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Quantum Measurements and Decoherence: Models and Phenomenology

Михаил Борисович Менский

Published Dec 15, 2010• 57 citations
OpenAlex

Abstract

List of Figures. Preface. 1. Introduction. I: The Nature of Quantum Measurements. 2. The Physics Behind Quantum Measurements. 3. Measurement induced uncertainties. II: Continuous Quantum Measurements: Theory. 4. Continuous Quantum Measurements: The General Notion. 5. Fuzzy Continuous Measurements: Phenomenology. 6. Restricted Path Integrals: General Features. III: Continuous Quantum Measurements: Applications. 7. The Monitoring of Energy. 8. Monitoring by a series of observations. 9. The Quantum Zeno effect in a passive setup. IV: Conceptual Problems and Prospects. 10. RPI and the Philosophy of Quantum Mechanics. 11. Conclusion: New Prospects. A. The Formalism of Quantum Mechanics. References. Index.

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List of Figures. Preface. 1. Introduction. I: The Nature of Quantum Measurements. 2. The Physics Behind Quantum Measurements. 3. Measurement induced uncertainties. II: Continuous Quantum Measurements: Theory. 4. Continuous Quantum Measurements: The General Notion. 5. Fuzzy Continuous Measurements: Phenomenology. 6. Restricted Path Integrals: General Features. III: Continuous Quantum Measurements: Applications. 7. The Monitoring of Energy. 8. Monitoring by a series of observations. 9. The Quantum Zeno effect in a passive setup. IV: Conceptual Problems and Prospects. 10. RPI and the Philosophy of Quantum Mechanics. 11. Conclusion: New Prospects. A. The Formalism of Quantum Mechanics. References. Index.
Preface INTRODUCTION TO CONTINUOUS QUANTUM MEASUREMENTS Quantum and Classical Systems Amplitudes and Alternatives Paths and Continuous Measurements The Action Uncertainty Principle INSTANTANEOUS AND SEQUENTIAL MEASUREMENTS Measurement of a Quantum System Quantum Zeno Paradox Approximate and Sequential Measurements TECHNIQUE OF PATH INTEGRALS Propagators and Path Integrals Definition of a Path Integral The Path Integral for an Oscillator Gaussian Path Integrals CONTINUOUS MEASUREMENT AND EVOLUTION OF THE MEASURED SYSTEM The Measurement Amplitude Effective Lagrangian Evolution of a Quantum System Subject to Continuous Measurement Scattering by the Measuring Medium CONTINUOUS MEASUREMENTS OF OSCILLATORS Position Monitoring (Path measurement) Estimation of Force Acting on an Oscillator Spectral Measurements of an Oscillator Evolution of a Harmonic Oscillator Subject to Spectral Measurement Measurement of a Path of a Nonlinear Oscillator CONTINUOUS QUANTUM NONDEMOLITION MEASUREMENTS Quantum Nondemolition Measurements Monitoring of Linear Momentum Velocity versus Momentum QND Measurements of Oscillators MEASUREMENT OF AN ELECTROMAGNETIC FIELD Exposition of the Method Measurement Amplitude Analysis of the Results Another Definition of the Field Strength Explicit Model of a Meter TIME IN QUANTUM COSMOLOGY Statement of the Problem Measurements in Quantum Cosmology Minisuperspace without Measurement Minisuperspace under Measurement Analysis of the results Concluding Remarks THE ACTION UNCERTAINTY PRINCIPLE Uncertainties in Continuous Measurements Classical Regime of Measurements Quantum Regime and AUP AUP and Equations of Motion Examples from Quantum Mechanics Quantum Nondemolition Measurements AUP in Quantum Gravity Concluding Remarks GROUP-THEORETICAL STRUCTURE OF QUANTUM CONTINUOUS MEASUREMENTS Evolution under Measurement Transverse Group for Alternatives Longitudinal Semigroup for Evolution Unification of Transverse and Longitudinal Structures Concluding Remarks PATHS AND MEASUREMENTS: FURTHER DEVELOPMENT Quantum and Classical Features in Continuous Measurement The Two-Slit Experiment Wave-Particle Dualism Conceptual Problems References Index
Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements (CQM). Reviewed are the various approaches to the CQM theory, and the approach based on the effective complex Hamiltonians is discussed in greater detail. The effective complex Hamiltonian is derived from the restricted path integral, which emphasizes the role of information in the dynamics of the system being measured. The complex Hamiltonian is used for analyzing the CQM of energy in a two-level system. Such measurement is demonstrated to be capable of monitoring the quantum transition, and the back effect of monitoring on the probability of transition is analyzed. The realization of this type of measurement by a long series
Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements (CQM). Reviewed are the various approaches to the CQM theory, and the approach based on the effective complex Hamiltonians is discussed in greater detail. The effective complex Hamiltonian is derived from the restricted path integral, which emphasizes the role of information in the dynamics of the system being measured. The complex Hamiltonian is used for analyzing the CQM of energy in a two-level system. Such measurement is demonstrated to be capable of monitoring the quantum transition, and the back effect of monitoring on the probability of transition is analyzed. The realization of this type of measurement by a long series of soft observations of the system is presented.
Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown considerably in recent years. Continuous Quantum Measurements and Path Integrals examines these measurements using Feynman path integrals. The path integral theory is developed to provide formulae for concrete physical effects. The main conclusion drawn from the theory is that an uncertainty principle exists for processes, in addition to the familiar one for states. This implies that a continuous measurement has an optimal accuracy-a balance between inefficient error and large quantum fluctuations (quantum noise). A well-known expert in the field, the author concentrates on the physical and conceptual side of the subject rather than the mathematical.
This chapter explores the path-integral theory of continuous quantum measurements. It explains the principal ideas of this theory on a qualitative level with a minimum of mathematical apparatus. Quantum mechanics appeared as a theory of microscopic bodies when it had been proved that the motion of microscopic systems cannot be described in the framework of classical physics. However, quantum effects may be important even for macroscopic bodies. From a certain point of view the main object in quantum mechanics is probability amplitude because it expresses the principal difference between quantum and classical theory. Quantum mechanics differs in that not probabilities but probability amplitudes should be summed up for a quantum system. The uncertainty principle is good for expressing features of instantaneous quantum measurements but it is inconvenient for continuous measurements. The variance of outputs of a precise measurement may be considered to be quantum measurement noise.
List of participants Preface Part I. Introduction: 1. The function of the colloquium - editorial 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsacker 4. On Bohr's views concerning the quantum theory D. Bohm Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman 9. Measurement theory and complex systems M. A. Garstens Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose 15. A note on discreteness, phase space and cohomology theory B. J. Hiley 16. Cohomology of observations R. H. Atkin 17. The origin of half-integral spin in a discrete physical space Ted Bastin Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsacker 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post 21. How does a particle get from A to B? Ted Bastin 22. Informational generalization of entropy in physics Jerome Rothstein 23. Can life explain quantum mechanics? H. H. Pattee 24. Discussion: phenomena and sense data in quantum theory D. S. Linney and C. F. von Weizsacker Index of persons Index of subjects.