Editor's Foreword xiii
Notation xvii
Chapter I Historical introduction: photons and measurements using photons 1
1.1 The discovery of photons 2
1.2 The wave and particle properties of photons 4
1.3 The Heisenberg uncertainty relations 7
1.4 When do macroscopic objects behave quantum mechanically? 12
1.5 Overview of this book 15
Chapter II The main principles of quantum mechanics 17
2.1 The wave function 17
2.2 Probabilistic interpretation of the wave function 19
2.3 Single measurements and ensembles of measurements 21
2.4 Reduction of a quantum state 24
2.5 von Neumann's postulate of reduction 27
2.6 Orthogonal measurements 30
2.7 Nonorthogonal measurements 32
2.8 Back action of the measuring device on the measured object 35
Chapter III Indirect measurements 38
3.1 The two main types of quantum measurements 38
3.2 An electron as the quantum probe 41
3.3 Electron probe -- detailed analysis 44
3.4 Formal description of an indirect measurement 46
Chapter IV Quantum nondemolition measurements 50
4.1 The standard quantum limit for the energy of an oscillator 50
4.2 How can one overcome the standard quantum limit? 53
4.3 The ponderomotive probe for energy 57
4.4 Criteria for QND measurements 60
Chapter V Linear measurements 64
5.1 The measurement process and the uncertainty relation 64
5.2 Measurement accuracy and perturbations for linear measurements 67
5.3 Sequences of linear measurements 70
Chapter VI Continuous linear measurements 76
6.1 Discrete and continuous measurements 76
6.2 Uncertainty relations for continuous linear measurements 77
6.3 Uncertainty relations for continuous linear measurements--rigorous analysis 82
6.4 Linear, quantum 2N-pole systems 84
6.5 The spectral representation 87
6.6 Internal fluctuations of a linear measuring device 89
Chapter VII Nonlinear systems for continuous measurements 93
7.1 Fluctuational and dynamical back action of the measuring device 93
7.2 Quantum Zeno paradox for exact measurements 95
7.3 The equation of motion for the density operator during a continuous monitoring 97
7.4 Quantum Zeno paradox for approximate measurements 101
Chapter VIII Detection of classical forces 105
8.1 Aspects of quantum limits for the detection of a classical force 105
8.2 Quantum probe oscillator 109
8.3 Continuous quantum nondemolition monitoring 112
8.4 Standard quantum limit for an oscillator 115
8.5 Optimal detection of a classical force 118
8.6 A probe oscillator coupled to a sensor that continuously monitors its number of quanta 122
Chapter IX Energetic quantum limitations 125
9.1 The energy of the probe and the minimum detectable force 125
9.2 Energetic limits on sensitivity: general analysis 129
9.3 Distinguishing evolutionary paths of a quantum object from each other 132
Chapter X Devices for measuring small mechanical displacements 136
10.1 Parametric transducer for mechanical displacements 136
10.2 Capacity transducer 139
10.3 Fluctuations in a capacity transducer in the stationary regime 143
10.4 Capacity transducer used to detect weak forces: stationary regime 148
10.5 Capacity transducer: nonstationary regime 151
10.6 Frequency upconverter 154
10.7 Capacity transducer with two-side-band pumping 157
Chapter XI Quantum nondemolition measurements of a resonator's energy 160
11.1 Review of methods of measurement 160
11.2 Measuring device based on cubic dielectric nonlinearity 162
11.3 The role of dissipation 165
11.4 Resonator coupled to a waveguide 167
Chapter XII Nonclassical states of electromagnetic waves as tools for quantum measurements 172
12.1 Quantum properties of a traveling electromagnetic wave 172
12.2 QND measurements of the energy of a traveling electromagnetic wave 175
12.3 Frequency-anticorrelated quantum state 178
12.4 Doppler measurements with frequency-anticorrelated photons 180
12.5 Statistical properties of a wave packet with a definite number of quanta 183
Conclusion 186
References 188
Subject Index 192