In this chapter we introduce the Glauber coherent states of a quantized field as eigenstates of the annihilation operator and as displaced vacuum states. The phase-space picture of coherent states is introduced, along with phase-space probability distributions, namely the Q distribution, the P distribution, and the Wigner function, and their interrelations are discussed.

In this chapter we discuss the application of entanglement to quantum optical interferometry and to quantum information processing. Quantum random number generation is discussed. Quantum cryptography is discussed, as is quantum computing. The quantum optical realization of some quantum gates is discussed.

In this chapter we discuss experiments in cavity QED and ion traps. We first discuss the nature of Rydberg atoms which are used in cavity QED experiments. The experimental realization of the Jaynes––Cummings model is discussed, as are the generation of Schrödinger-cat states in dispersive atom––field interactions in cavity QED. The quantum non-demolition measurement is discussed. The realization of the Jaynes––Cummings model in the context of trapped ions is discussed.

In this chapter we first describe the experiments of Grangier et al., which gave clear evidence of anti-correlation effects and of the interference effects where only a single photon is involved. We then provide a fully quantum mechanical treatment of a lossless beam splitter. Interferometry with single photons is then treated fully quantum mechanically. Interaction-free measurement is then discussed, followed by interferometry with coherent states of light. Next, the SU(2) formulation of beam splitters and interferometers is discussed.

In this chapter, we overview recent developments of a simulation framework capable of capturing the highly nonequilibrium physics of the strongly coupled electron and phonon systems in quantum cascade lasers (QCLs). In midinfrared (mid-IR) devices, both electronic and optical phonon systems are largely semiclassical and described by coupled Boltzmann transport equations, which we solve using an efficient stochastic technique known as ensemble Monte Carlo. The optical phonon system is strongly coupled to acoustic phonons, the dominant carriers of heat, whose dynamics and thermal transport throughout the whole device are described via a global heat-diffusion solver. We discuss the roles of nonequilibrium optical phonons in QCLs at the level of a single stage , anisotropic thermal transport of acoustic phonons in QCLs, outline the algorithm for multiscale electrothermal simulation, and present data for a mid-IR QCL based on this framework.

After more than 25 years of continuous and increasing investment in research and development, the quantum cascade laser (QCL) is now revolutionizing a multitude of applications which aim to address major global challenges, from climate change to the cost of health care, to the pollution of our atmosphere and oceans, to the protection of our soldiers and first-responders. This chapter provides an insider’s perspective and historical context to the present and rapid trajectory in widespread QCL deployment across multiple applications and markets which has been building over the past two decades and will likely continue to benefit our quality of life and standard of living over the next hundred years.

Quantum cascade lasers (QCL) can be powerful testing grounds of the fundamental physical parameters determined by their quantum nature. In this chapter we describe a set of experimental techniques to explore the linewidth, frequency and phase stability of far-infrared QCLs. By performing noise measurements with unprecedented sensitivity levels, we highlight the key role of gain medium engineering and demonstrate that properly designed semiconductor-heterostructure lasers can unveil the mechanisms underlying the laser-intrinsic phase noise, revealing the link between device properties and the quantum-limited linewidth. We discuss phase-locking of THz QCL to a free-space comb generated in a LiNbO3 waveguide, and present phase and frequency control of miniaturized QCL frequency combs. This work paves the way to novel metrological-grade THz applications, including high-resolution spectroscopy, manipulation of cold molecules, astronomy and quantum technologies. The physical processes and dynamics presented here open groundbreaking perspectives for the development of quantum sensors, quantum imaging devices and q-bits made by entangled teeth for photonic-based quantum computation.

Quantum cascade lasers provide a variety of challenges to theory, which are outlined in this review: (i) The choice of basis states is discussed, where energy eigenstates are badly defined if the full periodic structure is considered. (ii) The tunneling through barriers requires a treatment of quantum coherences, which sets particular demands on the formulation of the quantum kinetic equations. Here the advantages and disadvantages of different approaches such as rate equations, Monte-Carlo simulations, different density matrix approaches, and Green’s functions methods are addressed. (iii) The evaluation of gain is detailed, where broadening is of utmost importance. (iv) An overview regarding the electrical instabilities of the extended structure due to domain formation is given, which strongly affect the overall performance