Conditions for the existence of oscillations in the distribution of the vibrational quanta of squeezed states
Istok P. Mendaš, Duska B Popovic · Journal of Physics A Mathematical and General · 1992
The conditions for the existence of oscillations in the distribution of the vibrational quanta for the general case of the time-evolving squeezed state (which does not remain a minimum-uncertainty state) of the one-dimensional harmonic oscillator are investigated. To aid this, new parametrization of squeezed states is introduced. It is found that in addition to the usual conditions which produce oscillations, the value of the phase zeta of the complex parameter z (which is the argument of the Hermite polynomial H n appearing in the expression for the expansion coefficient a n of the squeezed state in the number state basis) must have a value in the vicinity of zeta =O or zeta = pi ( mod 1m(z) mod << mod z mod ). It is shown how this necessary condition results from the explicit expression for mod H n (z) mod 2 .