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80后老去,情怀不死 农产品也有“韩寒范儿”

80后老去,情怀不死 农产品也有“韩寒范儿”

  80后老去,情怀不死 农产品也有“韩寒范儿”

  罗曼罗兰曾说过:在认清生活的真相后依然热爱它。手植记的成功,正是因为这种热爱生活的态度和精神。

  诞生于奔三之前——寻找生活中的小甜蜜

  手植记的诞生可以称得上是一次意外怀孕。由某文化创意公司CEO发起了一次,为自己的员工发放健康食材福利的旅行,却意外发现了原生态食材市场的大需求量。

  光是活着就竭尽全力了,没错,世界复杂但这就是天朝HARD模式的生存法则,如果青春年少,这群创意人还大可趁年轻做个合格的浪子。但而立之年的他们,有了家庭的责任,青年不愤青,因为他们长大了,决定给自己和家人一份“健健康康”作为活至中年的礼物。

  这段话是理解手植记精神的核心,顺应生活不是妥协而是为了更好地生活。就是这样积极态度催生出不一样的品牌思维。

  成长在路上——手植之旅

  如今,手植之旅第二季刚刚结束。团队历时20天,途径蔚县-冀州-广灵-张北-凉城-岱海-斗泉乡-灵丘-沁县-红崖村-长治-娄烦-晋祠-晋中-社城-平遥-茌平等地。寻得天鹰椒、桃花米、口蘑、岱海葵花籽、红芸豆、仁用杏仁、核桃、黄小米、晋祠大米、娄烦蘑菇、黄豆、社城黑小米、茌平圆铃大枣等珍贵的原生食材。3680公里,1586张照片,20000文字,同时还找到了一批有共同爱好的人。

  发展在方圆中——一屋不扫何以扫天下

  手植记的诞生虽然任性,但发展却是步步为营的。将这五步总结便是:

  ①先有人物故事后有商品,说故事比商品和服务更重要

  房价,堵车,加班,雾霾和地沟油。这些标签是80的生活元素,一句光活着就已经竭尽全力能引起他们的共鸣。

  ②如何方法化最重要,借势和联合媒体的重要性

  舌尖2在整个热播的期间,手植之旅同步宣传,加上媒体的关注,带来了不错的效果。

  ③极致创意设计,体验式营销塑造品牌

  包装设采用原生态纸,古朴现代相互融合的排版,标明手植记原生态的品牌个性。

  ④执行力,所有员工成就品牌

  手植之旅第二季再次启程,团队始终保持着高效快速的执行力。为生活探寻原生态食材,共同的愿望为了家人的幸福。

  如今的手植记已经是拥有几十人的创意团队,这个以每年几倍增长的原生态品牌不断创造着电商的奇迹。我也相信,手植记会走得越来越远,因为他们一直懂得:不忘初心,方得始终。

A Group-Theoretical Approach to Quantum Optics



Contents
Preface IX
1 Atomic Kinematics 1
1.1 Kinematics of an Atom with Two Energy Levels 1
1.2 Dicke States 5
1.3 Atomic Coherent States 7
1.4 Squeezed Atomic States 12
1.5 Atoms with n > 2 Energy Levels 17
1.5.1 Systems with n Energy Levels 17
1.5.2 Systems with Three Energy Levels 20
1.6 Problems 21
2 Atomic Dynamics 23
2.1 Spin in a Constant Magnetic Field 23
2.2 A Two-level Atom in a Linearly Polarized Field 24
2.2.1 The Rotating Wave Approximation 24
2.3 A Two-level Atom in a Circularly Polarized Field 26
2.4 Evolution of the Bloch Vector 28
2.5 Dynamics of the Two-level Atomwithout the RWA 29
2.6 Collective Atomic Systems 33
2.7 Atomic System in a Field of a Single Pulse 39
2.8 Problems 42
3 Quantized Electromagnetic Field 45
3.1 Quantization of the Electromagnetic Field 45
3.2 Coherent States 47
3.3 Properties of the Coherent States 48
3.4 Displacement Operator 51
3.5 Squeezed States 54
3.6 Thermal States 58
3.7 Phase Operator 58
3.8 Regularized Phase Operator 63
A Group-Theoretical Approach to Quantum Optics: Models of Atom-Field Interactions
Andrei B. Klimov and Sergei M. Chumakov
Copyright ? 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 978-3-527-40879-5

VI Contents
3.9 Phase Distribution 65
3.10 Problems 69
4 Field Dynamics 71
4.1 Evolution of a Field with Classical Pumping 71
4.2 Linear Parametric Amplifier 72
4.3 Evolution in the Kerr Medium 75
4.4 Second Harmonic Generation in the Dispersive Limit 77
4.5 Raman Dispersion 79
4.6 Problems 81
5 The Jaynes–Cummings Model 83
5.1 The Interaction Hamiltonian 83
5.2 The Spectrum and Wave Functions 85
5.3 Evolution Operator 87
5.4 The Classical Field Limit 90
5.5 Collapses and Revivals 92
5.5.1 The Dispersive Limit 93
5.5.2 Exact Resonance 95
5.6 The JCM with an Initial Thermal Field 97
5.7 Trapping States 99
5.8 Factorization of the Wave Function 101
5.9 Evolution in Field Phase Space 104
5.10 The JCM without RWA 105
5.10.1 Diagonalization of the Hamiltonian 106
5.10.2 Atomic Inversion 109
5.10.3 Classical Field Limit 110
5.11 Problems 111
6 Collective Interactions 113
6.1 The Dicke Model (Exactly Solvable Examples) 113
6.2 The Dicke Model (Symmetry Properties) 118
6.3 The Dicke Model (Symmetric Case) 121
6.4 The Zeroth-Order Approximation 122
6.4.1 The Weak Field Case 122
6.4.2 The Strong Field Case 123
6.5 Perturbation Theory 124
6.6 Revivals of the First and Second Orders 128
6.6.1 Revivals of the Second Order 130
6.7 Atom-Field Dynamics for Different Initial Conditions 132
6.7.1 Initial Number States 132
6.7.2 Coherent and Thermal Fields 134
6.8 Three-Level Atoms Interacting with Two Quantum Field Modes 136
6.9 Problems 141

7 Atomic Systems in a Strong Quantum Field 143
7.1 Dicke Model in a Strong Field 143
7.2 Factorization of the Wave Function 146
7.3 Evolution in Phase Space 148
7.4 Dicke Model in the Presence of the Kerr Medium 152
7.5 Generation of the Field Squeezed States 154
7.6 Coherence Transfer Between Atoms and Field 157
7.7 Resonant Fluorescence Spectrum 159
7.8 Atomic Systems with n Energy Levels 162
7.8.1 Cascade Configuration 167
7.8.2 -Type Configuration 168
7.8.3 V-Type Configuration 169
7.9 Dicke Model in the Dispersive Limit 169
7.10 Two-Photon Dicke Model 172
7.11 Effective Transitions in Three-Level Atoms with Configuration 180
7.12 N-Level Atoms of Cascade Configuration 183
7.13 Problems 186
8 Quantum Systems Beyond the Rotating Wave Approximation 189
8.1 Kinematic and Dynamic Resonances in Quantum Systems 189
8.2 Kinematic Resonances: Generic–Atom Field Interactions 192
8.3 Dynamic Resonances 198
8.3.1 Atom–Quantized Field Interaction 203
8.3.2 Atom–Classical Field Interaction 204
8.3.3 Interaction of Atoms with the Quantum Field in the Presence of
Classical Fields 206
8.4 Dynamics of Slow and Fast Interacting Subsystems 212
8.4.1 Effective Field Dynamics 214
8.4.2 Effective Atomic Dynamics 215
8.5 Problems 216
9 Models with Dissipation 217
9.1 Dissipation and Pumping of the Quantum Field 217
9.2 Dicke Model with Dissipation and Pumping (Dispersive Limit) 219
9.3 Dicke Model with Dissipation (Resonant Case) 223
9.3.1 Initial Field Number State 226
9.3.2 Initial Field Coherent State 226
9.3.3 Factorized Dynamics 229
9.4 Strong Dissipation 231
9.4.1 Field–Field Interaction 234
9.4.2 Atom–Field Interaction 235
9.5 Problems 235

VIII Contents
10 Quasi-distributions in Quantum Optics 237
10.1 Quantization and Quasi-distributions 237
10.1.1 Weyl Quantization Method 237
10.1.2 Moyal–Stratonovich–Weyl Quantization 240
10.1.3 Ordering Problem in L(H) 241
10.1.4 Star Product 242
10.1.5 Phase–Space Representation and Quantum–Classical
Correspondence 243
10.2 Atomic Quasi-distributions 245
10.2.1 P Function 246
10.2.2 Q Function 247
10.2.3 Stratonovich–Weyl Distribution 250
10.2.4 s-Ordered Distributions 251
10.2.5 Star Product 252
10.2.6 Evolution Equations 255
10.2.7 Large Representation Dimensions (Semiclassical Limit) 256
10.3 Field Quasi-distributions 262
10.3.1 P Function 262
10.3.2 Q Function 264
10.3.3 Wigner Function 265
10.3.4 s-Ordered Distributions 266
10.4 Miscellaneous Applications 269
10.4.1 Kerr Hamiltonian 269
10.4.2 The Dicke Hamiltonian 271
10.5 Problems 276
11 Appendices 279
11.1 Lie Groups and Lie Algebras 279
11.1.1 Groups: Basic Concepts 279
11.1.2 Group Representations 281
11.1.3 Lie Algebras 282
11.1.4 Examples 284
11.2 Coherent States 294
11.2.1 Examples 295
11.3 Linear Systems 299
11.3.1 Diagonalization of the Time-independent Hamiltonian 301
11.3.2 Evolution Operator 302
11.3.3 Reference Formulas 303
11.4 Lie Transformation Method 304
11.5 Wigner d Function 306
11.6 Irreducible Tensor Operators 311
References 315
Index 321

Preface
Quantum Optics is a branch of physics that has developed rapidly over the past
few years thanks to the development of experimental techniques that currently
allow a single photon to be created and detected, as well as a single atom to be
studied in a superconducting cavity. New quantum optics applications such as cold
ions, Bose–Einstein condensate, quantum information, and quantum computing
motivate the study of the collective properties of quantum systems.
Currently, a number of textbooks on quantum optics are available. They cover
‘‘classical’’ quantum optics topics such as quantized field theories and atomic
system theories, basic interaction processes between them, and applications such
as resonance fluorescence, laser theory, etc. The purpose of this book is not to cover
all these topics, which are amply discussed in the standard textbooks. Our goal
is different – to show the advantage that may be offered by the algebraic methods
applied to problems in quantum optics.
The structure of the book is as follows: Chapters 1–4 are introductory and have
been included so that the book is self-consistent and can be read without needing to
constantly refer to some other textbooks. (However, these chapters were written in a
spirit that emphasizes algebraic methods.) In Chapters 5–10, we describe different
models of atom–field interactions, discussing in detail the Jaynes–Cummings and
the Dicke models and their generalizations, including the dissipative case using
different types of the algebraic perturbation theories. Appendices 1–6 are included
to provide the necessary information from the theory of Lie groups and algebras
and their representations.
We would like to thank our coauthors, collaborators, and friends: Professors
V.V. Dodonov, H. de Guise, V.P. Karassiov, M. Kozierowski, V.I. Manko, L. Roa,
C. Saavedra, L.L. Sanchez-Soto and K.B. Wolf for their suggestions. We are especially
grateful to Prof. H. de Guise, and Drs J.L. Romero and I. Sainz for invaluable
help in the preparation of the manuscript. We also acknowledge Grant 45704 of
CONACyT (Mexico).
Guadalajara, Mexico A.B. Klimov
December 2008 S.M. Chumakov
A Group-



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