Narrow Results

We show that the two-mode photon-subtracted squeezed state (TPSSS) is a squeezed two-variable Hermite polynomial excitation state, and we can therefore determine its normalization as a Jacobi polynomial of the squeezing parameter. Some new relations about the Jacobi polynomials are obtained by this analysis. We also show that the TPSSS can be treated as a two-variable Hermite-polynomial excitation on squeezed vacuum state. The technique of integration within an ordered product of operators brings convenience in our derivation.

As in two previous papers where nonclassical properties and entanglement dynamics were studied for entangled nonlinear coherent states (ENCS) [D. Afshar and A. Anbaraki, J. Opt. Soc. Am. B33, 558 (2016).] and for photon-added entangled nonlinear coherent states (PAENCS) [A. Anbaraki, D. Afshar and M. Jafarpour, Eur. Phys. J. Plus133, 2 (2018).], we study quantum mechanical treatments of photon-subtracted entangled nonlinear coherent states (PSENCS) introduced through applying annihilation operators on the ENCS, where the related nonlinearity functions are assumed to be harmonious. To gain insight into the effectiveness of photon subtracting from ENCS and comparing with the case already discussed as the PAENCS, we present a general analysis of nonclassical properties such as photon statistics and degree of polarization. We also derive the concurrence measure to quantify the entanglement of these states and look for conditions that provide information on whether they become maximally entangled. As a result, we can see that the photon depletion number m plays an important role in nonclassical effects. Especially, depending on whether the photon depletion number m is even or odd, one can observe different nonclassical effects.