Preface

      At the nanoscale, properties of matter cannot be explained by the laws of classical physics. To build models capable of interpreting the properties of matter on this scale, it is necessary to rely on the principles of quantum mechanics. The radical concepts of quantum mechanics and the development of nanotechnologies have contributed to the emergence of quantum engineering and a quantum information science.

      Quantum engineering includes very sensitive materials and sensors that open up new fields of application, nanometer-sensitive measurement systems based on photonics and communication systems that perform well in terms of security. Quantum computing includes quantum computers and the development of new algorithms. Quantum computers are made up of quantum systems with two energy levels that follow the same laws of behavior as atoms or electrons enabling, with the development of quantum computing algorithms, performance that cannot be achieved with classical computers. Quantum technologies, nanotechnologies and nanoscience are identified as the sources of disruptive innovations that will bring technologies considered essential in the 21st Century.

The purpose of Applications and Metrology at Nanometer Scale, a book in two volumes, is to provide essential knowledge that will lead to the industrial applications of quantum engineering and nanotechnologies. The authors, through their skills and experience, combine their know-how in fundamental physics, engineering sciences and industrial activities. As with Volume 1, Applications and Metrology at Nanometer Scale 2 is designed to provide applications for Nanometer-scale Defect Detection Using Polarized Light (Reliability of Multiphysical Systems Set Volume 2). It describes experimental and theoretical methods implemented in the framework of fundamental research to better understand physical–chemical processes at the nanoscale, presents examples of optical techniques based on the polarized light, allowing measurements to be made at the nanoscale, and illustrates the theoretical approaches with numerous applications.

      This book is intended for master’s and PhD students, engineering students, professors and researchers in materials science and experimental studies, as well as for industrialists of large groups and SMEs in the electronics, IT, mechatronics, or optical or electronic materials fields.

      Chapter 1 deals with optical systems that enable measurements to be made on a nanoscale: the Fabry–Pérot cavity, homodyne interferometry, heterodyne interferometry, the optical lambda meter and ellipsometry with a rotating analyzer. The emphasis is on applications through exercises or analysis of study results on the use of interference techniques to study matter and materials.

      Chapter 2 presents models of quantum physics that describe how a quantum two-energy level system interacts with its environment. As a free particle such as the electron that interacts with an external magnetic field with its spin, the derivation of the concept of spin from the Dirac equation is explained, which is the subject of an application exercise. The concept of density matrix (definition, propagation, equation of motion) is then presented and applied to a laser system with two energy levels and to a set of atoms interacting with the oscillating electric field of an electromagnetic wave. Finally, the Ising phenomenological model is presented, which is the subject of an application exercise.

Chapter 3 aims to provide theoretical foundations and examples of applications to understand the functioning of a quantum gate. A reminder is given on the modeling of light in quantum mechanics and on the representation by the Bloch sphere of the states of a two-level quantum system. The functioning of a quantum computer is introduced. Examples of applications show how to use the Bloch sphere, predict the evolution of an initial state of the system and obtain, by coupling, the oscillations of the Rabi population. Another application studies the coupling of an atom with light radiation and the effect on Rabi oscillations of a disagreement between the frequency of the atom and the frequency of the radiation. A final exercise deals with obtaining Ramsey fringes and their application to the functioning of a quantum gate.

      Chapter 4 presents a reliability-based design optimization (RBDO) method of mechanical structures. This method guarantees a balance between the cost of defining the system and the assurance of its performance under the planned conditions of use. It is based on taking into account uncertainties and on the simultaneous resolution of two issues: optimizing the cost of producing structures performing the expected functions while ensuring a sufficient probability of operation under conditions of use (reliability). The RBDO method is applied to the optimization of the parameters of several mechanical components and of a printed circuit of an electronic board, and to ensure the reliability of the estimate of the measurement of the mechanical properties of carbon nanotube structures (Young’s modulus of elasticity).

      Pierre Richard DAHOO

      Philippe POUGNET

      Abdelkhalak EL HAMI

      November 2020