Quantum Concepts and Techniques in Classical Domains: Phonons and Plasmons

The turning point which sparked the initiation of quantum theory was the Planck-Einstein postulate that the energy of a monochromatic radiation field is quantized in terms of photons and this was followed by the development of the principles of quantum mechanics by eminent contributors. Quantum mechanics as a well-established discipline continues to be regarded as key for unraveling the mysteries of matter in general. Today the influence of quantum mechanics is evident in its applications, with remarkable technological advances involving diverse aspects of the physical world. What appears to need drawing particular attention to, however, (after hundred years have elapsed since the birth of quantum mechanics) is the impact the concept of the `quantum' has had beyond traditional quantum mechanics. We describe how the `quantum' concept has influenced, and continues to influence developments in physical systems which are essentially classical in that they are basically governed, wholly, or in part, by non-quantum laws but in which the physics is distinguished by its own special quantum - the photon analogue. We outline the systematic quantization of plasmons and phonons, both of the polariton (transverse) forms and their longitudinal forms and discuss how these interact with quantum systems such as electrons, atoms and condensed matter. We demonstrate using one case, namely involving longitudinal plasmons, how utilizing quantum concepts and techniques facilitate their interaction with matter, as in electron energy loss spectroscopy (EELS).