Higher-order properties of photon-added coherent states

We have studied a higher-order squeezing and a higher-order sub-Poissonian photon statistics in photon-added coherent states. We obtained analytic forms of the degree of higher-order squeezing and the degree of higher-order sub-Poissonian statistics. We show that the photon-added coherent state |α,m〉|α,m〉 exhibits both higher-order squeezing and higher-order sub-Poissonian character. For two different types of higher-order squeezing, the degree of squeezing becomes bigger when the added photon number is increased. In single-photon-added coherent state, the degree of squeezing depends upon the order of squeezing N. When N is increased, the degree of squeezing becomes bigger in the Hong–Mandel-type higher-order squeezing but becomes smaller in the Hillery-type higher-order squeezing. Also, the higher-order sub-Poissonian character is more pronounced than the usual sub-Poissonian character in the single-photon-added coherent state.