  A parity-dependent squeezing operator is introduced which imposes different
SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator
Hilbert space. This operator is used to define parity-dependent squeezed states
which exhibit highly nonclassical properties such as strong antibunching,
quadrature squeezing, strong oscillations in the photon-number distribution,
etc. In contrast to the usual squeezed states whose $Q$ and Wigner functions
are simply Gaussians, the parity-dependent squeezed states have much more
complicated $Q$ and Wigner functions that exhibit an interesting interference
in phase space. The generation of these states by parity-dependent quadratic
Hamiltonians is also discussed.
