This chapter begins with a review of the semi-classical model of the interaction of charged particles with light, and then proceeds to the full quantum theory by replacing the classical fields with the corresponding field operators. A presentation of the quantum Maxwell equations and their behavior under parity and time reversal transformations is followed by a discussion of stationary density operators. The notion of positive- and negative-frequency parts of field operators is extended to interacting fields and used to define multi-time correlation functions that describe experimental results. The perturbation expansion is formulated by means of the interaction picture and combined with the dipole approximation to calculate the Einstein A- and B-coefficients. The chapter ends with a discussion of spontaneous emission in a cavity and Raman scattering.
This chapter begins with a review of the semi-classical model of the interaction of charged particles with light, and then proceeds to the full quantum theory by replacing the classical fields with the corresponding field operators. A presentation of the quantum Maxwell equations and their behavior under parity and time reversal transformations is followed by a discussion of stationary density operators. The notion of positive- and negative-frequency parts of field operators is extended to interacting fields and used to define multi-time correlation functions that describe experimental results. The perturbation expansion is formulated by means of the interaction picture and combined with the dipole approximation to calculate the Einstein A- and B-coefficients. The chapter ends with a discussion of spontaneous emission in a cavity and Raman scattering.
The classical or semiclassical theory presented in Chapter 2 gives a satisfactory account of light-matter interactions in some cases. However, a detailed understanding of different processes requires a quantum mechanical theory of radiation. The quantum theory of light, like classical theory, is also based on Maxwell's equations. However, in quantum theory the electric field F and the magnetic field H are treated as operators. This chapter develops the correspondence between the two and outlines the method for converting field vectors F and H into quantum mechanical operators. Topics discussed include wave equation in a rectangular cavity, quantization of the electric field, time-dependent perturbation theory, interaction of an electron with the magnetic field, and second-order perturbation theory. Exercises are provided at the end of the chapter.
Thus far, we have developed the properties of the electromagnetic field at optical frequencies, based on Maxwell’s equations. These equations further give a classical macroscopic perspective on the coupling of the propagation media to the field, as presented in Chapter 2. The macroscopic properties of a medium are based on averaged microscopic properties. The microscopic energy structure of matter was presented in Chapter 3, covering gases, solids, and liquids by employing mostly quantum models. We now proceed to the next level of development, the dynamic description of the interaction between the optical field and the propagation medium as a function of the field frequency and propagation media variables (e.g., energy structure, temperature, and pressure). In this chapter, the classical electromagnetic field is coupled to discrete frequency oscillators via Newton’s equation of motion. This approach leads to the popular classical oscillator model, often presented in introductory books on lasers. The classical oscillator model is an incomplete theory and can be only a semiempirical model. In the next chapter, a more detailed and comprehensive approach, which also includes statistical and quantum mechanics, is used leading to robust semiclassical and quantum oscillator models. This chapter and the next are the basis for the applied models presented in Part II of this book. Classical electrodynamics is based on Maxwell’s equations, as given in Chapter 2, and the Lorentz force relation, as given below: . . . F = q[E + (v × B)]. (4.1) . . . These equations cover the classical description of the interaction of light and matter. The first term in Eq. 4.1 represents coupling of the electric field to the medium. As discussed in Chapter 2 (Section 2.2), the leading mechanism for this is the electric dipole moment. To see that this is the coupling mechanism in the first term, consider the potential function driving this force, F = −∇V(r) = −∇(−qr · E). The above expression contains the dipole moment, as defined in Chapter 2. The second term in Eq. 4.1 represents coupling of the magnetic field to the medium.
How to deal with time-dependent potentials, what kinds of physical problems having time-dependent potentials can be solved exactly and which are to be solved with the use of perturbation theory, what are different possible forms of time-dependent perturbating fields, and semi-classical treatment of the interaction of fields with matter are the subject matters of this chapter. First order perturbation theory, computation of transition probability, transition rates and Fermi's Golden Rule for harmonic and constant perturbations, absorption, stimulated emission and dipole approximation when electromagnetic fields interact with matter, spontaneous emission and Einstein coefficients, and dipole selection rules are other topics which are dealt with in detail in the chapter. Discussions with properly justified mathematical treatment on time-dependent potentials and on the exactly solvable time-dependent two-state systems are the special foci of this chapter.
The perturbation expansion (Chapter 4) fails if the incident field — assumed to be resonant with an atomic transition — has a coherence time that is long compared to the spontaneous emission time. The dominance of resonance effects is used to replace the perturbation expansion by the resonant-wave approximation, which approximately describes the joint evolution of the field-atom system for long times. This approach is employed to describe quantum propagation of spontaneously emitted photons. When combined with the Markov approximation, it yields the Weisskopf-Wigner model for single-photon emission and two-photon cascade emission. The chapter ends with a discussion of the semi-classical limit, Rabi oscillations, the Bloch equation, and adiabatic elimination.
Abstract: An extensive review of the quantum theory of light-matter interaction is given in this chapter, beginning with its fundamental ideas and historical development. It covers the quantization of the electromagnetic field, atomic models, and important interaction Hamiltonians, including both semi-classical and completely quantum treatments. The role of vacuum fluctuations and fundamental processes like spontaneous and induced emission are examined. Quantum coherence, entanglement, decoherence, and its formal representation using master equations are also covered in this chapter. Modern applications such lasers, quantum sensors, and quantum communication systems are highlighted. The significance of light-matter interaction in furthering quantum science and technology is emphasized in the chapter's conclusion, which also discusses current research trends and future directions. Keywords: Laser, cryptography, Electromagnetic, Quantum, Atomic.
Abstract: An extensive review of the quantum theory of light-matter interaction is given in this chapter, beginning with its fundamental ideas and historical development. It covers the quantization of the electromagnetic field, atomic models, and important interaction Hamiltonians, including both semi-classical and completely quantum treatments. The role of vacuum fluctuations and fundamental processes like spontaneous and induced emission are examined. Quantum coherence, entanglement, decoherence, and its formal representation using master equations are also covered in this chapter. Modern applications such lasers, quantum sensors, and quantum communication systems are highlighted. The significance of light-matter interaction in furthering quantum science and technology is emphasized in the chapter's conclusion, which also discusses current research trends and future directions. Keywords: Laser, cryptography, Electromagnetic, Quantum, Atomic.