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A "squeezed-vacuum" state considered in quantum optics is shown to berealized in the ground-state wavefunction for the bilayer quantum Hall systemat the total Landau level filling of $\nu=1/m$ (m: odd integer). This isderived in the boson approximation, where a particle-hole pair creation acrossthe symmetric-antisymmetric gap, $\Delta_{SAS}$, is regarded as a boson. Interms of the pseudospin describing the layers, the state is a spin-squeezedstate, where the degree of squeezing is controlled by the layer separation and$\Delta_{SAS}$. An exciton condensation, which amounts to a rotatedspin-squeezed state, has a higher energy due to the degraded SU(2) symmetry for$\Delta_{SAS} \neq 0$.Comment: 4 pages, revtex, one figure, to appear in PRB Rapid Communicatio

Spin-squeezed ground states in the bilayer quantum Hall ferromagnet