Highly Amplitude-Squeezed States of the Radiation Field

We propose here a quantum state obtained by evolving a quadrature-squeezed state through a Kerr medium. We give a Mach-Zhender interferometer configuration to generate and displace this state to an appropriate position in phase space. The displaced state is highly amplitude squeezed when the direction of squeezing of the initial quadrature squeezed state is along the direction of coherent excitation. We show that the photon number uncertainty $〈(\Delta \hat{n}{)}^2〉<〈\hat{n}{〉}^{1/5}$, which is far below the previously achieved limits in similar schemes.