Photon-added coherent states and their quantum entanglement at a beam splitter

Abstract

Currently, the study of new quantum states and methods for their generation is an important part of the development of quantum technologies. One of the most important characteristics of such states is their quantum entanglement. Relatively recently, added coherent states were introduced, defined as $|\alpha ,n〉=N_n{\left({\hat{a}}^{†}\right)}^n|\alpha 〉$, where $N_n$ is a normalization constant, $|\alpha 〉$ is a coherent state, and ${\hat{a}}^{†}$ is a creation operator. In this paper, we consider the quantum entanglement of such states when they pass through a beam splitter, as well as the resulting new quantum states. It is shown that in special cases, this problem has an exact analytical solution. New quantum states have good prospects for their use in quantum technologies.