Amplitude-squeezed quantum states produced by the evolution of a quadrature-squeezed coherent state in a Kerr medium.

Abstract

The evolution of a quadrature-squeezed state through a Kerr medium is studied from the point of view of amplitude squeezing. We propose a Mach-Zehnder interferometer configuration, which incorporates a squeeze- state generator and a nonlinear Kerr medium, to generate and subsequently displace these states. The displaced states show amplitude squeezing for a proper choice of the initial quadrature squeezed state, and we study two such cases here in detail. In the limit where the evolution through a Kerr medium results in a macroscopic superposition, an initial phase-squeezed coherent state shows significant amplitude squeezing, and we have shown that the photon-number uncertainty 〈(\ensuremath{\Delta}n^${)}^{2}$〉 can be minimized to a value smaller than 〈n^${\mathrm{〉}}^{2/3}$. On the other hand, an initial quadrature-squeezed state, whose direction of squeezing is along the direction of excitation, upon evolving through a Kerr medium for a suitable small duration of time shows substantial amplitude squeezing for an appropriate displacement, and we show that the photon-number uncertainty in this case can be minimized to 〈n^${\mathrm{〉}}^{1/5}$, which is far below the previously achieved limits. \textcopyright{} 1996 The American Physical Society.