F. J. Duarte, Quantum Optics for Engineers: Quantum Entanglement, 2nd Edn (CRC Press, 2024)

ISBN: 978-1032499345

Quantum Optics for Engineers: Quantum Entanglement includes: 23 chapters, 11 appendices, 195 figures, more 1400 equations, many worked out examples, more than 150 problems, a large number of archival references, and a comprehensive index, in 403 pages.

1. Introduction

1.1 Introduction

1.2 Brief Historical Perspective

1.3 The Principles of Quantum Mechanics

1.4 The Feynman Lectures on Physics

1.5 The Photon

1.6 Quantum Optics

1.7 Quantum Optics for Engineers

1.7.1 Quantum Optics for Engineers 2nd Edition



2. Planck’s Quantum Energy Equation

2.1 Introduction

2.2 Planck’s Equation and Wave Optics

2.3 Planck’s Constant h

2.3.1 Back to E=hv



3. The Uncertainty Principle

3.1 Heisenberg’s Uncertainty Principle

3.2 The Wave-Particle Duality

3.3 The Feynman Approximation

3.3.1 Example

3.4 The Interferometric Approximation

3.5 The Minimum Uncertainty Principle

3.6 The Generalized Uncertainty Principle

3.7 Additional Versions of Heisenberg’s Uncertainty Principle

3.7.1 Example

3.8 Applications of the Uncertainty Principle in Optics

3.8.1 Beam Divergence

3.8.2 Beam Divergence in Astronomy

3.8.3 The Uncertainty principle and the Cavity Linewidth Equation

3.8.4 Tuning Laser Microcavities

3.8.5 Nanocavities



4. The Dirac-Feynman Quantum Interferometric Principle

4.1 Dirac’s Notation in Optics

4.2 Interferometric Quantum Principles

4.3 Interference and The Interferometric Equation

4.3.1 Examples: Double, Triple, and Quadruple-Slit Interference

4.3.2 Geometry of the N-slit Interferometer

4.3.3 The Diffraction Grating Equation

4.3.4 N-slit Interferometer Experiment

4.4 Coherent and Semi-Coherent Interferograms

4.5 The Interferometric Equation in Two and Three Dimensions

4.6 Classical and Quantum Alternatives



5. Interference, Diffraction, Refraction, and Reflection Via Dirac’s Notation

5.1 Introduction

5.2 Interference and Diffraction

5.2.1 Generalized Diffraction

5.2.2 Positive Diffraction

5.3 Positive and Negative Refraction

5.3.1 Focusing

5.4 Reflection

5.5 Succinct Description of Optics

5.6 Quantum Interference and Classical Interference



6. Dirac’s Notation Identities

6.1 Useful Identities

6.1.1 Example

6.2 Linear Operations

6.2.1 Example

6.3 Extension to Indistinguishable Quanta Ensembles



7. Interferometry Via Dirac’s Notation

7.1 Interference a la Dirac

7.2 The Hanbury Brown-Twiss Interferometer

7.3 The N-slit Interferometer

7.4 Reflective Interferometers

7.4.1 The Michelson Interferometer

7.4.2 The Sagnac Interferometer

7.4.3 The Mach-Zehnder Interferometer

7.4.4 The HOM Interferometer

7.5 Multiple Beam Interferometers

7.6 The Ramsey Interferometer



8. Quantum Interferometric Communications in Free Space

8.1 Introduction

8.2 Theory

8.3 N-Slit Interferometer for Secure Free-Space Optical Communications

8.4 Interferometric Characters

8.5 Propagation in Terrestrial Free Space

8.5.1 Clear Air Turbulence

8.6 Further Applications

8.7 Discussion



9. Schrödinger’s Equation

9.1 Introduction

9.2 A heuristic Explicit Approach to Schrödinger’s Equation

9.3 Schrödinger’s Equation Via Dirac’s Notation

9.4 The Time Independent Schrödinger Equation

9.4.1 Quantized Energy Levels

9.4.2 Semiconductor Emission

9.4.3 Quantum Wells

9.4.4 Quantum Cascade Lasers

9.4.5 Quantum Dots

9.5 Nonlinear Schrödinger Equation



10. Introduction to Feynman Path Integrals

10.1 Introduction

10.2 The Classical Action

10.3 The Quantum Link

10.4 Propagation Though a Slit and the Uncertainty Principle

10.4.1 Discussion

10.5 Feynman Diagrams in Optics



11. Matrix Notation in Quantum Mechanics and Quantum Operators

11.1 Introduction

11.2 Introduction to Vector and Matrix Algebra

11.2.1 Vector Algebra

11.2.2 Matrix Algebra

11.2.3 Unitary Matrices

11.3 Pauli Matrices

11.3.1 Pauli Matrices for Spin One-Half Particles

11.3.2 The Tensor Product

11.4 Introduction to the Density Matrix

11.5 Quantum Operators

11.5.1 The Position Operator

11.5.2 The Momentum Operator

11.3.3 Example

11.5.4 The Energy Operator

11.5.5 The Heisenberg Equation of Motion



12. Classical Polarization

12.1 Introduction

12.2 Maxwell Equations

12.2.1 Symmetry in Maxwell Equations

12.3 Polarization and Reflection

12.3.1 Plane of Incidence

12.4 Jones Calculus

12.4.1 Example

12.5 Polarizing Prisms

12.5.1 Transmission Efficiency in Multiple-Prism Arrays

12.5.2 Induced Polarization in a Double-Prism Expander

12.5.3 Double-Refraction Polarizers

12.5.4 Attenuation of the Intensity of Laser Beams Using Polarization

12.6 Polarization Rotators

12.6.1 Birefringent Polarization Rotators

12.6.2 Broadband Prismatic Polarization Rotators

12.6.3 Example



13. Quantum Polarization

13.1 Introduction

13.2 Linear Polarization

13.2.1 Example

13.3 Polarization as a Two State System

13.3.1 Diagonal Polarization

13.3.2 Circular Polarization

13.4 Density Matrix Notation

13.4.1 Stokes Parameters and Pauli Matrices

13.4.2 The Density Matrix and Circular Polarization

13.4.3 Example



14. Bell’s Theorem

14.1 Introduction

14.2 Bell’s theorem

14.3 Quantum Entanglement Probabilities

14.4 Example

14.5 Discussion



15. Quantum Entanglement Probability Amplitudes for n = N = 2

15.1 Introduction

15.2 The Dirac-Feynman Probability Amplitude

15.3 The Quantum Entanglement Probability Amplitude

15.4 Identical states of polarization

15.5 Entanglement of Indistinguishable Ensembles

15.6 Discussion



16. Quantum Entanglement Probability Amplitudes for n = N = 21, 22, 23, …2r

16.1 Introduction

16.2 Quantum Entanglement Probability Amplitude for n = N= 4

16.3 Quantum Entanglement Probability Amplitude for n = N= 8

16.4 Quantum Entanglement Probability Amplitude for n = N= 16

16.5 Quantum Entanglement Probability Amplitude for n = N = 21, 22, 23, …2r

16.5.1 Example

16.6 Summary



17. Quantum Entanglement Probability Amplitudes for n = N= 3, 6

17.1 Introduction

17.2 The quantum entanglement probability amplitude for n = N= 3

17.3 The quantum entanglement probability amplitude for n = N= 6

17.4 Discussion



18. Quantum Entanglement in Matrix Notation

18.1 Introduction

18.2 Quantum Entanglement Probability Amplitudes

18.3 Quantum Entanglement Via Pauli Matrices

18.3.1 Example

18.3.2 Pauli Matrices Identities

18.4 Quantum Entanglement Via the Hadamard gate

18.5 Quantum Entanglement Probability Amplitude Matrices

18.6 Quantum Entanglement Polarization Rotator Mathematics

18.7 Quantum Mathematics Via Hadamard’s Gate

18.8 Reversibility in Quantum Mechanics



19. Quantum Computing in Matrix Notation

19.1 Introduction

19.2 Interferometric Computer

19.3 Classical Logic Gates

19.4 von Neumann Entropy

19.5 Qbits

19.6 Quantum Entanglement Via Pauli Matrices

19.7 Rotation of Quantum Entanglement States

19.8 Quantum Gates

19.8.1 Pauli Gates

19.8.2 The Hadamard Gate

19.8.3 The CNOT Gate

19.9 Quantum Entanglement Via the Hadamard Gate

19.9.1 Example

19.10 Multiple Entangled States

19.11 Discussion



20. Quantum Cryptography and Quantum Teleportation

20.1 Introduction

20.2 Quantum Cryptography

20.2.1 Bennett and Brassard Cryptography

20.2.2 Quantum Entanglement Cryptography using Bell’s Theorem

20.2.3 All-Quantum Quantum Entanglement Cryptography

20.3 Quantum Teleportation



21. Quantum Measurements

21.1 Introduction

21.1.1 The Two Realms of Quantum Mechanics

21.2 The Interferometric Irreversible Measurement

21.2.1 Additional Irreversible Quantum Measurements

21.3 Quantum Non Demolition Measurements

21.3.1 Soft Probing of Quantum States

21.4 Soft Intersection of Interferometric Characters

21.4.1 Comparison Between Measured and Theoretical N-slit Interferograms

21.4.2 Soft Interferometric Probing

21.4.3 The Mechanics of Soft Interferometric Probing

21.5 The Quantum Measurer

21.5.1 External Intrusions

21.6 Discussion



22. Quantum Principles and the Probability Amplitude

22.1 Introdution

22.2 Fundamental Principles

22.3 The Probability Amplitude

22.3.1 Probability amplitude Refinement

22.4 From Probability Amplitudes to Probabilities

22.4.1 Interferometric Cascade

22.5 Nonlocality of the Photon

22.6 Indistinguishability and Dirac’s identities

22.7 Quantum entanglement and the Foundations of Quantum Mechanics

22.8 The Dirac-Feynman Interferometric Principle



23. Interpretational Issues in Quantum Mechanics

23.1 Introduction

23.2 Einstein Podolsky and Rosen (EPR)

23.3 Heisenberg’s Uncertainty Principle and EPR

23.4 Quantum Physicists on the Interpretation of Quantum Mechanics

23.4.1 Pragmatic Practitioners

23.4.2 Bell’s Criticims

23.5 On Hidden Variable Theories

23.6 On the Absence of ‘The Measurement Problem’

23.6.1 On the Quantum Measurer

23.7 The Physical Bases of Quantum Entanglement

23.8 The Mechanisms of Quantum Mechanics

23.8.1 The Quantum Interference Mechanics

23.8.2 The Quantum Entanglement Mechanics

23.9 Philosophy

23.10 Discussion



Appendix A: Laser Excitation

Appendix B: Laser Resonators and Laser Cavities Via Dirac’s Notation

Appendix C: Generalized Multiple-Prism Dispersion Theory

Appendix D: Multiple-Prism Dispersion Power Series

Appendix E: N-Slit Interferometric Calculations

Appendix F: Ray Transfer Matrices

Appendix G: Complex Numbers and Quaternions

Appendix H: Trigonometric Identities

Appendix I: Calculus Basics

Appendix J: Poincare’s Space

Appendix K: Physical Constants and Optical Quantities


F. J. Duarte, Quantum Optics for Engineers (Taylor & Francis, New York, 2014)

ISBN: 978-1-43-988853-7 (Note: title released on November 26, 2013.)

Quantum Optics for Engineers includes: some 190 figures, numerous tables, some 1000 equations, many worked out examples, about 100 problems, a large number of archival references, in about 472 pages. A corrigenda is available in PDF form.

Quantum Optics for Engineers at Amazon

Quantum Optics for Engineers Barnes & Noble

Call number at Library of Congress: QC446.2 .D83 2014

Quantum Optics for Engineers: corrigendum


"Duarte's book is a welcome addition to the family of optics texts because he stresses fundamental connections between classical and quantum optics. His review of the bedrock theory and experiments of several of the founders of quantum physics provides an instructive transition to recent developments in quantum optics, such as photon entanglement. Perhaps the most appealing aspect of this book is the treatment of classical optical concepts and phenomena in terms of a quantum formalism...Both graduate students and the experienced researcher will find this treatment of quantum optics to be illuminating and valuable...I look forward to having a copy in my personal library."

Professor J. Gary Eden, Electrical and Computer Engineering, University of Illinois

"Quantum Optics for Engineers is an original and unique book that describes classical and quantum optical phenomena, and the synergy between these two subjects, from an interferometric perspective. Dirac’s notation is used ... [to] provide a lucid explanation of quantum polarization entanglement. The book will serve engineers with a minimum knowledge of quantum mechanics ... to understand modern experiments with lasers, optical communications, and the intriguing world of quantum entanglement."

Professor Ignacio E. Olivares, Universidad de Santiago de Chile

"Quantum Optics for Engineers provides a transparent and succinct description of the fundamentals of quantum optics using Dirac’s notation and ample illustrations. Particularly valuable is the explanation and elucidation of quantum entanglement from an interferometric perspective. The cohesiveness provided by the unified use of Dirac’s notation, emphasizing physics rather than mathematics, is particularly useful for those trained in engineering. This will be a valuable asset to any optical engineer’s library."

Anne M. Miller, RR Donnelley, USA

"This book is a concise and comprehensive presentation of numerous fundamental concepts related to the light nature and its interaction with matter. A very structured and logical route reveals step by step the rigorous theory of quantum optics. To some extent, the whole project can be fairly defined as unique. One of the heaviest tools in quantum optics, operator representation, is introduced in a very clear and straightforward way. Nature foundations and rather complicated mathematical tools are brought in a very elegant manner such that readers suddenly find themselves as experts in areas they would consider untouchable magic. The intriguing world of quantum entanglement is revealed via many practical examples."

Professor Sergei Popov, Royal Institute of Technology, Sweden


Partial Author Index

Aguirre Gomez J. G., Aldag H. R., Allaria E., Anisimova E., Aspect A., Badurek G., Baer T., Baltakov F. N., Barbieri C., Barnes N. P., Bass I. L., Baving H. J., Beck R., Bell J. S., Bennett C. H., Bennett J. M., Bennett H. E., Benson S. V., Berger J. D., Berglund A. J., Bernhardt A. F., Bessette F., Black A. M., Blauensteiner B., Bleuler E., Bohm D., Bohr N., Born M., Bradt H. L., Brassard G., Braverman B., Bobrovskii A. N., Brito Cruz C. H., Brouwer W., Brune M., Butcher P. N., Byer R. L., Capasso F., Caro R. G., Chen H., Chen L., Cho A. Y., Chutjian A., Cirac J. I., Clauser J. F., Conrad R. W., Corzine S. W., Corson D., Costela A., Cotter D., Crépeau C., Csatári M., Cuadra J. A., Dalitz R. H., de Broglie L., DeLabachelerie M., Delfyett P. J., De Martini F., Demmler S., Demtröder W., Deutsch D., Diels J-C., Dienes A., Dietel W., Dinklage A., Dirac P. A. M., Duarte F. J., Dyson F. J., Ehrlich J. J., Einstein A., Ekert A. K., Erhart J., Everett P. N., Faist J., Falkenstein W., Fan Y. X., Favre F., Ferincz I. E., Feynman R. P., Flamant P. , Flanders H., Fleeming M. W., Fontaine J. J., Fork R. L., Fort J., Friberg A., Fujimoto J. G., Fürst M., Ganiel U., Garcia-Moreno I., Gavrilovic P., Gill P., Glashow S. L., Gobby C., Gordon J. P., Grangier P., Grebing C., Haag G., Hackel R. H., Hagemann C., Haken H., Hammond P., Hanbury Brown R., Hanna R. C., Hänsch T. W., Hardy A., Hargrove R. S., Haroche S., Harrison J., Harvey K. C., Hasegawa Y., Haub J. G., He Y., Heiner Z., Heisenberg W., Herbst R. L., Herbst T., Hertz H., Herzberg G., Hibbs A. R., Hillman L. W., Hogan F., Hollberg L., Holt R. A., Honna K., Hooker S., Hornbostel J., Horne M. A., Hugi A., Hullman J. D., Hutchinson, A. L., Itano W. M., James T. C., James R. O., Jenkins F. A., Jennewein T., Jensen C., Jones R. C., Johnson M. J., Johnston T. F., Jeong Y., Jordan P., Jordan T. F., Jozsa R., Judd B. R., Kafka J. D., Kaiser D., Kan T. K., Kasday L. R., Kaslin V. M., Kessler T., Kildal H., Kim Y-H., King B. E., Kintzer E. S., Klebniczki J., Kleinpoppen H., Kner P., Kocsis S., Koer J., Kogelnik H., Korfhage R. R., Kovács A. P., Kropatschek S., Kubota H., Kulik S. P., Kurdi G., Kwiat P. G., Lamb W. E., Landau L. D., Laudenslager J. B., Legero T., Leighton R. B., Levenson M. D., Liao L. S., Lifshitz E. M., Lindenthal M., Lokajczyk T., Loree T. R., Lorrain P., Ma X., Mandel L., Maiman T. H., Makarov V., Marowski G., Martin M. J., Martinez O. M., Maulini R., McDermid I. S., McKee T. J., Meaburn J., Mech A., Meekhof D. M., Mermin N. D., Meyenburg M., Michelson A. A., Miller A. M., Mirin R. P., Monroe C., Mooradian A., Morita T., Moulin C., Moulton P. F., Moyal J. E., Munz M., Nagaola S., Naik D. S., Nair L. G., Naylor, W., Neumann G., Newton I., Olivares I. E., Ömer B., Orr B. J., Osvay K., Ozawa M., Pacala T. J., Paine D. J., Pang L. Y., Patterson S. P., Pasternack S., Pelliccia D., Penzkofer A., Perdigues J., Peres A., Peterson C. G., Peterson O. G., Petrash G. G., Piper J. A. , Planck M., Podolsky B., Poicaré H., Popov S., Price J. J., Pryce M. H. L., Raimond J-M., Ramsey N. F., Rarity J., Rasmussen P., Ravets S., Riehle F., Robertson H. P., Robertson J. K., Robson B. A., Roger G., Rosen N., Rudolph W., Russell S. D., Salam A., Saleh B. E. A., Salvail L., Salvatore R. A., Sands M., Sargent M., Sastre R., Schäfer F. P., Scheidl T., Schettini V., Schiff L. I., Schimitschek E. J., Schmidt W., Schmitt-Manderbach T., Schröder T., Schrödinger E., Schumacher B., Schwinger J., Sciarrino F., Scully M. O., Selleri F., Shaknov I., Shalm L. K., Shan X., Shand M. L., Shank C. V., Shay T. M., Shields A. J., Shimony A., Sias C., Siegman A. E., Silfvast W. T., Singer P., Sirtori C., Sivco D. L., Smilanski I., Smolin J., Snyder, H. S., Sodnik Z., Sponar S., Srinivasan B., Steel W. H., Sterr U., Stevens M. J., Strome F. C., Sugii M., Suluok G., Sze R. C., Tang K. Y., Taylor T. S., Tavella F., Teich M. C., Tenenbaum J., Teschke O., Tiefenbacher F., Tomonaga S., Treves D., Trojek P., Tuccio S. A., Twiss R. Q., Uenishi Y., Ursin R., Vaeth K. M., van Kampen N. G, Varmette P. G., Volze J., von Neumann J. , Voumard C.,Wallace R. P., Wallenstein R., Walling, J. C., Wang D., Ward J. C., Webb C. E., Weier H., Weinberg S., Weinfurter H., Wellegehausen B., Wheeler J. A., Whinnery J. R., White A. G., White H. E., White R. T., Wilhelmi B., Willett C. S., Wineland D. J., Wittmann B., Wolf E., Wollnik H., Wootters W. K., Woodward B. W., Wu C. S., Wyatt R., Yakushev O. F., Yang T. T., Yanhua Shih Y, Yankelevich D. R., Yariv A., Ye J., Yeh C-H., Yuan Z. L., Zeilinger A., Zhang D., Zoller P., Zorabedian P.


Page published on the 12th of April, 2013. Updated on the 1st of March, 2024