Coherent states on a circle and quantum interference

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Abstract
As a generalization of the optical Schrödinger cats, discrete sets of coherent states are considered on a circle in the α plane. It is shown that simple superpositions of Schrödinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state.