A nonlinear Hamiltonian model is presented for which exact analytic results can be obtained. It is shown that macroscopically distinguishable quantum states can be generated and detected by means of a homodyne detector. The vacuum fluctuations may inhibit their observability; however, this contribution can be subtracted.
Here it is shown that, for a wide class of nonlinear Hamiltonians, an essentially classical initial state will evolve into the coherent superposition of distinguishable quantum states. The detection of the interference fringes can be performed by beating the light leaving the nonlinear optical medium with light from a local oscillator. A model for the loss in the detection apparatus is introduced. The squeezed-vacuum technique is introduced finally as a means of enhancing the interference fringes displaying the distinguishable quantum state.
A four-wave mixer model is presented for which exact analytic results can be obtained in a regime where the usual perturbation procedures no longer apply. It is shown that under suitable conditions the output of such a four-wave mixer consists of a superposition of macroscopically distinguishable states. Such states can be identified with a homodyne detector which is able to observe the interference between the macroscopically distinguishable components. Further, it is shown that the device can act as an even-odd filter which will switch incoming pump light between two output ports depending on whether there is an even or odd number of pump photons.
It is pointed out here that a coherent state propagating through an amplitude dispersive medium will, under suitable conditions, evolve into a quantum superposition of two coherent states 180\ifmmode^\circ\else\textdegree\fi{} out of phase with each other. The response of a homodyne detector to this superposition of macroscopically distinguishable states is calculated. Signatures which an experimentalist might look for in the homodyne detector's output in order to verify the generation of such states are described.