Statistical properties and the superposition of coherent and vacuum state

Abstract

The study of quantum light states has been a fundamental area of research, with squeezed states—specifically squeezed coherent and squeezed vacuum states, being of particular interest. This paper delves into the statistical characteristics and squeezing properties of these states, with a focus on their superposition. It is determined that the mean photon number of the combined state corresponds to the total mean photon numbers of the individual squeezed states. Additionally, when a coherent state and a squeezed vacuum state are superimposed, the resulting state behaves as a displaced squeezed vacuum state. A significant outcome is that the degree of squeezing effectively doubles due to superposition. Unlike single squeezed states, squeezing is observed for \(0< r<\frac{1}{2}\ln 2\ln\).