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

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 〈^^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 〈^^2〉〈^^2〉 (1/4). . AE