Abstract 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$\ddot{\rm o}$dinger'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$\ddot{\rm o}$dinger's cat state.
Received: 15 September 1995
Accepted manuscript online:
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