Nonlinear Coherent States and Some of Their Properties

Abstract

We construct nonlinear coherent states by the application of a deformed displacement operator acting upon the vacuum state and as approximate eigenstates of a deformed annihilation operator. These states are used to evaluate the temporal evolution of the average value of the momentum and the diplacement coordinate as well as their dispersions. We also construct even and odd combinations of these nonlinear coherent states and compute their second order correlation function in order to analyze their statistical behavior.

Photon-added nonlinear coherent states for a one-mode field in a Kerr medium

“…These two options correspond to the generalization of Glauber's first two definitions for the construction of a field coherent state. Recall that the different generalizations applied to systems with dynamical properties different from those of the harmonic oscillator yield to non-equivalent states [19][20][21][22]. Sivakumar has shown that the PACS may be regarded as NLCS for a particular deformation function [23] and in a recent publication the deformed photon added nonlinear coherent states (DPANCSs) |α (m) , f were introduced [24].…”

Approximate Coherent States for Nonlinear Systems

“…For the numerical results we have considered only the states obtained by application of a deformed displacement operator on the vacuum state, in Ref. [ 33] we discussed the nonlinear coherent states obtained as eigenstates of a deformed annihilation operator for the Morse potential. Although from an algebraic-structure point of view the coherent states obtained from each generalization (DOCS) or (AOCS) are different, as well as their respective statistical behavior [ 34], the average values and the phase space trajectories obtained with them are almost identical [ 10].…”

Bipartite Entanglement of Deformed Coherent States

“…that is our DCS are naturally normalized without any need to an additional normalization constant. This is a specific feature compared to many other constructions of DCS [41,46,31,43]. Also, Eq.…”