We study the dynamical squeezing of the photon-added coherent state (P
ACS) due to a time dependence of the frequency of the electromagnetic
field oscillator in a cavity or a vibrational frequency of an ion insi
de an electromagnetic trap. Explicit expressions for the time dependen
ce of various functions characterizing the quantum state, such as the
photon distribution, the Wigner function, the mean values and variance
s of the quadrature components and of the photon number, show that the
dynamically squeezed PACS possesses a larger squeezing coefficient th
an the usual squeezed states. The dynamical squeezing is accompanied b
y a change of the sub-Poissonian photon statistics to the super-Poisso
nian one. [S1050-2947(98)07410-1].