Quantum Measurement of Gravity for Geodesists and Geophysicists

Description

During the last thirty years a great advancement in low energy physics, particularly interactions of atoms with the electromagnetic field, has been achieved and the development of electronics and laser techniques has allowed to implement a fine manipulation of atoms with photons. A wealth of important applications has sprung out from the ability of manipulating large samples of cold atoms. Among them, the improvement of atomic clocks and the creation of atomic gyroscopes and of atomic gravity meters, which is obviously of great interest for geodesists and geophysicists, particularly for potential applications in satellite geodesy. This book explains the fundamental concepts necessary to understand atom manipulation by photons, including the principles of quantum mechanics. It is conceived as a road that leads the reader from classical physics (mechanics and electromagnetism, considered as a common scientific background of geodesists and geophysicists), to the basics of quantum mechanics in order to understand the dynamics of atoms falling in the gravity field, while interacting with suitably resonant laser beams. There are different types of measurements of gravity based on the manipulation of ultra-cold atoms; the book presents the principles of the instruments based on stimulated Raman transition, which can be easily worked out analytically. However, the concepts explained in the text can provide a good starting point to understand also the applications based on the so-called Block oscillations or on the Bose–Einstein condensation.  Preface Contents 1 Recalls of Classical Mechanics 1.1 Introduction 1.2 From Newton to Lagrange 1.3 From Lagrange to Hamilton 1.4 Poisson Parentheses 1.5 Canonical Transformations. Conjugate Variables 1.6 Dynamic Systems with Generalized Potentials References 2 Recalls of the Classical Theory of the Electromagnetic Field 2.1 Introduction 2.2 Maxwell Equations and Lorentz Equation 2.3 Electromagnetic Waves in Empty Space 2.4 Wave Packets 2.5 Electromagnetic Potentials, Lorentz Gauge 2.6 Energy Conservation 2.7 Momentum Conservation References 3 The Crisis of Classical Physics and the Dawn of Quantum Physics 3.1 Introduction 3.2 The Untenable Planetary Model of the Atom 3.3 The Birth of Quanta 3.4 The Electromagnetic Radiation Behaves Like a Flow of Particles 3.5 The Quantized Atom of Niels Bohr 3.6 Overcoming the Dualism Waves–Particles. … 3.7 The Heisenberg Indetermination Principle References 4 The Principles of Quantum Mechanics 4.1 Introduction 4.2 A Theorem on Fourier Transform 4.3 Some Facts About Hermitian Operators in Hilbert Spaces 4.4 A More Precise Formulation of Seven Principles of Quantum Mechanics 4.5 The Time Evolution of a Quantum State: Schrödinger Equation 4.6 Stationary States; Constants of Motion References 5 First Applications of Quantum Theory 5.1 Introduction 5.2 The Free Particle 5.3 The Hydrogen Atom as an Example 5.4 The Quantum Theory of Angular Momentum 5.5 First-Order Spectral Analysis of Static Perturbations … 5.6 The Zeeman Effect, the Spin, and the Atomic Spectrum 5.7 Time-Dependent Perturbations of the Hamiltonian References 6 The Quantum Measurement of Gravity 6.1 Introduction 6.2 The Dipole Approximation of the Optical Radiation—Atom Interaction 6.3 Rabi Equation 6.4 Adding Momentum Exchange to the Atom–Photon Interaction 6.5 The Atom Interferometry and the Measurement of g- .4 6.6 Complements and Improvements 6.7 Results and Perspectives References