Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer

Abstract

The output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty. This interferometer includes an optical Kerr medium in one arm with a coherent-state input. Unusual ‘‘crescent’’-shaped squeezing which preserves photon number is revealed in the unitary evolution associated with a self-phase-modulation in the Kerr medium. Photon-number uncertainty 〈Δn${^}^2$〉 can be reduced by interference with a coherent-state reference wave. It can be minimized to 〈n^${〉}^{1/3}$, far below the limit 〈n^${〉}^{2/3}$ achieved by an ordinary squeezed state. The increased phase uncertainty due to self-phase-modulation and the reduced photon-number uncertainty still preserve the minimum-uncertainty product 〈Δn${^}^2$〉〈ΔΦ${^}^2$〉∼(1/4). .AE