The concept of photon added two-mode Schr\"odinger cat states in which both
modes are independent is introduced, their non-classical properties and
entanglement are studied. The introduced states emerge as the eigenstates of
f1βf2βa1βa2β, where f1β,f2β are nonlinear functions of the number operator
and a1β,a2β are annihilation operators. We study the evolution of these
states under the canonical transformation using the parity operator for the
case of standard coherent states of the harmonic oscillator. The non-classical
properties of these states are evaluated especially by considering
sub-Poissonian photon statistics and photon number distribution. Interestingly,
the addition of photons leads to shifting the region in which photon number
distribution shows oscillatory behavior. In addition, the entanglement of
introduced states has been quantitatively analyzed using concurrence. We
observe that the state approaches the maximum entanglement more rapidly after
the addition of photons.Comment: 11 pages, 9 figure