1 Introduction
3.2 Order parameter
3.3 The Gross-Pitaevskii equation
3.4 Ground state solutions of the Gross-Pitaevskii equation
3.5 Hydrodynamic equations
3.6 Excited state solutions of the Gross-Pitaevskii equation
3.7 References and further reading
4 Spin dynamics of atoms
4.1 Introduction
4.2 Spin degrees of freedom
4.3 Interaction between spins
4.4 Electromagnetic transitions between spin states
4.5 The ac Stark shift
4.6 Feshbach resonances
4.7 Spontaneous emission
4.8 Atom loss
4.9 Quantum jump method
4.10 References and further reading
5 Spinor Bose-Einstein condensates
5.1 Introduction
5.2 Spin coherent states
5.3 The Schwinger boson representation
5.4 Spin coherent state expectation values
5.5 Preparation of a spin coherent state
5.6 Uncertainty relations
5.7 Squeezed states
5.8 Entanglement in spin ensembles
5.9 The Holstein-Primakoff transformation
5.10 Equivalence between bosons and spin ensembles
5.11 Quasiprobability distributions
5.12 Other properties of spin coherent states and Fock states
5.13 Summary
5.14 References and further reading
6 Diffraction of atoms using standing wave light
6.1 Introduction
6.2 Theory of diffraction
6.3 Ultra-cold atom interaction with standing light wave
6.4 Bragg diffraction by standing wave light
6.5 Bragg diffraction by Raman pulses
6.6 References and further reading
7 Atom Interferometry
7.1 Introduction
7.2 Optical Interferometry
7.3 BEC interferometry
7.4 References and further reading
8 Atom interferometry beyond the standard quantum limit
8.1 Introduction
8.2 Two-component atomic Bose-Einstein condensates
8.3 Husimi Q-function
8.4 Ramsey interferometry and Bloch vector
8.5 Error propagation formula and squeezing parameter
8.6 Fisher information
8.7 Controlling the nonlinear phase per atom
8.8 References and further reading
9 Quantum simulation
9.1 Introduction
9.2 Problem statement: What is quantum simulation?
9.3 Digital quantum simulation
9.4 Toolbox for analogue quantum simulators
9.5 Example: The Bose-Hubbard model
9.6 References and further reading
10 Entanglement between atom ensembles
10.1 Introduction
10.2 Inseparability and quantifying entanglement
10.3 Correlation based entanglement criteria
10.4 One-axis two-spin squeezed states
10.5 Two-axis two-spin squeezed states
10.6 References and further reading
11 Quantum information processing with atomic ensembles
11.1 Introduction
11.2 Continuous variables quantum information processing
11.3 Spinor quantum computing
11.4 Deutsch's algorithm
11.5 Adiabatic quantum computing
11.6 References and further reading
Notes
References
Index
