# An Introduction to Quantum Optics by Grynberg G., Aspect A., Fabre C.

By Grynberg G., Aspect A., Fabre C.

Protecting a few vital matters in quantum optics, this textbook is a superb advent for complicated undergraduate and starting graduate scholars, familiarizing readers with the fundamental techniques and formalism in addition to the newest advances. the 1st a part of the textbook covers the semi-classical technique the place topic is quantized, yet gentle isn't. It describes major phenomena in quantum optics, together with the foundations of lasers. the second one half is dedicated to the entire quantum description of sunshine and its interplay with topic, masking issues corresponding to spontaneous emission, and classical and non-classical states of sunshine. an summary of photon entanglement and purposes to quantum info is usually given. within the 3rd half, non-linear optics and laser cooling of atoms are awarded, the place utilizing either methods enables a entire description. every one bankruptcy describes simple techniques intimately, and extra particular options and phenomena are provided in 'complements'.

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8 (a): (1, n) series EI 2 1, k E1, ∞ = −EI 1234 E 2, 2 = − 1234 (b): (2, n′) series Energy levels of the helium atom at the approximation of independent electrons. (a) Levels corresponding to one electron in ground state n = 1 and the other in any bound or ionized state; (b) levels corresponding to one electron in the first excited state n = 2 and the other in any bound or ionized state. a continuum of states (1, k) above −EI describing the ion He+ in its ground state plus a free electron. 8b), one observes that the state (2, 2) has an energy which is greater than −EI , and lies therefore within the continuum of states (1, k), which means that there is an ionized state (1, k0 ) having the same energy as the bound state (2, 2).

These will be of use to us later to provide a physical illustration of the results obtained. Interaction of an atom with a classical electromagnetic field ˆ 0 and which interacts with an Consider an atom4 described by the atomic Hamiltonian H incident classical electromagnetic wave of which the electric field at the position of the (stationary) atom is 3 See, for example, CDL, Chapter XIII. 4 More precisely, we consider for simplicity a one-electron atom such as hydrogen. t 6 The evolution of interacting quantum systems E(t) = E cos(ωt + ϕ).

39): Pi→k (T) = T 2π 2 w δT (kε). 75) We consider the case in which the separation of consecutive continuum levels ε is small compared to the width 2πh/T ¯ of δT . 74) can be replaced by an integral. 76) since the total area of the function δT is unity. We obtain then, in the framework of the current model, an evolution of the probability of occupation of the initial level that is linear in T. 64)). 77) 2π 2 1 w . 78) with = The term , which has the dimensions of reciprocal time, is also known as the transition probability per unit time, or transition rate, to the quasi-continuum.