Quantum Measurement

by Vladimir B. Braginsky , Farid Ya Khalili , Kip S. Thorne

• ISBN13: 9780521419284
• ISBN10: 052141928X
• Format: Hardcover
• Copyright: 1992-09-25
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Editor's Foreword	xiii
Notation	xvii
Historical introduction: photons and measurements using photons	1	(16)
The discovery of photons	2	(2)
The wave and particle properties of photons	4	(3)
The Heisenberg uncertainty relations	7	(5)
When do macroscopic objects behave quantum mechanically?	12	(3)
Overview of this book	15	(2)
The main principles of quantum mechanics	17	(21)
The wave function	17	(2)
Probabilistic interpretation of the wave function	19	(2)
Single measurements and ensembles of measurements	21	(3)
Reduction of a quantum state	24	(3)
von Neumann's postulate of reduction	27	(3)
Orthogonal measurements	30	(2)
Nonorthogonal measurements	32	(3)
Back action of the measuring device on the measured object	35	(3)
Indirect measurements	38	(12)
The two main types of quantum measurements	38	(3)
An electron as the quantum probe	41	(3)
Electron probe - detailed analysis	44	(2)
Formal description of an indirect measurement	46	(4)
Quantum nondemolition measurements	50	(14)
The standard quantum limit for the energy of an oscillator	50	(3)
How can one overcome the standard quantum limit?	53	(4)
The ponderomotive probe for energy	57	(3)
Criteria for QND measurements	60	(4)
Linear measurements	64	(12)
The measurement process and the uncertainty relation	64	(3)
Measurement accuracy and perturbations for linear measurements	67	(3)
Sequences of linear measurements	70	(6)
Continuous linear measurements	76	(17)
Discrete and continuous measurements	76	(1)
Uncertainty relations for continuous linear measurements	77	(5)
Uncertainty relations for continuous linear measurements - rigorous analysis	82	(2)
Linear, quantum 2N-pole systems	84	(3)
The spectral representation	87	(2)
Internal fluctuations of a linear measuring device	89	(4)
Nonlinear systems for continuous measurements	93	(12)
Fluctuational and dynamical back action of the measuring device	93	(2)
Quantum Zeno paradox for exact measurements	95	(2)
The equation of motion for the density operator during a continuous monitoring	97	(4)
Quantum Zeno paradox for approximate measurements	101	(4)
Detection of classical forces	105	(20)
Aspects of quantum limits for the detection of a classical force	105	(4)
Quantum probe oscillator	109	(3)
Continuous quantum nondemolition monitoring	112	(3)
Standard quantum limit for an oscillator	115	(3)
Optimal detection of a classical force	118	(4)
A probe oscillator coupled to a sensor that continuously monitors its number of quanta	122	(3)
Energetic quantum limitations	125	(11)
The energy of the probe and the minimum detectable force	125	(4)
Energetic limits on sensitivity: general analysis	129	(3)
Distinguishing evolutionary paths of a quantum object from each other	132	(4)
Devices for measuring small mechanical displacements	136	(24)
Parametric tranducer for mechanical displacements	136	(3)
Capacity tranducer	139	(4)
Fluctuations in a capacity transducer in the stationary regime	143	(5)
Capacity transducer used to detect weak forces: stationary regime	148	(3)
Capacity transducer: nonstationary regime	151	(3)
Frequency upconverter	154	(3)
Capacity transducer with two-side-band pumping	157	(3)
Quantum nondemolition measurements of a resonator's energy	160	(12)
Review of methods of measurement	160	(2)
Measuring device based on cubic dielectric nonlinearity	162	(3)
The role of dissipation	165	(2)
Resonator coupled to a waveguide	167	(5)
Nonclassical states of electromagnetic waves as tools for quantum measurements	172	(14)
Quantum properties of a traveling electromagnetic wave	172	(3)
QND measurements of the energy of a traveling electromagnetic wave	175	(3)
Frequency-anticorrelated quantum state	178	(2)
Doppler measurements with frequency-anticorrelated photons	180	(3)
Statistical properties of a wave packet with a definite number of quanta	183	(3)
Conclusion	186	(2)
References	188	(4)
Subject Index	192