Excited K-quantum nonlinear coherent states

We define the excited K-quantum nonlinear coherent state and prove that it is indeed a K-quantum nonlinear coherent state characterized by another nonlinear function whose general expression is found in an explicit form. We also demonstrate that antibunching is more prominent in the excited K-quantum nonlinear coherent state than in the corresponding K-quantum nonlinear coherent state.

A large number of nonclassical states (see, e.g., [1-5]) have been recognized so far. They are, however, not all independent. For example, the so-called photon-added coherent state [6,7] has recently been shown [8] to belong to the nonlinear coherent state (NCS) [9, 10] and the excited NCS has been proved [11] to remain a NCS. The q -deformed oscillator [12, 13] was known just as a particular case of the more general f oscillator [10, 14] whose eigenstate is nothing other than the NCS. The NCS also embraces the negative binomial state [11, 15], etc.Re-classification of nonclassical states proves of great interest in understanding and distinguishing the physics underlying such states.

Recently the K-quantum nonlinear coherent state (KNCS) has been introduced, whose generation schemes as well as various nonclassical properties such as multi-peaked number distribution, self-splitting, antibunching and squeezing, have been studied in detail in [16-19]. The KNCS, |ξ , K, j, f 〉, is defined as the right eigenstate of the non-Hermitian operator aK f ( ˆn):

aK f ( ˆn)|ξ , K, j, f 〉 = ξK |ξ , K, j, f 〉, (1)

with a the boson annihilation operator, f a nonlinear operator-valued function of ˆn = a+a,

ξ the complex eigenvalue, K a positive integer and j = 0, 1, . . . , K − 1. This kind of state

includes the Peremolov K-photon coherent state [20, 21].

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