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Alter O., Yamamoto Y. — Quantum Measurement of a Single System
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Название: Quantum Measurement of a Single System
Авторы: Alter O., Yamamoto Y.
Аннотация: A groundbreaking look at the nature of quantum mechanics.
With new technologies permitting the observation and manipulation of single quantum systems, the quantum theory of measurement is fast becoming a subject of experimental investigation in laboratories worldwide. This original new work addresses open fundamental questions in quantum mechanics in light of these experimental developments.
Using a novel analytical approach developed by the authors, Quantum Measurement of a Single System provides answers to three long-standing questions that have been debated by such thinkers as Bohr, Einstein, Heisenberg, and Schrodinger. It establishes the quantum theoretical limits to information obtained in the measurement of a single system on the quantum wavefunction of the system, the time evolution of the quantum observables associated with the system, and the classical potentials or forces which shape this time evolution. The technological relevance of the theory is also demonstrated through examples from atomic physics, quantum optics, and mesoscopic physics.
Suitable for professionals, students, or readers with a general interest in quantum mechanics, the book features recent formulations as well as humorous illustrations of the basic concepts of quantum measurement. Researchers in physics and engineering will find Quantum Measurement of a Single System a timely guide to one of the most stimulating fields of science today.
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Рубрика: Физика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2001
Количество страниц: 136
Добавлена в каталог: 19.03.2010
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Предметный указатель
(QND) see quantum measurement nondemolition
(QND) nondestructive measurement see quantum measurement nondestructive
Adiabatic approximation 5 66 67 69-73 118
Adiabatic measurement see quantum measurement adiabatic
Aharonov 3 11 12 61 65 67
Annihilation operator 54
Atom, two-level 6 77-86 89 113 114
Back-action noise 7 24 28 29 32 45 47 49 91 99 104 106 108
Bohr 3 12
Brownian motion 24 37-39 44 47
Channel, quantum, encoding and decoding of information 42 43
Coherences of the density operator see density operator coherences
Collapse see reduction communication
Communication channel, quantum, upper limit to capacity 34 41 43
Complementarity 3 12
Completeness of quantum mechanics 8 94 105 109 116 119
Contractive state measurement see quantum measurement contractive
Creation operator 54
Density operator, coherences of 83
Density operator, of a mixed state 41
Density operator, of a pure state after a measurement 18
Density operator, of a pure state before a measurement 17
Dephasing (or decoherence) 1 2 6 75 78 83 90 91 113 118
Destructive measurement see quantum measurement destructive
Disentanglement see entanglement
Displacement (or translation) operator 59
Doppler speed meter 99
Einstein, I 107 109 of
Electromagnetic cavity, single-mode 6 77 78-86 89 114
Energy eigenstate 3 12 65 73
Energy number of quanta of 7 8 42 78 85 92 94 95 111 116
Entanglement (of a quantum probe and a quantum signal) see interaction unitary
Entanglement (of a quantum probe and a quantum signal), approximated as disentanglement see adiabatic approximation
Entanglement (of a quantum probe and a quantum signal), measurement without see quantum measurement without
Entanglement entropy 41
Ergodicity 21
Estimation 12 13 15
Estimation of expectation value 18 19
Estimation of uncertainty 19-21
Evolution see time evolution; Heisenberg and Schr dinger pictures
Force, fundamental quantum limit to detection of 2 7-9 91-116 118-121
Frame of reference 77 80 81 88 89
Free mass (or particle), driven by a classical force 7 8 91-109 110 113 115 119 121
Frequency difference 97-99
Generalized projection operator 27 49 50
Gravitational wave detection 2 91
Hamiltonian of a free mass driven by a classical force 95
Hamiltonian of a harmonic oscillator driven by a classical force 59 110
Hamiltonian of a two-level atom in a single-mode cavity 78
Hamiltonian of two coupled harmonic oscillators 54 68
Harmonic oscillator(s) 52-56 68-71 coupled)1
Harmonic oscillator(s), driven by a classical force 2 7-9 91-95 118-121
Harmonic oscillator(s), state, coherent 55 59
Harmonic oscillator(s), state, energy (or number) eigenstate 68-71 111-115
Harmonic oscillator(s), state, squeezed 7 52-61 92 96
Heisenberg 6 28 54 77 78 86-89 95 105-107 118 Heisenberg;
Heisenberg microscope 105
Interaction (of a quantum probe with a quantum signal), unitary 12 17 24 51 62 63 66 86 unitary)
Interaction (of a quantum probe with a quantum signal), unitary, of a free mass and a wavepacket of light 97-99
Interaction (of a quantum probe with a quantum signal), unitary, of two harmonic oscillators 54-56 68-71
Interaction (of a quantum probe with a quantum signal), unitary, of two wavepackets of light, linear, in a beam splitter 54-56
Interaction (of a quantum probe with a quantum signal), unitary, of two wavepackets of light, nonlinear, in a Kerr medium 31 82
Interferometric measurement see quantum measurement interferometric
Inverse quantum Zeno effect of a single system 89 (see also quantum Zeno effect)
Momentum, change 92 95-99 119
Momentum, generalized 53-58 68-71
Number of quanta of energy see energy number quantum
Observable(s), canonically conjugate 24 26 28 45 46 49 65 110
Observable(s), commuting 24 33
Observable(s), eigenvalues and eigenstates of 12 13 26 45 48-50 62-64 eigenstate
Observable(s), expectation value and uncertainty of 5 9 13 15 18-21 26-31 67 96 117
Observable(s), noncommuting 67 106 107 109
Observable(s), symmetric 33 34 38 39 44
Observable(s), time-varying 77 81 88 89
Pauli's first-kind measurement see quantum measurement Pauli's
Phase, relative 1 8 31 32 56 60 63 66-68 82 94 111-116 121
Photon-number 5 24 26 31-48 77 80-86 89 114
Picture, Heisenberg 6 54 78 86-90 118
Picture, Schr dinger 6 55 77 86-90 118
Position change (or displacement) 92 99-105 119
Position, generalized 53-58 68-71
Precision measurements 2 7-9 91 93
Preparation (or resetting) of a quantum state see quantum wavefunction (or state) preparation
Probability, conservation of 13 115
Probability, density, after a measurement 18
Probability, density, before a measurement 18
Probability, density, conditional 19
Probability, of transition 27 30 32 66 69 111 112
Probability-amplitude operator 17 32-34 48 50 82 88 89
Projection postulate 3 12 13 26 31 44
Projection postulate, generalized 5 17 24
Protective measurement see quantum measurement protective
QND condition, necessary 24
QND condition, sufficient 24 49 53 62
Quadrature amplitudes, slowly varying 5 8 24 26 31-33 45-48 57 64 82 94 110 115
Quantum measurement, adiabatic 3 5 11 12 65-73 118
Quantum measurement, contractive state 7 92 99-105 113
Quantum measurement, destructive 1 8 94 113 116 119
Quantum measurement, interferometric 97-99
Quantum measurement, nondemoliton (QND) 5 7 8 23 50 53 62 64 77 82-86 88 89 92 94 111 113 114 116 119
Quantum measurement, nondestructive 1 2
Quantum measurement, of two entangled particles 107
Quantum measurement, Pauli's first-kind 17
Quantum measurement, protective 3 11 12 26 48-50 52 53 58-64 65 67
Quantum measurement, reversible 3
Quantum measurement, simultaneous, of noncommuting observables 8 94 105-109 110 115 119
Quantum measurement, utilizing a priori information see quantum measurement without
Quantum measurement, von Neumann's (or ideal) 12 14
Quantum measurement, weak (or imprecise) 13 16 31-45
Quantum measurement, without entanglement 5 51 64 117
Quantum wavefunction (or state), change (or evolution) of, deterministic, in unitary interaction or time evolution 5 12 24 25 49 51-56 62 64 73 78 86 117 unitary; unitary)
Quantum wavefunction (or state), change (or evolution) of, stochastic, in a quantum measurement process 3 5 12 24 25 49 51 52 55 62-64 89
Quantum wavefunction (or state), collapse (or reduction) of see reduction
Quantum wavefunction (or state), collapse (or reduction) of, meaning of, epistemological (or statistical) 2 11 15 26 31 53 64 67 68 73 117 118
Quantum wavefunction (or state), collapse (or reduction) of, meaning of, ontological (or physical) 2 3 6 11 61 64 65 67 117 118
Quantum wavefunction (or state), collapse (or reduction) of, of a single system, impossibility of, determining 3-9 11-21 23-50 51-64 65-73 77 86-90 92 104 105 115 117 118
Quantum wavefunction (or state), collapse (or reduction) of, of an ensemble, determination of 2 5 11 15 18 20 21 35-37 39 40 44 53 57 58 60 61 63
Quantum wavefunction (or state), collapse (or reduction) of, preparation (or resetting) of 7 8 12 17 48 62 63 86 92 94 95 99-104 105 113 119
Quantum Zeno effect 6 75 76
Quantum Zeno effect, of a single system 2 6 9 75-90 92 94 113-115 118
Rabi oscillations 80 81
Rabi oscillations, damped 82-86
Reduction (or collapse) 3-6 7 12 14 15 21 23-50 51-53 62-64 67 70-73 75 78 89 117 118
Reversible measurement see quantum measurement reversible
Rotating wave approximation 78
Schr dinger 6 55 77 86-90 107 118 Schr
Signal-to-noise ratio 61 111 112
Simultaneous measurement of noncommuting observables see quantum measurement simultaneous of
Spin 1, 2, 3 fictitious 78-81 89 114
Standard quantum limit (SQL) 7 8 91-96 99-105 113 119
Statistics of the result of a quantum measurement of a single system 15 17-19
Statistics of the result of a quantum measurement of an ensemble, II 13 15 20 21
Statistics of the result of the results of a series of measurements of a single system 5 13 15 19-21
Time evolution of a single quantum system, unitary see also interaction of a quantum probe with a quantum signal unitary;
Time evolution of a single quantum system, unitary, limit to monitoring of see quantum Zeno effect of a single system
Time evolution of a single quantum system, unitary, of a free mass driven by a classical force 95
Time evolution of a single quantum system, unitary, of a harmonic oscillator driven by a classical force 110 111
Time evolution of a single quantum system, unitary, of a two-level atom in a single-mode cavity 80 81
Time evolution of a single quantum system, unitary, of a wavepacket of light driven by a classical electromagnetic field 58-60
Transition probability see probability of
Uncertainty principle 5 8 9 25 28 49 94 99 105-109 116 117 119
Unitarity see conservation of probability
Unitary interaction see interaction unitary
Unitary time evolution see time evolution unitary
von Neumann 12 (see also projection postulate; quantum measurement von
Wavepacket(s) of light, coupled, linear coupling, in a beam splitter 54-56
Wavepacket(s) of light, coupled, nonlinear coupling, in a Kerr medium 31 82
Wavepacket(s) of light, coupled, nonlinear coupling, in a parametric amplifier 33 45-48
Wavepacket(s) of light, driven by a classical electromagnetic field 61
Wavepacket(s) of light, state, coherent 55 58 59 61 68 71
Wavepacket(s) of light, state, photon-number eigenstate 24 39
Wavepacket(s) of light, state, squeezed 1 5 24 31-48
Weak (or imprecise) measurement see quantum measurement weak
Zeno, quantum see inverse quantum Zeno effect; quantum Zeno effect
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