Entangled nonlinear coherent states of trapped ion motion and their non-classical properties

Several superpositions of two-mode nonlinear coherent states of trapped ion are constructed and their non-classical properties including sub-Poissonian distribution of photon numbers, photon antibunching effect and squeezing are studied. We use Mandel parameter and cross-correlation function to study sub-Poissonian distribution and photon antibunching effect, respectively. Then, using concurrence, we study the entanglement properties of these states. We have obtained three superposed states which are maximally entangled and also show antibunching effect for all the ranges of the parameters involved. We have also found that superposed states may be squeezed or not and may display sub-Poissonian statistics contingent on the pertinent parameters.