### Abstract

Approximating a continuous superposition by a discrete one leads to an understanding of the role of quantum interference in generating squeezed coherent states, and in its quantum properties. It was shown that discrete superposition with a large enough number of coherent states with appropriate coefficients can have practically the same features as the squeezed coherent state. Dependent on the parameters W, r and 8, different numbers of coherent states are required for the interference fringe to form a Wigner function resembling that of the squeezed vacuum state and to reduce the deviation below a certain value. For the case of rotating the direction of squeezing, about 20 states were required to lower the deviation to 0.05%, while 640 states would be necessary when a unit displacement along the imaginary axis is included. When only a few coherent states are superimposed, the resulting state changes chaotically. In the case when the approximated squeezed coherent state was displaced along the imaginary axis an interesting Schrodinger cat-like state was found with about 20 coherent states on the real axis. At this point a significant peak occurs in the variances of the quadratures. It turned out that non-classical states can be effectively produced by a discrete superposition of coherent states with the coefficients derived from the one-dimensional representation of the given state.

Original language | English |
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Article number | 005 |

Pages (from-to) | 187-199 |

Number of pages | 13 |

Journal | Quantum Optics: Journal of the European Optical Society Part B |

Volume | 6 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 1 1994 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Engineering(all)