Generation of photon-added coherent states via photon-subtracted generalised coherent states

Abstract

Based on previous work [A. Dehghani, B. Mojaveri, J. Phys. A 45, 095304 (2012)], we introduce photon-subtracted generalised coherent states (PSGCSs) |z,m⟩ r : = a m |z⟩ r , where m is a nonnegative integer and |z⟩ r denote the generalised coherent states (GCSs). We have shown that the states |z,m⟩ r are eigenstates of a non-Hermitian operator f(n ,m)â, where f(n ,m) is a nonlinear function of the number operator N . Also, the states | z, − m ⟩ r can be considered as another set of eigenstates for negative values of m. They span the truncated Fock space without the first m lowest-lying basis states: | 0 ⟩ , | 1 ⟩ , | 2 ⟩ ,...,| m − 1 ⟩ which are reminiscent of the so-called photon-added coherent states. The resolution of the identity property, which is the most important property of coherent states, is realised for |z,m⟩ r as well as for |z, − m⟩ r . Some nonclassical features such as sub-Poissonian statistics and quadrature squeezing of the states |z, ± m⟩ r are compared. We show that the annihilation operator diminishes the mean number of photons of the initial state |z⟩ r . Finally we show that |z,m⟩ r can be produced through a simple theoretical scheme.