An application of the arithmetic Euler function to the construction of nonclassical states of a quantum harmonic oscillator

All quantum superpositions of two equal intensity coherent states exhibitin g infinitely many zeros in their Fock distributions are explicitly construc ted and studied. Our approach is based on results from number theory and, i n particular, on the properties of arithmetic Euler function. The nonclassi cal nature of these states is briefly pointed out. Some interesting propert ies are brought to light.