Description
This book is an up-to-date introduction to the quantum theory of measurement, a fast developing field of intense current interest to scientists and engineers for its potential high technology applications. It is also a subject of importance to students for its central role in the foundations of quantum mechanics. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neumann and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as squeezed light, single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book contains a pedagogical introduction to the relevant theory written at a level accessible to those with only a modest background in quantum mechanics. It then goes on to discuss aspects of the design of practical quantum measurement systems. This book is essential reading for all scientists and engineers interested in the potential applications of technology near the quantum limit. It will also serve as an ideal supplement to standard quantum mechanics textbooks at the advanced undergraduate or graduate level.
Chapter
1.1 The discovery of photons
1.2 The wave and particle properties of photons
1.3 The Heisenberg uncertainty relations
1.4 When do macroscopic objects behave quantum mechanically?
1.5 Overview of this book
Chapter II The main principles of quantum mechanics
2.2 Probabilistic interpretation of the wave function
2.3 Single measurements and ensembles of measurements
2.4 Reduction of a quantum state
2.5* von Neumann's postulate of reduction
2.6* Orthogonal measurements
2.7* Nonorthogonal measurements
2.8* Back action of the measuring device on the measured object
Chapter III Indirect measurements
3.1 The two main types of quantum measurements
3.2 An electron as the quantum probe
3.3* Electron probe — detailed analysis
3.4* Formal description of an indirect measurement
Chapter IV Quantum nondemolition measurements
4.1 The standard quantum limit for the energy of an oscillator
4.2 How can one overcome the standard quantum limit?
4.3 The ponderomotive probe for energy
4.4* Criteria for QND measurements
Chapter V Linear measurements
5.1 The measurement process and the uncertainty relation
5.2* Measurement accuracy and perturbations for linear measurements
5.3* Sequences of linear measurements
Chapter VI Continuous linear measurements
6.1 Discrete and continuous measurements
6.2 Uncertainty relations for continuous linear measurements
6.3* Uncertainty relations for continuous linear measurements-rigorous analysis
6.4* Linear, quantum 2/V-pole systems
6.5* The spectral representation
6.6* Internal fluctuations of a linear measuring device
Chapter VII Nonlinear systems for continuous measurements
7.1 Fluctuational and dynamical back action of the measuring device
7.2 Quantum Zeno paradox for exact measurements
7.3* The equation of motion for the density operator during a continuous monitoring
7.4* Quantum Zeno paradox for approximate measurements
Chapter VIII Detection of classical forces
8.1 Aspects of quantum limits for the detection of a classical force
8.2 Quantum probe oscillator
8.3 Continuous quantum nondemolition monitoring
8.4* Standard quantum limit for an oscillator
8.5* Optimal detection of a classical force
8.6* A probe oscillator coupled to a sensor that continuously monitors its number of quanta
Chapter IX Energetic quantum limitations
9.1 The energy of the probe and the minimum detectable force
9.2* Energetic limits on sensitivity: general analysis
9.3* Distinguishing evolutionary paths of a quantum object from each other
Chapter X Devices for measuring small mechanical displacements
10.1 Parametric transducer for mechanical displacements
10.3 Fluctuations in a capacity transducer in the stationary regime
10.4 Capacity transducer used to detect weak forces: stationary regime
10.5* Capacity transducer: nonstationary regime
10.6* Frequency upconverter
10.7* Capacity transducer with two-side-band pumping
Chapter XI Quantum nondemolition measurements of a resonator's energy
11.1 Review of methods of measurement
11.2 Measuring device based on cubic dielectric nonlinearity
11.3 The role of dissipation
11.4* Resonator coupled to a waveguide
Chapter XII Nonclassical states of electromagnetic waves as tools for quantum measurements
12.1 Quantum properties of a traveling electromagnetic wave
12.2 QND measurements of the energy of a traveling electromagnetic wave
12.3 Frequency-anticorrelated quantum state
12.4 Doppler measurements with frequency-anticorrelated photons
12.5* Statistical properties of a wave packet with a definite number of quanta
Quantum Measurement
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