The Mth Coherent State

Abstract

In this article, we propose a new kind of quantum states based on acting the number operator M times $$ {\hat{n}}^M $$ on the coherent state. We term this state the Mth coherent state, based on the value of the power M. We find that it is strongly similar to the coherent state as the analysis of the photonic statistical distributions and the overlap with the coherent state illustrate. Also, we find that it asymptotically reaches the minimum uncertainty and has a localized behavior in the Husimi function. However, in contrast to coherent state, the Mth coherent state has strong nonclassical features such as antibunching and squeezing for a relatively long range. Other parameters and measurements are discussed and studied. Finally, we highlight the similarity between the higher orders of the near coherent states and the Mth coherent states in order to potentially generate our proposed state.