## A Group-Theoretical Approach to Quantum Optics: Models of Atom-Field InteractionsWritten by major contributors to the field who are well known within the community, this is the first comprehensive summary of the many results generated by this approach to quantum optics to date. As such, the book analyses selected topics of quantum optics, focusing on atom-field interactions from a group-theoretical perspective, while discussing the principal quantum optics models using algebraic language. The overall result is a clear demonstration of the advantages of applying algebraic methods to quantum optics problems, illustrated by a number of end-of-chapter problems. An invaluable source for atomic physicists, graduates and students in physics. |

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### Contents

2 Atomic Dynamics | 23 |

3 Quantized Electromagnetic Field | 45 |

4 Field Dynamics | 71 |

5 The JaynesCummings Model | 83 |

6 Collective Interactions | 113 |

7 Atomic Systems in a Strong Quantum Field | 143 |

8 Quantum Systems Beyond the Rotating Wave Approximation | 189 |

9 Models with Dissipation | 217 |

10 Quasidistributions in Quantum Optics | 237 |

11 Appendices | 279 |

315 | |

321 | |

### Other editions - View all

A Group-Theoretical Approach to Quantum Optics Andrei B. Klimov,Sergei M. Chumakov Limited preview - 2009 |

A Group-Theoretical Approach to Quantum Optics Andrei B. Klimov,Sergei M. Chumakov No preview available - 2009 |

### Common terms and phrases

amplitude applying atomic inversion atomic operators atomic system atomic transition average number basis Bloch sphere Bloch vector Casimir operator classical field coefﬁcients collapses and revivals commutation relations corresponding deﬁned density matrix diagonal Dicke model distribution dynamics effective Hamiltonian eigenstates eigenvalues eigenvectors energy levels evolution operator expansion factorized ﬁeld ﬁnd ﬁrst ﬂuctuations free Hamiltonian Heff Hilbert space humps initial atomic initial coherent initial conditions integral of motion interaction Hamiltonian irreducible representation Kerr medium Lie algebra linear matrix elements mode nonlinear number of atoms number of excitations number of photons obtain phase operator phase space photon number Q function quantization quantum field Quantum Optics quantum system Rabi frequency resonance condition satisﬁes satisfy small parameter spectrum squeezing subalgebra subspace subsystems takes the form transformation two-level atoms unitary vacuum wave function Wigner function zero zeroth-order approximation