Nanoscience, nanotechnologies and the laws of quantum physics aresources of disruptive innovation that open up new fields of application.Quantum engineering enables the development of very sensitivematerials, sensor measurement systems and computers. Quantumcomputing, which is based on two-level systems, makes it possible tomanufacture computers with high computational power.This book provides essential knowledge and culminates with an industrialapplication of quantum engineering and nanotechnologies. It presentsoptical systems for measuring at the nanoscale, as well as quantumphysics models that describe how a two-state system interacts with itsenvironment. The concept of spin and its derivation from the Diracequation is also explored, while theoretical foundations and exampleapplications aid in understanding how a quantum gate works. Applicationof the reliability-based design optimization (RBDO) method of mechanicalstructures is implemented, in order to ensure reliability of estimates fromthe measurement of mechanical properties of carbon nanotubestructures.This book provides valuable support for teachers and researchers but isalso intended for engineering students, working engineers and Master sstudents.

Preface ixIntroduction xiiiChapter 1. Measurement Systems Using Polarized Light 11.1. Introduction 11.2. Matrix optics 21.3. Photon emission and detection 121.4. Application exercises on interferometry 161.4.1. Propagation of electromagnetic waves in a Fabry-Pérot cavity 181.4.2. Propagation of electromagnetic waves in a material 191.4.3. Interferometry and optical lambda meter 211.4.4. The homodyne interferometer and refractometer 341.4.5. The heterodyne interferometer 401.4.6. Application exercises on ellipsometry 511.5. Appendices 561.5.1. Conventions used for Jones vectors and Jones ABCD matrices 561.5.2. 2×2 transfer dies 591.5.3. 2×2 matrix multiplication 591.5.4. Trigonometric forms 601.5.5. Solution by MATLAB (exercises 1.4.3, 1.4.4 and 1.4.5) 611.6. Conclusion 66Chapter 2. Quantum-scale Interaction 672.1. Introduction 672.2. The spin through the Dirac equation 692.2.1. Theoretical background 692.2.2. Application: the Dirac equation and Pauli matrices 742.3. The density matrix for a two-level laser system 1052.3.1. Definition of the density matrix 1062.3.2. Density matrix properties 1102.3.3. Equation of motion of the density matrix 1132.3.4. Application to a two-level system 1162.4. Ising's phenomenological model for cooperative effects 1232.4.1. The Ising 1D model 124Chapter 3. Quantum Optics and Quantum Computers 1353.1. Introduction 1353.2. Polarized light in quantum mechanics 1363.3. Introduction to quantum computers 1403.4. Preparing a qubit 1583.4.1. Application of the Bloch sphere 1583.5. Application: interaction of a qubit with a classical field 1723.5.1. Answer to question 1 1733.5.2. Answer to question 2 1763.6. Applying Ramsey fringes to evaluate the duration of phase coherence 1813.6.1. Answer to question 1 1813.6.2. Answer to question 2 183Chapter 4. Reliability-based Design Optimization of Structures 1854.1. Introduction 1854.2. Deterministic optimization 1864.3. Reliability analysis 1874.3.1. Optimal conditions 1894.4. Reliability-based design optimization 1914.4.1. The objective function 1924.4.2. Taking into account the total cost 1924.4.3. Design variables 1934.4.4. Response of a system by RBDO 1934.4.5. Limit states 1944.4.6. Solving methods 1944.5. Applications 1944.5.1. Application on a bending beam 1944.5.2. Application on a circular plate with different thicknesses 1964.5.3. Application: hook A 2014.5.4. Application: optimization of the materials of an electronic board 2114.6. Reliability-based design optimization in nanotechnology 2224.6.1. Thin-film SWCNT structures 2224.6.2. Digital model of thin-film SWCNT structures 2244.6.3. Numerical results 2254.7. Conclusion 231Appendix 233References 237Index 245