SUPERPOSITION OF COHERENT STATES IN KERR MEDIUM

The evolution of the input coherent state in the Kerr medium is studied. Upon the derivation we know that the output state at time t which corresponds to a rational number is Schr\ddot\rm odinger's cat state. Using Fourier integral of the evolution operator, we obtain the integral expression of the output state at time t which corresponds to an irrational number. It is a kind of one-dimensional continuous superposition of coherent states, not an ordinary Schr\ddot\rm odinger's cat state.