On the Cerenkov effect and non-classical states of electromagnetic vacuum: from classical pattern to quantum approach

In this paper, using the quantum approach, we consider the Cerenkov radiation in the case in which an electron moves in the background of the non-classical state of the electromagnetic field, such as the squeezed state. In the first part we briefly describe: the standard results by Frank and Tamm for the Cerenkov effect based on the principles of classical electrodynamics; Fermi's results based on the radiative attenuation of the charged particle; the results of quantum-mechanical calculations. The quantum approach gives an important conclusion on the essence of the Cerenkov effect: in contrast to the classical approach, where the Cerenkov effect explains as a result of interaction of the charged particle with a medium, in the quantum case this effect can be explained as the result of interaction of the charged particle with the electromagnetic vacuum changed by a medium. Within the quantum approach, we obtained also the explicit analytic expression for the Cerenkov radiation in the case when an electron moves in the background of the squeezed state of electromagnetic vacuum (only quantum approach can be applied in this case due to a non-classical essence of the squeezed electromagnetic vacuum). Also, we obtained the explicit analytic expression for the Cerenkov radiation in an external laser field. In this case, the Cerenkov radiation can be interpreted as a stimulated process in contrast to the "classical" case, where the Cerenkov radiation has a spontaneous essence.