LEGENDRE POLYNOMIALS AS THE NORMALIZATION OF PHOTON-SUBTRACTED SQUEEZED STATES
Hong-Yi Fan, Liyun Hu, Xue-xiang Xu · Modern Physics Letters A · 2009
By converting the photon-subtracted squeezed state (PSSS) to a squeezed Hermite-polynomial excitation state we find that the normalization factor of PSSS is an m-order Legendre polynomial of the squeezing parameter, where m is the number of subtracted photons. Some new relations about the Legendre polynomials are obtained by this analysis. We also show that the PSSS can also be treated as a Hermite-polynomial excitation on squeezed vacuum state.